Linear Algebra: Math 338--9213:  Spring 2009 Syllabus

Prof. Ilya Kofman

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

Course Time and Place:

Mondays:    6:30pm - 8:10pm   in 1S-115

Wednesdays:   6:30pm - 8:10pm   in 1S-102

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 1:30-3:00pm and Wednesdays 3:30-4:30pm in my office, 1S-209.

Optimal Method of Study:  (1.) Come to class.  (2.) Read the relevant sections after class.  (3.) Do the homework. Leave time to think--do 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
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

Old exams for review (PDF):

  • S07 Exam 1
  • S07 Exam 2
  • S07 Exam 3
  • Sample Exam 1  SOLUTIONS to Sample Exam 1
  • Sample Exam 2  SOLUTIONS to Sample Exam 2