Course Modules

Course Introduction & Review of Linear Algebra Theory

Course Introduction & Review of Linear Algebra Theory
Module Completed Module In Progress Module Locked
Course Introduction & Review of Linear Algebra Theory 193075    
  • Context Module Sub Header
    Check here for references, assignments, and quizzes. I will upload class notes after class for each module
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  • Context Module Sub Header
    Read Ch. 3-5 for review of EA1 and 4 Linear algebra material (subspaces and eigenvalue/vector decompostion)
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  • Attachment
    Lect1_Sept25.pdf Lect1_Sept25.pdf
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  • Quiz
    Quiz 1: Linear Algebra Theory Quiz 1: Linear Algebra Theory
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  • Assignment
    PS1 Coding problem 1 PS1 Coding problem 1
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  • Assignment
    PS1 Coding Problem 2 Determinant PS1 Coding Problem 2 Determinant
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  • Assignment
    PS1 Coding Problem 3 Transpose PS1 Coding Problem 3 Transpose
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Inner Products, Orthogonality, and Norms

Inner Products, Orthogonality, and Norms
Module Completed Module In Progress Module Locked
Inner Products, Orthogonality, and Norms 193077    
  • Page
    Course Schedule Inner Products, Orthogonality, and Norms Course Schedule Inner Products, Orthogonality, and Norms
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  • Attachment
    Lect2_InnerProd_Norms_Sept30.pdf Lect2_InnerProd_Norms_Sept30.pdf
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  • Discussion Topic
    Discussion PS1 Linear Algebra Review & Orthogonality Discussion PS1 Linear Algebra Review & Orthogonality
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  • Assignment
    PS1 Coding Problem 4 Cauchy-Schwarz PS1 Coding Problem 4 Cauchy-Schwarz
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  • Assignment
    PS1 Coding Problem 5 Vector Projection PS1 Coding Problem 5 Vector Projection
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  • Attachment
    Lect3_Oct2.pdf Lect3_Oct2.pdf
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  • Quiz
    CQ2. Orthogonality, Norms, Error, and Flop Counts CQ2. Orthogonality, Norms, Error, and Flop Counts
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  • Assignment
    PS 2: Coding Problem 1 Orthogonal Matrices PS 2: Coding Problem 1 Orthogonal Matrices
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  • Assignment
    PS 2: Coding Problem 2 Properties of a Norm PS 2: Coding Problem 2 Properties of a Norm
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Error Analysis, Algorithm Efficiency, and Conditioning

Error Analysis, Algorithm Efficiency, and Conditioning
Module Completed Module In Progress Module Locked
Error Analysis, Algorithm Efficiency, and Conditioning 193078    
  • Page
    Course Schedule: Error Analysis, Algorithm Efficiency, and Conditioning Course Schedule: Error Analysis, Algorithm Efficiency, and Conditioning
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  • Attachment
    Lect3_Oct2.pdf Lect3_Oct2.pdf
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  • Attachment
    Lect4_Oct7.pdf Lect4_Oct7.pdf
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  • Discussion Topic
    Discussion Board for Problem Set 2 and CQ2 Discussion Board for Problem Set 2 and CQ2
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  • Context Module Sub Header
    Some code to examine the discrete steps between numbers in Matlab
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  • Attachment
    Floating Point Arithmetic Matlab Code Floating Point Arithmetic Matlab Code
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  • Quiz
    CQ2. Orthogonality, Norms, Error, and Flop Counts CQ2. Orthogonality, Norms, Error, and Flop Counts
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  • Assignment
    PS2 Coding Problem 3 Condition Number PS2 Coding Problem 3 Condition Number
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  • Assignment
    PS2 Coding Problem 4 Truncation Error PS2 Coding Problem 4 Truncation Error
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  • Assignment
    PS2 Coding Problem 5 Matrix Exponential PS2 Coding Problem 5 Matrix Exponential
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  • Assignment
    PS2 Coding Problem 6 Optimizing Matrix Addition PS2 Coding Problem 6 Optimizing Matrix Addition
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Solving Linear Systems of Equations Numerically

Solving Linear Systems of Equations Numerically
Module Completed Module In Progress Module Locked
Solving Linear Systems of Equations Numerically 193079    
  • Page
    Course Schedule: LU decompostion and Gaussian Elimination Course Schedule: LU decompostion and Gaussian Elimination
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  • Attachment
    Lect4_Oct7.pdf Lect4_Oct7.pdf
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  • Attachment
    Lect5_Oct9.pdf Lect5_Oct9.pdf
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  • Context Module Sub Header
    Lecture 6: Avoiding Errors during LU and Computational Complexity
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  • External Url
    Video 1: Errors during Gaussian Elimination Video 1: Errors during Gaussian Elimination
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  • External Url
    Video 2: Partial Pivoting in GE Video 2: Partial Pivoting in GE
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  • External Url
    Video 3 Creating a Partial Pivot Matrix Video 3 Creating a Partial Pivot Matrix
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  • External Url
    Video 4: Using the LUP decomposition Video 4: Using the LUP decomposition
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  • External Url
    Video 5: Computational Complexity of LU Video 5: Computational Complexity of LU
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  • External Url
    Video 6: LUP algorithm Video 6: LUP algorithm
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  • Quiz
    CQ3. Gaussian Elimination and LU decomposition CQ3. Gaussian Elimination and LU decomposition
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  • Discussion Topic
    Discussion PS3 LU decomposition and solving linear systems Discussion PS3 LU decomposition and solving linear systems
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Exam 1 in Class Exam Monday 10/28

Exam 1 in Class Exam Monday 10/28
Module Completed Module In Progress Module Locked
Exam 1 in Class Exam Monday 10/28 193082    
  • Context Module Sub Header
    Covers Lect 1-6: Practice review problems and notes will go here.
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  • Attachment
    MidtermReview_Fall2019.pdf MidtermReview_Fall2019.pdf
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  • Discussion Topic
    Exam 1: Discussion of Midterm Review Exam 1: Discussion of Midterm Review
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  • Attachment
    Midterm_Fall2019_answerKey.pdf Midterm_Fall2019_answerKey.pdf
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Least squares regression

Least squares regression
Module Completed Module In Progress Module Locked
Least squares regression 193080    
  • Page
    Course Schedule: Least squares regression Course Schedule: Least squares regression
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  • Attachment
    Lect7_Oct16.pdf Lect7_Oct16.pdf
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  • Attachment
    Fish_Example.m Fish_Example.m
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  • Attachment
    Lect8_Oct21.pdf Lect8_Oct21.pdf
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  • Discussion Topic
    Discussion PS4 Least Squares, Cholesky, and QR Discussion PS4 Least Squares, Cholesky, and QR
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  • Assignment
    Problem 1: Linear and Quadratic Equations Fit to data Problem 1: Linear and Quadratic Equations Fit to data
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  • Assignment
    Problem 2: Least Squares for exponential equation Problem 2: Least Squares for exponential equation
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  • Assignment
    Problem 3: Polynomial Fitting Problem 3: Polynomial Fitting
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  • Assignment
    Problem 4: Cholesky vs GE to solve Ax=b Problem 4: Cholesky vs GE to solve Ax=b
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  • Assignment
    Problem 5: Cholesky on Hilbert Matrices Problem 5: Cholesky on Hilbert Matrices
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  • Quiz
    Quiz 4. Least Squares, Cholesky and QR decomposition Quiz 4. Least Squares, Cholesky and QR decomposition
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Gram Schmidt and QR factorization

Gram Schmidt and QR factorization
Module Completed Module In Progress Module Locked
Gram Schmidt and QR factorization 193081    
  • Page
    Course Schedule: Matrix decomposition to orthonormal matrices Course Schedule: Matrix decomposition to orthonormal matrices
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  • Attachment
    Lect8_Oct21.pdf Lect8_Oct21.pdf
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  • Attachment
    Lect9_Oct23.pdf Lect9_Oct23.pdf
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  • Quiz
    Quiz 4. Least Squares, Cholesky and QR decomposition Quiz 4. Least Squares, Cholesky and QR decomposition
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    QR_Examples.m QR_Examples.m
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  • Assignment
    Problem 6: Linear independence and QR Problem 6: Linear independence and QR
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  • Assignment
    Problem 7: Create A and R given Q Problem 7: Create A and R given Q
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Eigenvalues and Eigenvectors

Eigenvalues and Eigenvectors
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    Course Schedule: Eigenvalue problems Course Schedule: Eigenvalue problems
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  • Attachment
    Lect10_Oct30 Lect10_Oct30
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  • Attachment
    Lect11_Nov4.pdf Lect11_Nov4.pdf
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  • External Url
    More reading on Eigenvectors and values (multiplicity): Prof. Hetmaniuk's Notes pg 146-152 More reading on Eigenvectors and values (multiplicity): Prof. Hetmaniuk's Notes pg 146-152
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  • Attachment
    Diagonalization_Complex_eigenvalues.pdf Diagonalization_Complex_eigenvalues.pdf
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  • Quiz
    Quiz 5. Eigenvalues and Eigenvectors Quiz 5. Eigenvalues and Eigenvectors
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  • Assignment
    Problem 1: Diagonalize a Matrix Problem 1: Diagonalize a Matrix
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  • Assignment
    Problem 2: Cayley Hamilton Theorem Problem 2: Cayley Hamilton Theorem
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  • Assignment
    Problem 3: Ranking Problem Problem 3: Ranking Problem
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  • Assignment
    Problem 4: Power Method iterations Problem 4: Power Method iterations
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  • Assignment
    Problem 5: Inverse Power Method iterations Problem 5: Inverse Power Method iterations
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  • Assignment
    Problem 6: Calculate largest and smallest eigenvalues and associated vectors Problem 6: Calculate largest and smallest eigenvalues and associated vectors
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  • Discussion Topic
    Discussion for eigenvalues/vectors, PS5 Discussion for eigenvalues/vectors, PS5
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SVD decompositions

SVD decompositions
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SVD decompositions 193083    
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    Course Schedule: Singular Value Decomposition Course Schedule: Singular Value Decomposition
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  • Attachment
    Lect12_Nov6.pdf Lect12_Nov6.pdf
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  • Attachment
    Lect13_SVDpart2.pdf Lect13_SVDpart2.pdf
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  • Discussion Topic
    Discussion PS6 SVD Discussion PS6 SVD
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  • Context Module Sub Header
    Quiz and Coding Problems:
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  • Quiz
    CQ 6. SVD CQ 6. SVD
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  • Assignment
    PS 6 Problem 1 Find the subspaces using SVD PS 6 Problem 1 Find the subspaces using SVD
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  • Assignment
    PS6 Problem 2: Construct an SVD with given singular values PS6 Problem 2: Construct an SVD with given singular values
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  • Assignment
    PS6 Problem 3: Image Compression PS6 Problem 3: Image Compression
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  • Assignment
    PS 6 Problem 4: SVD of Hilbert Matrix PS 6 Problem 4: SVD of Hilbert Matrix
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  • Assignment
    PS 6 Problem 5: Solve Ax = b using SVD calculated inverse PS 6 Problem 5: Solve Ax = b using SVD calculated inverse
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  • Assignment
    PS 6 Problem 6: Calculate Matrix square root using SVD PS 6 Problem 6: Calculate Matrix square root using SVD
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  • Context Module Sub Header
    Matlab Code for SVD examples
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  • Attachment
    jaguar_example.m jaguar_example.m
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  • Attachment
    jaguar.jpg jaguar.jpg
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  • Attachment
    Example_Code.zip Example_Code.zip
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Least Squares Regression Using QR and SVD

Least Squares Regression Using QR and SVD
Module Completed Module In Progress Module Locked
Least Squares Regression Using QR and SVD 193084    
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    Course Schedule: Least Squares using different decompositions Course Schedule: Least Squares using different decompositions
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  • Attachment
    Lect14_LeastSquaresFormal.pdf Lect14_LeastSquaresFormal.pdf
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  • Attachment
    Lect15_LeastSquares_QRandSVD.pdf Lect15_LeastSquares_QRandSVD.pdf
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  • Discussion Topic
    Discussion: Least Squares part 2 Discussion: Least Squares part 2
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  • Context Module Sub Header
    Quiz and Coding Problems:
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  • Quiz
    CQ 7. Least Square using a variety of methods. CQ 7. Least Square using a variety of methods.
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  • Assignment
    PS7 Problem 1: Use all methods to do Least Squares PS7 Problem 1: Use all methods to do Least Squares
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  • Assignment
    PS7 Problem 2: Fitting a plane to noisy data PS7 Problem 2: Fitting a plane to noisy data
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  • Assignment
    PS7 Problem 3: Check if solvable using QR PS7 Problem 3: Check if solvable using QR
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  • Assignment
    PS7 Problem 4: Examine an overdetermined system PS7 Problem 4: Examine an overdetermined system
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  • Assignment
    PS7 Problem 5: Compare accuracy of method to pinv(A) PS7 Problem 5: Compare accuracy of method to pinv(A)
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  • Context Module Sub Header
    Further Reading if Interested:
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  • External Url
    More thorough analysis of Computational complexity for Cholesky, QR and SVD More thorough analysis of Computational complexity for Cholesky, QR and SVD
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Extra Topic: Generalized Eigenvectors & Jordon Normal Form

Extra Topic: Generalized Eigenvectors & Jordon Normal Form
Module Completed Module In Progress Module Locked
Extra Topic: Generalized Eigenvectors & Jordon Normal Form 208309    
  • Attachment
    Lect17_JordonForm.pdf Lect17_JordonForm.pdf
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Exam 2 In class Monday 12/02

Exam 2 In class Monday 12/02
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Exam 2 In class Monday 12/02 204769    
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    Exam2Review_Fall2019.pdf Exam2Review_Fall2019.pdf
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Final Project due 12/10

Final Project due 12/10
Module Completed Module In Progress Module Locked
Final Project due 12/10 193087    
  • Assignment
    "Quiz 8": Final Project Proposal "Quiz 8": Final Project Proposal
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  • Assignment
    PS8: Submit Code For Final Project PS8: Submit Code For Final Project
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  • Assignment
    Final Project Final Project
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  • Discussion Topic
    Discussion: Final Project Discussion: Final Project
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minimum score must view must submit must contribute