Prof. Ilya Kofman 
Office: 1S209 phone: (718) 9823615
Email: ikofmanmath.csi.cuny.edu Website: http://www.math.csi.cuny.edu/~ikofman/ 
Course Time and Place: 
Mondays: 6:30pm  8:10pm in 1S115 Wednesdays: 6:30pm  8:10pm in 1S102 
Textbook: Bernard Kolman and David R. Hill, Introductory Linear Algebra: An Applied First Course Eighth Edition, 2005. ISBN 0131437402. Available at the University Bookstore or online: AddALL.
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.
Homework: Assignments will be announced in class and then posted on this website in the column marked "Due". Any changes will be announced in class. Late homework will not be accepted. The listed exercises from the textbook are strongly recommended as practice, but they will not be collected. Answers for almost all of these are in the back of the book. 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 an online program that generates individualized computational problems, and provides immediate feedback. Incorrect answers may be corrected, so that I hope you will often submit perfect homework sets. You cannot learn linear algebra without doing these kinds of computational problems, so Webwork is the major part of your HW score.
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 many homework problems designed for MATLAB. Using MATLAB will be required for this course. For an introduction to MATLAB, see Chapter 12 of our textbook.
Grading: The course grade will be determined as follows: 18% HW and Webwork + 18% Exam 1 + 18% Exam 2 + 18% Exam 3 + 28% Final Exam. Without exception, you must take the final exam at the time scheduled by the university.
Help: My office hours are Mondays 1:303:00pm and Wednesdays 3:304:30pm in my office, 1S209.
Optimal Method of Study: (1.) Come to class. (2.) Read the relevant sections after class. (3.) Do the homework. Leave time to thinkdo not put homework off until it is due! (4.) Compare your solutions with other students to improve what you hand in. (5.) Come to office hours or the help room with any remaining questions.
Class  Topic  Read  Exercises  Due 
Jan 26  Linear systems, matrices  §1.1, 1.2  1.1: 5,7,9,11,13,15,22,27,T4
1.2: 1,5,7,9,T1,T5,T7 
WeBWorK 
Jan 28  Matrix operations  §1.3, 1.4  1.3: 1,5,7,9,11,13,15,19,21,25,T1,T3,T4,T7,T10
1.4: 9,11,13,15,T6,T9,T23,T24,T27 

Feb 02  Solving linear systems  §1.6  3,5,8,9,13,19,23,27,31,47,T8,T11  
Feb 04  Inverse matrix  §1.7  3,5ab,11,13,15,18,25,T7,T9,T10  problem set 1:1.1/26; 1.2/T5; 1.3/T6,T9 
Feb 09  Determinants  §3.1  3,5abv,9,15,17,22,23,T5,T9,T16  
Feb 11  Cofactor expansion  §3.2, 3.3  3.2: 1,5,9,11,15,19,23,T4,T5,T10,T11  problem set 2:1.6/T13,ML8,ML11; 1.7/T8,ML4 
Feb 18  Vectors  §4.1, 4.2  4.1: 9,13,15,19,21,24,27,T5,T9
4.2: 1,4,11,13,17,21,23,26,27,T5,T13 

Feb 23  Review  
Feb 25  EXAM 1  
Mar 02  Linear transformations  §4.3  1,7,13,15,17,21,25,27,29,T5,T11  
Mar 04  Matrix transformations  §1.5  1,5,9,15,19  
Mar 09  Vector spaces  §6.1, 6.2  6.1: 1,3,4,9,13,15,20,T5
6.2: 3,7,9,17,19,20e,23,25,27,T3,T12 
Problem 2 on Exam 1 
Mar 11  Linear independence  §6.3  1ab,3ac,5,7,9,11bc,12ab,13ab,14,16,T2,T8,T11,T13  
Mar 16  Basis, dimension  §6.4  1,3ab,5bc,9,11,13,19,23,27,29,31,33,35,T3,T4,T8,T12,T15  
Mar 18  Homogeneous systems  §6.5  3,5,11,13,21,T3  
Mar 23  EXAM 2, Matrix rank  §6.6  1,3,5,7,11,17,19,21,23,27,29,33,T7,T12  
Mar 25  Change of basis  §6.7  1,3,5,7,11,13,15,17,21,25,T4,T7c  
Mar 30  Orthonormal bases  §6.8  1,3,5,9,11,15,17,19,21,T6,T9  
Apr 01  Orthogonal complements  §6.9  1,3,7,9ab,11,13,T5  
Apr 06  Linear transformations  §10.1, 10.2  10.1/1,3,5,17,19,T5; 10.2/1,3,9,11,17,T2  
Apr 20  Matrix of linear transformation  §10.3, B2  1,3,13,15,17  
Apr 22  Eigenvalues, eigenvectors  §8.1  5,9,11,13,15,17cd,19,21,25,T6,T9,T11,T15  MIT web demo MIT web lecture 
Apr 27  EXAM 3  
Apr 29  Diagonalization  §8.2  1,3,5,9,13,15,19,23,25,29,39,41,46,T2,T6,T7  
May 04  Symmetric matrices  §8.3  1,2,5,9,17,T1,T6,T8  
May 06  Dynamical systems  §9.3  1,2,3,4,5  
May 11  Review  
May 13  Review  Application: How Google Finds Your Needle in the Web's Haystack 