http://webwork.maa.org/w/api.php?action=feedcontributions&user=Jim+Fischer&feedformat=atomWeBWorK - User contributions [en]2019-12-07T22:16:24ZUser contributionsMediaWiki 1.18.0http://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-25T11:37:17Z<p>Jim Fischer: /* Complete Model Courses */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWorK course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWorK. <br />
<br />
Here are further instructions for importing or exporting problem sets:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
== Complete Model Courses ==<br />
<br />
The following model course was used by one of the PREP members Fall term 2011. The course was taught on the quarter system at Oregon Institute of Technology. These WeBWorK assignments were supplemented by several written assignments, both applied and theoretic. The textbook used was "Linear Algebra a Geometric Approach", 2nd Ed. by Shifrin and Adams.<br />
<br />
Download 17 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWorK course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Upload to a WeBWorK course and then import problem sets using the Problem Sets Editor.<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-25T11:36:16Z<p>Jim Fischer: /* Instructions for Importing and Exporting Problem Sets */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWorK course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWorK. <br />
<br />
Here are further instructions for importing or exporting problem sets:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
== Complete Model Courses ==<br />
<br />
The following model course was used by one of the PREP members Fall term 2011. The course was taught on the quarter system at Oregon Institute of Technology. These WeBWorK assignments were supplemented by several written assignments, both applied and theoretic. The textbook used was "Linear Algebra a Geometric Approach", 2nd Ed. by Shifrin and Adams.<br />
<br />
Download 17 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Upload to a WeBWorK course and then import problem sets using the Problem Sets Editor.<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-24T18:00:01Z<p>Jim Fischer: /* Instructions for Importing and Exporting Problem Sets */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. <br />
<br />
Here are further instructions for importing or exporting problem sets:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
== Complete Model Courses ==<br />
<br />
The following model course was used by one of the PREP members Fall term 2011. The course was taught on the quarter system at Oregon Institute of Technology. These WeBWorK assignments were supplemented by several written assignments, both applied and theoretic. The textbook used was "Linear Algebra a Geometric Approach", 2nd Ed. by Shifrin and Adams.<br />
<br />
Download 17 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Upload to a WeBWorK course and then import problem sets using the Problem Sets Editor.<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-24T17:56:55Z<p>Jim Fischer: /* Complete Model Courses */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. Here are further instructions:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
== Complete Model Courses ==<br />
<br />
The following model course was used by one of the PREP members Fall term 2011. The course was taught on the quarter system at Oregon Institute of Technology. These WeBWorK assignments were supplemented by several written assignments, both applied and theoretic. The textbook used was "Linear Algebra a Geometric Approach", 2nd Ed. by Shifrin and Adams.<br />
<br />
Download 17 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Upload to a WeBWorK course and then import problem sets using the Problem Sets Editor.<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txtFile:PREP 2011 Linear Algebra Quarter Course.tgz.txt2011-12-24T17:54:28Z<p>Jim Fischer: uploaded a new version of "File:PREP 2011 Linear Algebra Quarter Course.tgz.txt"</p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txtFile:PREP 2011 Linear Algebra Quarter Course.tgz.txt2011-12-23T19:51:19Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-23T19:48:52Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. Here are further instructions:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
== Complete Model Courses ==<br />
<br />
The following model course was used by one of the PREP members Fall term 2011. The course was taught on the quarter system. These WeBWorK assignments were supplemented by several written assignments, both applied and theoretic. <br />
<br />
Download 17 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Quarter_Course.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Upload to a WeBWorK course and then import problem sets using the Problem Sets Editor.<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T21:37:30Z<p>Jim Fischer: /* Introduction */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This WeBWorK Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWorK course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WeBWorK library browser that allows one to search for problems from within the course. Essentially this method gives a refinement of the National Problem Library, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. Here are further instructions:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Unit2.tgz.txtFile:PREP 2011 Linear Algebra Unit2.tgz.txt2011-12-22T20:28:54Z<p>Jim Fischer: uploaded a new version of "File:PREP 2011 Linear Algebra Unit2.tgz.txt"</p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Unit2.tgz.txtFile:PREP 2011 Linear Algebra Unit2.tgz.txt2011-12-22T19:47:34Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T19:47:06Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. Here are further instructions:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
* Rank of a Matrix<br />
<br />
Download 3 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit2.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
<br />
<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T19:13:48Z<p>Jim Fischer: /* Instructions for Importing and Exporting Problem Sets */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files (listed below), you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
After removing .txt, you can upload the file to your WeBWork course. The set definition files and headers will automatically unpack. To see the problem sets, you will need to import the sets from within WeBWork. Here are further instructions:<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Unit1.tgz.txtFile:PREP 2011 Linear Algebra Unit1.tgz.txt2011-12-22T19:11:16Z<p>Jim Fischer: uploaded a new version of "File:PREP 2011 Linear Algebra Unit1.tgz.txt"</p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Unit1.tgz.txtFile:PREP 2011 Linear Algebra Unit1.tgz.txt2011-12-22T19:00:55Z<p>Jim Fischer: uploaded a new version of "File:PREP 2011 Linear Algebra Unit1.tgz.txt"</p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T18:58:42Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files, you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T18:58:19Z<p>Jim Fischer: /* Instructions for Importing and Exporting Problem Sets */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files, you must rename the file without the .txt ending. The archive files should end with .tgz. This will ensure that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T18:54:32Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
<br />
IMPORTANT: After downloading Unit or Course archive files, you must rename the file without the .txt ending. The archive files should end it .tgz so that WeBWork will recognize the file when uploaded. <br />
<br />
Instructions for allowing Windows to see file extensions:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
<br />
<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. <br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_Linear_Algebra_Unit1.tgz.txtFile:PREP Linear Algebra Unit1.tgz.txt2011-12-22T18:50:12Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T18:00:08Z<p>Jim Fischer: /* Preliminary Topic List - 2011-06-23 */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Instructions for Windows users:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T17:59:20Z<p>Jim Fischer: /* Unit 2 - Systems of Equations and Elimination */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Instructions for Windows users:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T17:58:59Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Instructions for Windows users:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T17:58:14Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Instructions for Windows users:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-22T17:55:35Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
<br />
* Dot product and Vector projections, Orthogonal Decomposition<br />
* Lines and Planes<br />
<br />
Download 2 problem sets and header files as an archive. These files will be unarchived when uploaded to your WeBWork course:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading. Instructions for Windows users:<br />
<br />
[7 or Vista] Start -> Control Panel -> Appearance & Personalization -><br />
Folder Options, click View, Advanced Settings, and unclick the "Hide<br />
extensions for known file types" check box.<br />
<br />
[XP] My Computer -> Tools -> Folder Options -> View -> unclick "Hide<br />
extensions..." <br />
<br />
<br />
Chapter/sections used from the NPL that came from outside of Linear Algebra:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:SetLA_12_Lines_and_Planes.def.txtFile:SetLA 12 Lines and Planes.def.txt2011-12-21T22:03:16Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:59:16Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:setLA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:setLA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.pg.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
Download all 4 files as an archive. These files can be unarchived when uploading to WW:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:50:01Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:setLA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:setLA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.pg.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
Download all 4 files as an archive. These files can be unarchived when uploading to WW:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz]] <br />
<br />
Note: Rename this file without the .txt extension after downloading<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:PREP_2011_Linear_Algebra_Unit1.tgz.txtFile:PREP 2011 Linear Algebra Unit1.tgz.txt2011-12-21T21:42:14Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:41:26Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:setLA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:setLA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.pg.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
Download all 4 files as an archive. These files can be unarchived when uploading to WW:<br />
<br />
: [[File:PREP_2011_Linear_Algebra_Unit1.tgz.txt]] <br />
<br />
Note: Rename this file without the .txt extension after downloading<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/File:LA_setHeader11_Dot_Products_and_Projections.pg.txtFile:LA setHeader11 Dot Products and Projections.pg.txt2011-12-21T21:13:17Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/File:SetLA_11_Dot_Products_and_Projections.def.txtFile:SetLA 11 Dot Products and Projections.def.txt2011-12-21T21:12:21Z<p>Jim Fischer: </p>
<hr />
<div></div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:11:55Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:setLA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:setLA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.pg.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:04:21Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:LA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:LA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.pg.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:03:58Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:LA_11_Dot_Products_and_Projections.def.txt]] <br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] <br />
<br />
: [[File:LA_12_Lines_and_Planes.def.txt]] <br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.def.txt]] <br />
<br />
Note: All of the above files should be renamed without the .txt extension after downloading<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T21:01:25Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - Lines and Planes<br />
* Dot product and Vector projections<br />
* Orthogonal Decomposition<br />
<br />
Set definition files and set header files:<br />
<br />
: [[File:LA_11_Dot_Products_and_Projections.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:LA_setHeader11_Dot_Products_and_Projections.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:LA_12_Lines_and_Planes.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:LA_setHeader12_Lines_and_Planes.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T20:53:59Z<p>Jim Fischer: /* Working group members */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_model_linear_algebra.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== PREP Linear Algebra Group Members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T20:53:14Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_model_linear_algebra.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T18:24:47Z<p>Jim Fischer: /* Unit 2 - Systems of Equations and Elimination */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_model_linear_algebra.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination <br />
* Free variables & Consistency of solutions<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T18:11:29Z<p>Jim Fischer: /* Unit 2 - Systems of Equations and Elimination */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_model_linear_algebra.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_model_linear_algebra.def.txt]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] <br />
<br />
''(Both files should be renamed without the .txt extension after downloading)''<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T18:09:29Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_model_linear_algebra.def.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_Systems_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T18:07:15Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def.txt|Download Set Definition File]] ''(Rename without the .txt extension after downloading)''<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_Systems_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T18:00:13Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic02_Systems_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic02_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:58:28Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
Set definition file and set header file:<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
: [[File:setTopic02_Systems_of_equations_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:57:26Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
: [[File:setHeaderTopic01_model_linear_algebra.pg.txt]] ''(Rename without the .txt extension after downloading)''<br />
<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
: [[File:setTopic02_Systems_of_equations_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:47:32Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
Chapter/sections used from the NPL that came from outside the Linear Algebra course:<br />
<br />
=== Unit 2 - Systems of Equations and Elimination ===<br />
<br />
* Row operations and Row Echelon Form <br />
* Gaussian elimination (Free variables & Consistency of solutions)<br />
<br />
: [[File:setTopic02_Systems_of_equations_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:42:00Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - Vectors ===<br />
<br />
* Geometric objects - lines and planes<br />
* Dot product and Vector Projections<br />
* Orthogonal decomposition<br />
<br />
: [[File:setTopic01_Vectors_model_linear_algebra.def|Download Set Definition File]]<br />
<br />
Non-Linear Algebra Chapter/Sections from the NPL that were used:<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:38:20Z<p>Jim Fischer: /* Unit 1 - Vectors */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - [[ModelCourses/Calculus/Vectors/Vectors in Space|Vectors]] ===<br />
* Space Coordinates<br />
* The Dot Product of Two Vectors<br />
* The Cross Product of Two Vectors in Space<br />
<br />
: [[File:setTopic01_Vectors_model_multivariate_calculus.def|Download Set Definition File]]<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:36:56Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
=== Unit 1 - [[ModelCourses/Calculus/Vectors/Vectors in Space|Vectors]] ===<br />
* Space Coordinates<br />
* The Dot Product of Two Vectors<br />
* The Cross Product of Two Vectors in Space<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:33:34Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
<br />
== Problem Sets ==<br />
<br />
<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:32:10Z<p>Jim Fischer: /* Introduction */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
It is expected that an instructor will first import some or all of these problem sets into their WebWork course. Once the course is created and these problem sets are imported, there are a couple of options for how to use the problem sets. One way to use these sets is to make new problem sets and use the option in the WW library browser that allows one to search for problems from within the course (the local course created by the instructor). Essentially this method gives a refinement of the NPL, making it easier to find problems. Another option would be to use these problems sets and edit the sets as needed.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:25:35Z<p>Jim Fischer: /* Introduction */</p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
One could first import these problem sets into their WebWork course and then use them as a resource for building new problem sets. To do this, simply use the option in the WW library browser that allows one to search for problems within the course. This could be an easier method then to edit the problem sets themselves.<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischerhttp://webwork.maa.org/wiki/ModelCourses/Linear_AlgebraModelCourses/Linear Algebra2011-12-21T17:24:22Z<p>Jim Fischer: </p>
<hr />
<div>= Model Courses/ Linear Algebra =<br />
<br />
== Introduction ==<br />
This PREP Linear Algebra model course is still a work in progress. Some of the problem sets below will likely be adjusted over the next several months (Winter/Spring 2012). Future updates will be indicated by the date when the changes are made. <br />
<br />
A first-term Linear Algebra course could be taught in many different ways. A course in Linear Algebra could have more emphasis on applications than theory or vise-versa. The course could be taught on the quarter system or the semester system (or other time frame). Because of these and other variables, it is likely that an instructor who uses this model course will need to adjust some problem sets. <br />
<br />
One could first import these problem sets into their WebWork course and then use them as a resource for building new problem sets. To do this, simply use the option in the WW library browser that allows one to search for problems within the course. This could be an easier method then to edit the problem sets themselves. <br />
<br />
<br />
== Working group members ==<br />
* [[User:AlinaDuca|Alina Duca]]<br />
* [[User:William D. Emerson|William Emerson]]<br />
* [[User:Tuco|Jim Fischer]]<br />
* [[User:Tbflowers|Tim Flowers]]<br />
* [[User:Charles Fortin|Charles Fortin]]<br />
* [[User:Malcolm|Malcolm Harper]]<br />
<br />
<br />
== Instructions for Importing and Exporting Problem Sets ==<br />
[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]<br />
<br />
[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]<br />
<br />
<br />
== Preliminary Topic List - 2011-06-23 ==<br />
* Vectors<br />
** Geometric objects - lines and planes<br />
** Dot product and Vector Projections<br />
** Orthogonal decomposition<br />
* Systems of equations and elimination<br />
** Row operations and Row Echelon Form <br />
** Gaussian elimination (Free variables & Consistency of solutions)<br />
* Matrix operations and algebra<br />
** Matrix arithmetic<br />
** Matrix inverse<br />
** Matrix equations<br />
** Determinant and Cramer's Rule<br />
** Elementary matrices and LU Decomposition<br />
* Vector space preliminaries<br />
** Definition of a vector space and subspaces<br />
** Euclidean vector spaces<br />
** Linear combinations and span<br />
** Linear independence<br />
** Basis and orthogonal basis<br />
** Coordinate vectors and change of basis<br />
** Row space, column space, and null space<br />
** Dimension and rank<br />
** Geometric examples<br />
* Linear transformations<br />
** Definition of a linear transformation<br />
** Matrix of a linear transformation<br />
** Reflections, rotations, dilations and projections<br />
** Inverse of a transformation<br />
** Kernel, range, injection, surjection<br />
* Applications<br />
** Graph theory: Adjacency matrix and Incidence Matrix<br />
** Least squares<br />
** Curve/surface fitting<br />
** Mixture problems<br />
** Simplex method<br />
** Approximation of a function by a Fourier polynomial<br />
* Eigenvalues and eigenvectors<br />
** Finding eigenvalues and eigenvectors<br />
** Eigenspaces<br />
** Diagonalization<br />
** Symmetric matrices & Trace <br />
** Quadratic forms<br />
* Inner product spaces and abstract vector spaces<br />
=[[ModelCourses|Other Model Courses]]=<br />
<br />
[[Category:PREP 2011]]<br />
[[Category:Events]]</div>Jim Fischer