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: 
Tuesdays: 6:30pm  8:10pm in 1S217 Thursdays: 6:30pm  8:10pm in 1S116 
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.
Material Covered: This course is an introduction to linear algebra. The central part is the study of linear equations, matrices, real vector spaces, and linear transformations.
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 problems, and provides immediate feedback. Incorrect answers may be corrected, so that I hope you will often submit perfect homework sets. These problems will be mostly computational exercises. This will count as 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: 20% HW + 20% Midterm Exam 1 + 10% Midterm Quiz + 20% Midterm Exam 2 + 30% Final Exam.
Without exception, you must take the final exam at the time scheduled by the university.
Help: My office hours are Tuesdays 2:304:30pm and Thursdays 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.
Written work: We write to communicate. Work must be neat and legible to receive consideration. You must explain your work to obtain full credit. For specific suggestions see A guide to writing in mathematics classes.
Goals: 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.
Class  Topic  Read  Exercises  Due 
Jan 30  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 
Feb 01  Matrix multiplication  §1.3  1,5,7,9,11,13,15,19,21,25,T1,T3,T4,T7,T10  
Feb 06  Matrix operations  §1.4  9,11,13,15,T6,T9,T23,T24,T27  
Feb 08  Solving linear systems  §1.6  3,5,8,9,13,19,23,27,31,47,T8,T11  
Feb 13  Inverse matrix  §1.7  3,5ab,11,13,15,18,25,T7,T9,T10  problem set 1:1.1/26; 1.2/6,T5; 1.3/8,T6,T9 
Feb 20  Determinants  §3.1  3,5abv,9,15,17,22,23,T5,T9,T16  problem set 2:1.4/14,16,ML1,ML6,ML7; 1.5/16,18 
Feb 22  Cofactor expansion  §3.2, 3.3  3.2: 1,5,9,11,15,19,23,T4,T5,T10,T11  
Feb 27  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 
problem set 3:1.6/28,30,32,ML8,ML11; 1.7/8,22,T8,ML4 
Mar 01  MIDTERM EXAM 1  SAMPLE EXAM 1 (PDF) SOLUTIONS to SAMPLE EXAM 1 

Mar 06  Linear transformations  §4.3  1,7,13,15,17,21,25,27,29,T5,T11  
Mar 08  Matrix transformations  §1.5  1,5,9,15,19  problem set 4:3.1/18, T10, ML2; 3.2/6, 18, 22, ML2 
Mar 13  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 

Mar 15  Linear independence  §6.3  1ab,3ac,5,7,9,11bc,12ab,13ab,14,16,T2,T8,T11,T13  problem set 5:4.3/32, T9 
Mar 20  Basis, dimension  §6.4  1,3ab,5bc,9,11,13,19,23,27,29,31,33,35,T3,T4,T8,T12,T15  
Mar 22  Homogeneous systems  §6.5  3,5,11,13,21,T3  problem set 6:6.2/T3, T12; 6.3/10,18 
Mar 27  MIDTERM QUIZ, Matrix rank  §6.6  1,3,5,7,11,17,19,21,23,27,29,33,T7,T12  In class Midterm Quiz 
Mar 29  Change of basis  §6.7  1,3,5,7,11,13,15,17,21,25,T4,T7c  problem set 7:6.7/14 
Apr 12  Orthonormal bases  §6.8  1,3,5,9,11,15,17,19,21,T6,T9  
Apr 17  Orthogonal complements  §6.9  1,3,7,9ab,11,13,T5  problem set 8:6.8/10, 6.9/6,8 
Apr 19  Linear transformations  §10.1, 10.2  10.1/1,3,5,17,19,T5; 10.2/1,3,9,11,17,T2  
Apr 24  Matrix of linear transformation  §10.3, B2  1,3,13,15,17  Sample Exam 2 (PDF) 
Apr 26  MIDTERM EXAM 2  SOLUTIONS to Sample Exam 2 ** NEW! **  
May 01  Eigenvalues, eigenvectors  §8.1  5,9,11,13,15,17cd,19,21,25,T6,T9,T11,T15  MIT web demo MIT web lecture 
May 03  Diagonalization  §8.2  1,3,5,9,13,15,19,23,25,29,39,41,46,T2,T6,T7  problem set 9: 10.2/4,6,20, 10.3/20 
May 08  Symmetric matrices  §8.3  1,2,5,9,17,T1,T6,T8  
May 10  Dynamical systems  §9.3  1,2,3,4,5  
May 15  Review  
May 17  Review  
May ??  FINAL EXAM  Application: How Google Finds Your Needle in the Web's Haystack 