Difference between revisions of "ModelCourses/Linear Algebra"

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[http://webwork.maa.org/wiki/Prep_2011_workshop_Linear_Algebra_Assignment_Status#Current_status_of_Linear_Algebra_Model_Course_Assignments]
  
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= Working page for the Linear Algebra group at PREP 2011 =
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== Preliminary Topic List - 2011-06-23 ==
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* Vectors
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** Geometric objects - lines and planes
  +
** Dot product and Vector Projections
  +
** Orthogonal decomposition
  +
* Systems of equations and elimination
  +
** Row operations and Row Echelon Form
  +
** Gaussian elimination (Free variables & Consistency of solutions)
  +
* Matrix operations and algebra
  +
** Matrix arithmetic
  +
** Matrix inverse
  +
** Matrix equations
  +
** Determinant and Cramer's Rule
  +
** Elementary matrices and LU Decomposition
  +
* Vector space preliminaries
  +
** Definition of a vector space and subspaces
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** Euclidean vector spaces
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** Linear combinations and span
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** Linear independence
  +
** Basis and orthogonal basis
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** Coordinate vectors and change of basis
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** Row space, column space, and null space
  +
** Dimension and rank
  +
** Geometric examples
  +
* Linear transformations
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** Definition of a linear transformation
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** Matrix of a linear transformation
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** Reflections, rotations, dilations and projections
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** Inverse of a transformation
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** Kernel, range, injection, surjection
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* Applications
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** Graph theory: Adjacency matrix and Incidence Matrix
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** Least squares
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** Curve/surface fitting
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** Mixture problems
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** Simplex method
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** Approximation of a function by a Fourier polynomial
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* Eigenvalues and eigenvectors
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** Finding eigenvalues and eigenvectors
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** Eigenspaces
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** Diagonalization
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** Symmetric matrices & Trace
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** Quadratic forms
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* Inner product spaces and abstract vector spaces
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== Working group members ==
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* [[User:AlinaDuca|Alina Duca]]
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* [[User:William D. Emerson|William Emerson]]
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* [[User:Tuco|Jim Fischer]]
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* [[User:Tbflowers|Tim Flowers]]
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* [[User:Charles Fortin|Charles Fortin]]
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* [[User:Malcolm|Malcolm Harper]]
   
 
=[[ModelCourses|Other Model Courses]]=
  
=[[ModelCourses|Other Model Courses]]=

Revision as of 12:06, 21 December 2011

Working page for the Linear Algebra group at PREP 2011

Preliminary Topic List - 2011-06-23

  • Vectors
    • Geometric objects - lines and planes
    • Dot product and Vector Projections
    • Orthogonal decomposition
  • Systems of equations and elimination
    • Row operations and Row Echelon Form
    • Gaussian elimination (Free variables & Consistency of solutions)
  • Matrix operations and algebra
    • Matrix arithmetic
    • Matrix inverse
    • Matrix equations
    • Determinant and Cramer's Rule
    • Elementary matrices and LU Decomposition
  • Vector space preliminaries
    • Definition of a vector space and subspaces
    • Euclidean vector spaces
    • Linear combinations and span
    • Linear independence
    • Basis and orthogonal basis
    • Coordinate vectors and change of basis
    • Row space, column space, and null space
    • Dimension and rank
    • Geometric examples
  • Linear transformations
    • Definition of a linear transformation
    • Matrix of a linear transformation
    • Reflections, rotations, dilations and projections
    • Inverse of a transformation
    • Kernel, range, injection, surjection
  • Applications
    • Graph theory: Adjacency matrix and Incidence Matrix
    • Least squares
    • Curve/surface fitting
    • Mixture problems
    • Simplex method
    • Approximation of a function by a Fourier polynomial
  • Eigenvalues and eigenvectors
    • Finding eigenvalues and eigenvectors
    • Eigenspaces
    • Diagonalization
    • Symmetric matrices & Trace
    • Quadratic forms
  • Inner product spaces and abstract vector spaces

Working group members

Other Model Courses

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