Prof. Allen TesdallEmail: atesdallmath.csi.cuny.edu Website: http://www.math.csi.cuny.edu/~atesdall/ |
Textbook: Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, 2016. ISBN 9780980232776. You can rent or buy, new or used, from any store. See the CSI online bookstore link here: MTH 338 D002 - Linear Algebra .
Goals: Linear algebra is the study of linear equations, matrices, real vector spaces, and linear transformations. Many problems in linear algebra are computational -- the first goal is to make calculations with accuracy, intelligence and flexibility. But linear algebra is also a course filled with new concepts and new vocabulary, often with a geometric flavor -- the second goal is to explain the basic concepts clearly, reason logically with them, and use them to solve extended problems.
Videos: I recommend that you view each video listed in the class schedule below before class, so that we can discuss the material further in class.
Homework: Reading and textbook exercises for each class meeting are assigned in the schedule below. Partial solutions to these exercises are available at https://math.mit.edu/~gs/linearalgebra, so they are not graded. However, I highly recommend that you try to work out full solutions for all of them. Working jointly on these with fellow students is encouraged. Additionally, Webwork exercises are assigned for each class meeting in the schedule. Webwork exercises are submitted online, and are graded (see the discussion on Webwork below).
Webwork: Webwork is a free online system that provides individualized homework problems, gives immediate feedback, and allows you to correct mistakes until the due date. Later, you can see solutions online. Webwork is required in this course. Webwork assignments are shown in the class schedule below.
Matlab: Matlab is a powerful computer algebra platform designed to solve linear algebra problems. Our textbook has quite a bit of Matlab material, and we may have some optional Matlab assignments during the semester. You can access MATLAB online using the CUNY Virtual Desktop, and it is also free for CUNY students to download and install.
Exams: There will be two in-class midterm exams and one in-class cumulative final exam. See the class schedule below for the dates of the exams. All exams, including the final exam, must be taken at the time and on the day scheduled. Make-up exams will not be given.
Grading: The course grade will be determined as follows: two midterm exams 25% each, final exam 35%, online Webwork homework 15%. Without exception you must pass the final exam to pass the class.
Help: Free math tutoring is available at The Center for Academic Student Assistance, Room 1L-117. The mathematics department also has tutoring available: see math department tutoring.
Class | Topic | Videos | Reading | Textbook exercises | Webwork |
Aug 29 | Vectors and Linear Combinations, Lengths and Dot Products | 3B1B-E1 and
3B1B-E2 and KA-dot product |
§1.1, 1.2 | 1.1: p.8: 2,4,6,9,10,17,26
1.2: p.18: 1,3,4,6,8,9,12,19,21,29 |
Set 1 |
Aug 31 | Matrices, Vectors and Linear Equations | Strang 1 | §1.3, 2.1 | 1.3: p. 29: 1,2,4,5,7
2.1: p. 41: 4,5,6,7,9,10,13,18,27 |
Set 2 |
Sep 5 | Elimination | Strang 2 and another example | §2.2, 2.3 | 2.2: p. 53: 1,2,4,5,11,12,13
2.3: p. 66: 1,3,4,8,11,14,18,25,27,28 |
Set 3 |
Sep 7 | Matrix Operations, Inverse Matrices | Strang 3 | §2.4 | 2.4: p. 77: 1,3,5,7,13,14,15,17,19,27 | Set 4 |
Sep 12 | Inverse Matrices (continued) | §2.5 | 2.5: p. 92: 1,4,6,7,8,11,15,16,21,22,24,27 | Set 5 | |
Sep 14 | Factorization A=LU | Strang 4 |
§2.6 | p. 104: 1,2,3,4,6,9,12,15, MATLAB examples for which you must import the function slu.m | Set 6 |
Sep 19 | Transposes and Permutations | Strang 5 | §2.7 | p.117: 2,4,8,16,17,20,22 | |
Sep 21 | Spaces of Vectors | Strang 6 | §3.1 | p. 131: 1,3,5,9,11,15,19,20,23,25 | Set 7 |
Sep 26 | Nullspace of A | Strang 7 | §3.2 | p. 142: 1,2,3,5,8,9,11,13,14,16,24,29 | Set 8 |
Sep 28 | Complete Solution to Ax=b | Strang 8 | §3.3 | p. 158: 1,2,4,6,8,12,13,14,16,18,25 | Set 9 |
Oct 3 | Review Independence, Basis and Dimension |
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Oct 5 | TEST 1 | ||||
Oct 12 | Independence, Basis and Dimension (continued) | Strang 9 | §3.4 | p. 175: 1,2,3,6,8,9,11,12,15,18,20,25 | Sets 10,11,12 |
Oct 17 | Dimensions of the Four Subspaces | Strang 10 | §3.5 | p. 190: 1,2,4,6,9,11,12,16,24 | Set 13 |
Oct 19 | Orthogonality of the Four Subspaces | Strang 14 | §4.1 | p. 202: 1,3,5,6,8,9,10,11,12,16,28 | Set 14 |
Oct 24 | Projections and Least Squares Approximations | Strang 15 and Strang 16 | §4.2, 4.3 | 4.2: p. 214: 1,3,8,9,11,13,17,21,24,29
4.3: p. 229: 1,2,3,4,5,8,12 |
Sets 15,16 |
Oct 26 | Orthogonal Bases and Gram-Schmidt | Strang 17 | §4.4 | p. 242: 1,2,4,5,21 | Set 17 |
Oct 31 | Properties of Determinants | Strang 18 | §5.1 | 5.1: p.254: 1,3,8,9,10,11,14,23,24,27,28 | Set 18 |
Nov 2 | Determinant Formulas and Cofactors | Strang 19 and 3B1B-E6 | §5.2 | 5.2: p.266: 1,2,3,4,5 | Set 18 |
Nov 7 | Cramer's Rule, Inverses, and Volumes | Strang 20 and 3B1B-E12 | §5.3 | p. 283: 2,3,16,17 | Set 19 |
Nov 9 | Eigenvalues and Eigenvectors Review |
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Nov 14 | TEST 2 | ||||
Nov 16 | Eigenvalues and Eigenvectors (continued) | Strang 21 and 3B1B-E14 | §6.1 | p. 298: 1,3,5,6,8,16,17,21,23,27. See Explained Visually | Set 20 |
Nov 21 | Diagonalizing a Matrix | Strang 22 | §6.2 | p.314: 1,3,4,6,11,12,13,14,15,21,26 | Set 21 |
Nov 28 | Linear Transformations | 3B1B-E3 and 3B1B-E4 and 3B1B-E5 | §8.1 | p.407: 1,3,6,10,12 | Set 22 |
Nov 30 | Linear Transformations (continued) | 3B1B-E3 and 3B1B-E4 and 3B1B-E5 | §8.1 | p.407: 1,3,6,10,12 | Set 22 |
Dec 5 | Matrix of a Linear Transformation | Strang 30 | §8.2 | p.418: 5,6,7,10,11,14,15,16. See Mathinsight.org applet | Set 23 |
Dec 7 | Matrix of a Linear Transformation (continued) Review |
Strang 34 |
Online resources:
MIT OpenCourseWare Linear Algebra Complete online linear algebra course.
Khan Academy Linear Algebra Complete online linear algebra course.
3Blue1Brown Essence of Linear Algebra Excellent online videos.
Mathmatize Linear algebra problems in an online app
Eigenvectors and Eigenvalues Explained Visually
Mathinsight.org linear transformations applet
How Google Finds Your Needle in the Web's Haystack
Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Office for Disability Services. Prior to granting disability accommodations in this course, the instructor must receive written verification of student's eligibility from the Office of Disability Services, which is located in 1P-101. It is the student's responsibility to initiate contact with the Office for Disability Services staff and to follow the established procedures for having the accommodation notice sent to the instructor.
Integrity policy: CUNY's Academic Integrity Policy is available online at https://www2.cuny.edu/about/administration/offices/legal-affairs/policies-procedures/academic-integrity-policy
Important Dates: www.csi.cuny.edu/currentstudents/academiccalendars