Math 310: Applied Linear Algebra
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Course Information Heading link
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Course Prerequisites
Grade of C or better in MATH 181 (Calculus II)
Course Description
Matrices, Gaussian elimination, vector spaces, LUdecomposition, orthogonality, GramSchmidt process, determinants, inner products, eigenvalue problems, diagonalization of symmetric matrices, applications to differential equations and Markov processes. Credit is not given in both MATH 310 and MATH 320 (Linear Algebra I).
Calculators not permitted on exams.
Credit Awarded
3 hours
Course Materials
Textbook
 The course uses a free textbook that can be found here: A First Course in Linear Algebra, K. Kuttler, Lyryx version 2023B (publisher: Lyryx with Open Texts). An alternative resource is Linear Algebra and its Applications, D. Lay, S. Lay, and J. McDonald, fifth edition.
MyOpenMath
 The course uses the MyOpenMath platform for online homework. No purchase for this is required.
Linear Algebra Internet Resources
 Lots of interesting material (including video lectures on many topics) can be found on the MIT open course linear algebra site.
 The Mathematics Archives maintains an excellent guide to Web Sites related to Linear Algebra.
 Mathematics Archives – Topics in Mathematics – Linear Algebra
 The Linear algebra toolkit. Contains a number of tools that show computations of linear algebra in action.
 See also the Glossary file in the link below.
Sample Exams and Material Heading link
Course Schedule Heading link
Sections  Topics 

Week 1

Systems of linear equations Row reduction and echelon Forms 
Week 2 
Solutions of linear Equations Homogeneous systems Rank 
Week 3

Applications of linear systems Matrix operations Matrix inverses 
Week 4

More on matrix inverses Linear transformations 
Week 5 
More on linear transformations Review for exam 1 Exam 1 LU factorization 
Week 6

Determinants 
Week 7

Span Linear independence Subspaces Bases Dimension 
Week 8

More on bases Null space and column space Ranknullity theorem 
Week 9

Eigenvalues and eigenvectors Review for exam 2 Exam 2 
Week 10

Diagonalization Markov chains 
Week 11

Dot product Orthogonality GramSchmidt 
Week 12

QR factorization Orthogonal projection Leastsquares solutions 
Week 13

Orthogonal Diagonalization Review for exam 3 Exam 3 Singular values 
Week 14

Singular value decomposition applications of the SVD The matrix exponential (time permitting) 
Week 15 
Review for final exam 
Week 16
Finals Week 
Final Exam 