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General Course Information
Undergraduate Catalog Description: Systems of linear equations, matrices, linear programming, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, linear transformations, and numerical methods. Credit not given for both Math 3110 and Math 3120. Spring semester. Prerequisite: A grade of "C-" or better in Math 1520 and a knowledge of vectors.
Important (for students): the official class syllabus is available on Canvas. Read it.
Text: Gilbert Strang, Introduction to Linear Algebra (Sixth Edition), Wellesley-Cambridge Press, 2023. (Do NOT try to use the old Fifth Edition or earlier, since the text was significantly reorganized for the Sixth Edition.)
Objectives
- Develop a thorough understanding of the concepts and techniques of linear algebra
- Further develop the ability to apply your knowledge to solve problems
- (Further) develop skills for working effectively with others on mathematics problems
Student Learning Objectives
- Students will be able to demonstrate the ability to write formal definitions of fundamental concepts of the course, e.g., linear independence, vector space, subspace, determinant, linear transformation, inner product, eigenvalues, eigenvectors.
- Students will be able to demonstrate the ability to perform the basic computations of linear algebra, e.g., row reduction of matrices, solving linear systems of equations, finding inverses of matrices, computing determinants, finding eigenvalues and eigenvectors.
- Students will be able to demonstrate the ability to correctly write the statements of important theorems.
- Students will be able to demonstrate the ability to recognize when and how to apply important theorems.
- Students will be able to demonstrate the ability to work with and devise examples that illustrate basic concepts of the course.
- Students will be able to demonstrate readiness for more advanced study of algebraic structures and other areas of mathematics that use linear algebra.
Topics Covered
Chapter 1: Vectors and Matrices
Chapter 2: Solving Linear Equations Ax=b (omit 2.5)
Chapter 3: The Four Fundamental Subspaces
Chapter 4: Orthogonality (omit 4.5)
Chapter 5: Determinants
Chapter 6: Eigenvalues and Eigenvectors (omit 6.4, 6.5)
Chapter 7: Single Value Decomposition (SVD)
Chapter 8: Linear Transformations
Chapter 10: Learning from Data
Assessment
| 1. | Homework | 25% |
| 2. | Tests | 45% |
| 3. | Final Examination | 30% |
Each homework work assignment must be submitted in class on paper by the listed deadline. The deadlines are provided in Canvas and on the assigned work pages of this site. Late homework may be accepted in unusual pre-approved circumstances, and will be subject to a 10\% late penalty. Homework cannot be submitted for credit after 2:10 pm the next class day (since assignments will be returned graded then (except under emergency circumstances) and solutions will be posted in Canvas that day).
Important: the test dates listed below are subject to adjustment, for example, for unexpected/unpredictable events; the tests and final exam must be taken on the scheduled dates.
Test Schedule
Test 1: Monday, September 23
Test 2: Monday, October 21
Test 3: Monday, November 18
Final: Thursday, December 12, at 2:00 p.m.