Department of Mathematics, College of Staten Island, City University of New York (CUNY)

Linear Algebra: MTH 338, Section D002 - Fall 2023 Course Outline

Class Hours: Tuesday & Thursday, 4:40 pm - 6:20 pm
Office Hours: Monday 12:00 pm - 3:00 pm

Prof. Allen Tesdall


Email:   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
       
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
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