Linear Algebra MTH 338, Section 28381, Fall 2024 Mon-Wed 2:30 - 4:25 3S-107

Information	Course Outline	Policies	Useful Links	Webwork	Blackboard	Department of Mathematics

Instructor: Abhijit Champanerkar
Office: 1S-230
Phone: 718-982-3613
Email :
Office Hours: Mondays & Wednesdays 4:30 - 5:45 pm
Class Homepage: http://www.math.csi.cuny.edu/abhijit/338/
Academic Calendar

Course Information


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.


Course description: This course gives an introduction to the computational and theoretical aspects of linear systems and linear transformations and to the writing of mathematical proofs. This is a core topic in mathematics, with applications in many fields. Topics include systems of linear equations, matrices, matrix, equations, determinants, vector spaces, linear transformations, linear independence, eigenvalues, and eigenvectors; with selected applications.
Prerequisite: Calculus II MTH 232 or equivalent.


Text Book: Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, 2016. ISBN: 978-09802327-7-6. You can rent or buy, new or used, from any store.

Syllabus: See course outline below. Here is pdf format (for a different semester) course outline pdf.

Videos:  You are expected to view each video listed below before class, so that we can discuss the material further in class. Video Lectures

Homework:  Webwork problems must be submitted online. To pass this course, the Webwork problems are the minimum requirement; to earn an excellent grade, you will have to do the other assigned problems in your textbook. Answers to exercises in the textbook are at >https://math.mit.edu/~gs/linearalgebra . I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.

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, and it is a major part of your grade. Webwork

Grading:  The course grade will be determined (subject to changes announced in class) by your scores on Webwork homework, exams and final exam. Without exception, you must pass the exams to pass this course, and you must take the final exam at the time scheduled by the college. The course grade will be approximately determined as follows: Exams - 13% each exam, Webwork - 15 %, Final Exam - 33%.

IMPORTANT DATES There will be 4 exams during the semester and a comprehensive Final exam at the end of the semester. Here are the tentative dates:

• Exam 1: Wed Sep 18 Review: Mon Sep 16
• Exam 2: Wed Oct 16 Review: Tues Oct 15
• Exam 3: Wed Nov 6 Review: Mon Nov 4
• Exam 4: Wed Dec 4 Review: Mon Dec 2
• Final Exam: Wed Dec 18, class time Review: Wed Dec 11
• See the Fall 2024 Academic Calendar for other important dates

Help

Help:  My office hours are Mondays and Wednesdays, 4:30pm-5:45pm. Email is the fastest way to contact me.

How to Study:  (1) Watch the appropriate video before class. (2) Attend class (attendance is mandatory).  (3) Read the relevant sections after class.  (4) Do the homework. Leave time to think about it!  (5) Use the Blackboard discussion board or visit me during office hours with any remaining questions.  (6) To study for a math exam, you must DO MORE PROBLEMS from past exams, homework and textbook.

Course Outline, Topics & Other Resources

Here is a tentative list topics covered by date, related classworks and other resources. Course outline pdf.

Class	Topic	Videos	Read	Exercises	Webwork
Wed Aug 28	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
Mon Sep 2	No Class
Wed Sep 4	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
Mon Sep 9	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
Wed Sep 11	Matrix Operations, Inverse Matrices	Strang 3	§2.4, 2.5	2.4: p. 77: 1,3,5,7,13,14,15,17,19,27 2.5: p. 92: 1,4,6,7,8,11,15,16,21,22,24,27	Sets 4,5
Mon Sep 16	Review
Wed Sep 18	EXAM 1 Factorization A=LU		§2.6	p. 104: 1,2,3,4,6,9,12,15, MATLAB examples for which you must import the function slu.m
Mon Sep 23	Factorization A=LU Transposes and Permutations	Strang 4 Strang 5	§2.7	p.117: 2,4,8,16,17,20,22*	Set 6
Wed Sep 25	Spaces of Vectors	Strang 6	§3.1	p. 131: 1,3,5,9,11,15,19,20,23,25	Set 7
Mon Sep 30	Nullspace of A	Strang 7	§3.2	p. 142: 1,2,3,5,8,9,11,13,14,16,24,29	Set 8
Wed Oct 2	No Class
Mon Oct 7	Complete Solution to Ax=b	Strang 8	§3.3	p. 158: 1,2,4,6,8,12,13,14,16,18,25	Set 9
Wed Oct 9	Independence, Basis and Dimension	Strang 9	§3.4	p. 175: 1,2,3,6,8,9,11,12,15,18,20,25	Sets 10,11,12
Tues Oct 15*	Review
Wed Oct 16	EXAM 2 Independence, Basis and Dimension
Mon Oct 21	Dimensions of the Four Subspaces	Strang 10	§3.5	p. 190: 1,2,4,6,9,11,12,16,24	Set 13
Wed Oct 23	Orthogonality of the Four Subspaces	Strang 14	§4.1	p. 202: 1,3,5,6,8,9,10,11,12,16,28	Set 14
Mon Oct 28	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
Wed Oct 30	Orthogonal Bases and Gram-Schmidt	Strang 17	§4.4	p. 242: 1,2,4,5,21	Set 17
Mon Nov 4	Review
Wed Nov 6	EXAM 3 Orthogonal Bases and Gram-Schmidt
Mon Nov 11	Determinants	Strang 18 and Strang 19	§5.1, 5.2	5.1: p.254: 1,3,8,9,10,11,14,23,24,27,28 5.2: p.266: 1,2,3,4,5	Set 18
Wed Nov 13	Cramers Rule, Inverses, and Volumes Eigenvalues	Strang 20 and 3B1B-E12	§5.3	p. 283: 2,3,16,17	Set 19
Mon Nov 18	Eigenvalues	Strang 21 and 3B1B-E14	§6.1	p. 298: 1,3,5,6,8,16,17,21,23,27. See Explained Visually	Set 20
Wed Nov 20	Diagonalizing a Matrix	Strang 22	§6.2	p.314: 1,3,4,6,11,12,13,14,15,21,26	Set 21
Mon Nov 25	Linear Transformations	3B1B-E3 and 3B1B-E4 and 3B1B-E5	§8.1	p.407: 1,3,6,10,12	Set 22
Wed Nov 27	No Class
Mon Dec 2	Review
Wed Dec 4	EXAM 4 Linear Transformations
Mon Dec 9	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
Wed Dec 11	Review	Strang 34
Wed Dec 18	Final Exam	Wed Dec 18 2:30 - 4:25 PM 3S107

* Please note that Tuesday Oct 15th is a CUNY Monday

Useful links

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

Course Policies

• Attendance is mandatory.


• Cell phone usage of any kind during class and on exams is not allowed.


• Missing the Final exam will result in an F grade. Any changes to the grading policy will be announced in the class.


• You must take the Final exams at the time scheduled by the university.


• Students are not allowed to step out of the classroom during exams, except in case of emergencies.


• Academic dishonesty: Cheating in any form will not be tolerated. Please see CUNY Policy on Academic Integrity.


• Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Center for Student Accessibility. Please provide written verification of student's eligibility from the CSA. Prior to granting disability accommodations in this course, the instructor must receive written verification of student’s eligibility from the Center for Student Accessibility, which is located in 1P-101. It is the student’s responsibility to initiate contact with the Center for Student Accessibility staff and to follow the established procedures for having the accommodation notice sent to the instructor.