Difference between revisions of "Prep 2011 workshop Linear Algebra Assignment Status"

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! NPL
  
! NPL
 
! Custom
  
! Custom
  +
! Header
 
! Updated
  
! Updated
 
! Notes
  
! Notes
 
|-
  
|-
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| colspan="5" | '''Vectors'''
 +
| colspan="6" | '''Vectors'''
−
|-
  
−
| Geometric objects - lines and planes || 14 || || 2011-06-25 ||
  
 
|-
 
|-
−
| Dot product and Vector Projections || 15 || || 2011-06-25 ||
 +
| Dot product and Vector Projections || 15 || || || 2011-06-25 ||
  +
|-
  +
| Geometric objects - lines and planes || 14 || || X || 2011-06-25 || This set could use some work in connecting to linear algebra. For example given standard equation of plane, find parametric equations
 
|-
  
|-
−
| Orthogonal decomposition || || || ||
 +
| Orthogonal decomposition || || || || ||
 
|-
 
|-
−
| colspan="5" | '''Systems of equations and elimination'''
+
| colspan="6" | '''Systems of equations and elimination'''
 
|-
 
|-
−
| Row operations and Row Echelon Form || 11 || || 2011-06-25 ||
+
| Row operations and Row Echelon Form || 11 || || X || 2011-06-25 ||
 
|-
 
|-
−
| Gaussian elimination (Free variables & Consistency of solutions) || 27 || || 2011-06-25 ||
+
| Gaussian elimination (Free variables & Consistency of solutions) || 27 || || X || 2011-06-25 ||
 
|-
 
|-
−
| colspan="5" | '''Matrix operations and algebra'''
 
  +
| Rank of a Matrix || 2 || || || 2011-06-26 || There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
|-
 
|-
−
| Matrix arithmetic || 16 || || 2011-06-25 ||
 
  +
| colspan="6" | '''Matrix operations and algebra'''
 
|-
 
|-
−
| Matrix inverse || 16 || || 2011-06-25 || ||
 +
| Matrix arithmetic || 15 || 1 || X || 2011-06-25 ||
 
|-
 
|-
−
| Matrix equations || 5 || || 2011-06-25 ||
+
| Matrix inverse || 17 || || X || 2011-06-26 || ||
 
|-
 
|-
−
| Determinant and Cramer's Rule || 28 || || 2011-06-25 || Need to add Cramer's rule Qs
 +
| Matrix equations || 5 || || X || 2011-06-25 ||
 
|-
 
|-
−
| Elementary matrices and LU Decomposition || 5 || || 2011-06-25 || There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants
  
  +
| Determinant and Cramer's Rule || 30 || 1 || X || 2011-06-26 || Need to add Cramer's rule Qs
 
|-
 
|-
−
| colspan="5" | '''Vector space preliminaries'''
 
  +
| Elementary matrices and LU Decomposition || 3 || 2 || X || 2011-06-25 || There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants
 
|-
 
|-
−
| Definition of a vector space and subspaces || 4 || || 2011-06-25 ||
 
  +
| colspan="6" | '''Vector space preliminaries'''
 
|-
 
|-
−
| Euclidean vector spaces || 4 || || 2011-06-25 ||
+
| Definition of a vector space and subspaces || 8 || || X || 2011-06-26 ||
 
|-
 
|-
−
| Linear combinations and span || 6 || || 2011-06-25 ||
+
| Euclidean vector spaces || 4 || || || 2011-06-25 ||
 
|-
 
|-
−
| Linear independence || || || ||
+
| Linear combinations and span || 14 || || X || 2011-06-26 ||
 
|-
 
|-
−
| Basis and orthogonal basis || || || ||
 
  +
| Linear independence || 13 || || X || 2011-06-26 ||
 
|-
 
|-
−
| Coordinate vectors and change of basis || || || ||
 
  +
| Basis and dimension || 26 || || X || 2011-07-22 || Several problems say "kernel" and "image." Change to Column space & null space? Or include both in some/all? Need some Rank and Nullity questions?
 
|-
 
|-
−
| Row space, column space, and null space || || || ||
 
  +
| Coordinate vectors and change of basis || || || || || Not finding problems in NPL yet
 
|-
 
|-
−
| Dimension and rank || || || || There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
  +
| Row space, column space, and null space. Rank and Nullity || 0 || || X || 2011-07-22 || This set was deleted by JF since it is redundant with 45_Basis and Dimension.
 
|-
 
|-
−
| Geometric examples || || || ||
+
| Geometric examples || || || || ||
 
|-
 
|-
−
| colspan="5" | '''Linear transformations'''
+
| colspan="6" | '''Linear transformations'''
 
|-
 
|-
−
| Matrix of a linear transformation || || || ||
+
| Definition of a linear transformation || 5 || || || 2011-06-26 || The NPL needs a few more problems
 
|-
 
|-
−
| Reflections, rotations, dilations and projections || || || ||
 
  +
| Matrix of a linear transformation || 18 || || || 2011-06-26 || There are some problems in the NPL on transformation of vector spaces of matrices, but not included in model course. There are some more abstract problems that could go into chapter 6
 
|-
 
|-
−
| Inverse of a transformation || || || ||
+
| Reflections, rotations, dilations and projections || 9 || || || ||
 
|-
 
|-
−
| Kernel, range, injection, surjection || || || ||
 
  +
| Inverse of a transformation ||4|| || || 2011-07-11 || NPL has only a few problems
 
|-
 
|-
−
| colspan="5" | '''Applications'''
 
  +
| Kernel, range, injection, surjection || 11 || || || 2011-07-11 ||
 
|-
 
|-
−
| Adjacency matrix || || || ||
 
  +
| colspan="6" | '''Applications'''
 
|-
 
|-
−
| Least squares Approximation|| || || || should this be in Inner Product Spaces?
  
  +
| Graph Theory || 1 || || || 2011-07-22 || NPL needs a couple more new problems for example Incidence matrix. Name changed from "Adjancency Matrix" to allow more problems.
 
|-
 
|-
−
| Curve/surface fitting || || || ||
 
  +
| Least squares Approximation || 2 || || || 2011-08-09 || Some problems have awkward wording could use some editing. New problem were added by JF July 25 and Aug 9.
  +
 
|-
 
|-
−
| Mixture problems || || || ||
+
| Mixture problems || || || || ||
 
|-
 
|-
−
| Simplex method || || || ||
+
| Simplex method || || || || ||
 
|-
 
|-
−
| Graph theory || || || ||
+
| Approximation of a function by a Fourier polynomial || || || || ||
 
|-
 
|-
−
| Approximation of a function by a Fourier polynomial || || || ||
 
  +
| Quadratic Forms || || || || ||
 
|-
 
|-
−
| Singular Value Decomposition || || || 2011-06-25 || should this be in Inner Product Spaces?
  
  +
| colspan="6" | '''Eigenvalues and eigenvectors'''
 
|-
 
|-
−
| Quadratic Forms || || || ||
+
| Finding eigenvalues and eigenvectors || 12 || || || 2011-06-25 ||
 
|-
 
|-
−
| colspan="5" | '''Eigenvalues and eigenvectors'''
 
  +
| Eigenspaces || || || || 2011-06-25 ||
 
|-
 
|-
−
| Finding eigenvalues and eigenvectors || 12 || || 2011-06-25 ||
+
| Diagonalization || || || || 2011-06-25 ||
 
|-
 
|-
−
| Eigenspaces || || || 2011-06-25 ||
 
  +
| Symmetric matrices & Trace || || |||| 2011-06-25 || There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
|-
 
|-
−
| Diagonalization || || || 2011-06-25 ||
+
| Quadratic forms || || || || 2011-06-25 ||
 
|-
 
|-
−
| Symmetric matrices & Trace || || || 2011-06-25 || There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
  
  +
| colspan="6" | '''Inner product spaces and abstract vector spaces'''
 
|-
 
|-
−
| Quadratic forms || || || 2011-06-25 ||
 
  +
| Inner Product Spaces, Length, Orthogonality || || || || ||
−
|-
 
−
| colspan="5" | '''Inner product spaces and abstract vector spaces'''
  
−
|-
 
−
| Inner Product Spaces, Length, Orthogonality || || || ||
 
 
|-
 
|-
−
| Orthonormal Bases || || || ||
+
| Orthonormal Bases || || || || ||
 
|-
 
|-
−
| Orthonormal Projections || || || ||
+
| Orthogonal Projections. Orthogonal Complements || || || || ||
 
|-
 
|-
−
| Gram-Schmidt Process || || || 2011-06-25 ||
+
| Gram-Schmidt Process || || || || 2011-06-25 ||
 
|-
 
|-
−
| Orthogonal Complements || || || ||
+
| QR Factorization || || || || ||
−
|-
 
−
| Diagonalization of Symmetric Matrices || || || ||
  
 
|-
  
|-
−
| || colspan="3" | ||
  
  +
| Diagonalization of Symmetric Matrices || || || || ||
  +
|-
  +
| Singular Value Decomposition || || || || ||
  +
|-
  +
| || colspan="4" | ||
  +
  +
[[Category:PREP 2011]]
  +
[[Category:Events]]

Latest revision as of 13:20, 9 August 2011

Current status of Linear Algebra Model Course Assignments

Topic NPL Custom Header Updated Notes
Vectors
Dot product and Vector Projections 15 2011-06-25
Geometric objects - lines and planes 14 X 2011-06-25 This set could use some work in connecting to linear algebra. For example given standard equation of plane, find parametric equations
Orthogonal decomposition
Systems of equations and elimination
Row operations and Row Echelon Form 11 X 2011-06-25
Gaussian elimination (Free variables & Consistency of solutions) 27 X 2011-06-25
Rank of a Matrix 2 2011-06-26 There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
Matrix operations and algebra
Matrix arithmetic 15 1 X 2011-06-25
Matrix inverse 17 X 2011-06-26
Matrix equations 5 X 2011-06-25
Determinant and Cramer's Rule 30 1 X 2011-06-26 Need to add Cramer's rule Qs
Elementary matrices and LU Decomposition 3 2 X 2011-06-25 There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants
Vector space preliminaries
Definition of a vector space and subspaces 8 X 2011-06-26
Euclidean vector spaces 4 2011-06-25
Linear combinations and span 14 X 2011-06-26
Linear independence 13 X 2011-06-26
Basis and dimension 26 X 2011-07-22 Several problems say "kernel" and "image." Change to Column space & null space? Or include both in some/all? Need some Rank and Nullity questions?
Coordinate vectors and change of basis Not finding problems in NPL yet
Row space, column space, and null space. Rank and Nullity 0 X 2011-07-22 This set was deleted by JF since it is redundant with 45_Basis and Dimension.
Geometric examples
Linear transformations
Definition of a linear transformation 5 2011-06-26 The NPL needs a few more problems
Matrix of a linear transformation 18 2011-06-26 There are some problems in the NPL on transformation of vector spaces of matrices, but not included in model course. There are some more abstract problems that could go into chapter 6
Reflections, rotations, dilations and projections 9
Inverse of a transformation 4 2011-07-11 NPL has only a few problems
Kernel, range, injection, surjection 11 2011-07-11
Applications
Graph Theory 1 2011-07-22 NPL needs a couple more new problems for example Incidence matrix. Name changed from "Adjancency Matrix" to allow more problems.
Least squares Approximation 2 2011-08-09 Some problems have awkward wording could use some editing. New problem were added by JF July 25 and Aug 9.
Mixture problems
Simplex method
Approximation of a function by a Fourier polynomial
Quadratic Forms
Eigenvalues and eigenvectors
Finding eigenvalues and eigenvectors 12 2011-06-25
Eigenspaces 2011-06-25
Diagonalization 2011-06-25
Symmetric matrices & Trace 2011-06-25 There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
Quadratic forms 2011-06-25
Inner product spaces and abstract vector spaces
Inner Product Spaces, Length, Orthogonality
Orthonormal Bases
Orthogonal Projections. Orthogonal Complements
Gram-Schmidt Process 2011-06-25
QR Factorization
Diagonalization of Symmetric Matrices
Singular Value Decomposition
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