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

Linear Algebra: MATH 338--41444:  Spring 2016 Course Outline

Tuesday & Thursday, 12:20 pm - 2:15 pm, Room 1S-112

Prof. Ilya Kofman

Office:   1S-209   phone: (718) 982-3615

Textbook:  Gilbert Strang, Introduction to Linear Algebra, Fourth Edition, 2009. ISBN 978-0-9802327-1-4.

Homework:  Answers to many exercises are in the back of the book. 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. 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 website

MATLAB:  MATLAB is powerful computer algebra software designed to solve linear algebra problems. The CSI Math Department has computer labs with access to MATLAB, and our textbook has a lot of MATLAB material. Learning to use MATLAB will help you in this course.

Grading:  The course grade will be determined as follows (subject to change announced in class):  18% HW and Webwork + 18% Exam 1 + 18% Exam 2 + 18% Exam 3 + 28% 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.

Help:  My office hours are Tuesdays and Thursdays 11am-12:15pm in my office, 1S-209. Also, free math tutoring is available.

How to Study:  (1.) Come to class (attendance is mandatory).  (2.) Read the relevant sections after class.  (3.) Do the homework. Leave time to think about it!  (4.) Come to my office hours or the help room with any remaining questions.  (5.) To study for a math exam, you must DO MORE PROBLEMS from past exams, homework and textbook.

Class Topic Read Exercises
Feb 2 Vectors and Linear Combinations, Lengths and Dot Products §1.1, 1.2 1.1: p.8: 2,4,6,9,10,17,26
1.2: p.19: 1,3,4,6,8,9,12,19,21
Feb 4 Matrices, Vectors and Linear Equations §1.3, 2.1 1.3: p. 29: 1,2,4,5,7
2.1: p. 40: 4,5,6,7,9,10,13,18,27
Feb 11 Elimination §2.2, 2.3 2.2: p. 51: 1,2,4,5,11,12,13
2.3: p. 63: 1,3,4,8,11,14,18,25,27,28
Feb 16 Matrix Operations, Inverse Matrices §2.4, 2.5 2.4: p. 75: 1,3,5,6,7, 12,13,14,16,18,27,32
2.5: p. 89: 1,4,6,7,8,11,1516,21,22,24,27
Feb 18 Factorization A=LU §2.6 p. 102: 1,2,3,4,6,9,12,15, MATLAB examples for which you must import the function slu.m
Feb 23 Transposes and Permutations §2.7 p.115: 2,4,8,16,17,20,22*
Feb 25 Review   Sample Exam 1
Mar 1 EXAM 1    
Mar 3 Spaces of Vectors §3.1 p. 127: 1,3,5,9,11,15,19,20,23,25
Mar 8 Nullspace of A §3.2 p. 140: 1,2,3,4,5,6,9,10,13,14,16,24,26
Mar 10 Rank and Row Reduced Form §3.3 p. 151: 1,2,7,8,9
Mar 15 Solution to Ax=b §3.4 p. 163: 1,2,4,6,8,12,13,14,16,18,25
Mar 17 Independence, Basis and Dimension §3.5 p. 178: 1,2,3,6,8,9,11,12,15,18,20,25
Mar 22 Dimensions of the Four Subspaces §3.6 p. 190:1,2,4,6,9,11,12,16,24
Mar 24 Review   Sample Exam 2 and Solutions to Problems 9 and 10
Mar 29 EXAM 2    
Mar 31 Orthogonality of the Four Subspaces §4.1 p. 202: 1,3,5,6,8,9,10,11,12,16,28
Apr 5 Projections §4.2 p. 214: 1,3,8,9,11,13,17,21,2 4,29
Apr 7 Least Squares Approximations Orthogonal Bases and Gram-Schmidt §4.3, 4.4 4.3: p. 226: 1,2,17,18,21
4.4: p. 239: 3,4,5,11,13,15,21
Apr 12 Determinants §5.1, 5.2 5.1: p. 251: 1,3,8,9,10,11,14,23,24,27,28
5.2: p.263: 1,2,3,4,5
Apr 14 Cramer's Rule, Inverses, and Volumes §5.3 p. 279: 2,3,16 ,17
Apr 19 Review   Sample Exam 3
Apr 21 EXAM 3    
May 3 Eigenvalues §6.1 p. 293: 1,3,5,6,8,16,17,21,23,27. See Explained Visually
May 5 Diagonalizing a Matrix §6.2 p.307: 1,3,4,6,11,12,13,14,15,21,26
May 10 Linear Transformations §7.1 p.380: 1,3,6,10,12
May 12 Matrix of a Linear Transformation §7.2 p.395: 5,6,7,10,11,14,15,16. See applet
May 17 Review   Sample problems for chapters 6-7

Online resources: 

MIT Linear Algebra  MIT Videos, Problem Sets and Exams

MIT OpenCourseWare Linear Algebra  Complete online linear algebra course.

Khan Academy Linear Algebra  Complete online linear algebra course.

Eigenvectors and Eigenvalues Explained Visually 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