MATH 423, Spring 2007

6:00-7:15 pm, M W, DU 310

Professor John Beachy, Watson 355, 753-6753, email: beachy@math.niu.edu
Office hours: 4:30 - 5:30 M W

COURSE: LINEAR AND MULTILINEAR ALGEBRA (3)
The general theory of vector spaces, linear transformations, and matrices. Topics selected from determinants, tensor products, canonical forms, and bilinear and quadratic forms.

PREREQUISITE: Math 240 and Math 420, or consent of department.
See MATH 240 summary (pdf format, 8 pages)   and   Abstract Algebra OnLine

TEXTS: Linear Algebra: An Introductory Approach, by C.W. Curtis, (Springer Verlag, 1984, ISBN 0387909923))
      Elementary Linear Algebra, 8th Edition (2004), by Kolman and Hill

TENTATIVE SYLLABUS: I plan to cover at the following sections.

Chapter 2, Vector Spaces and Systems of Linear Equations

Chapter 3, Linear Transformations and Matrices

Chapter 5, Determinants

Chapter 4, Vector Spaces with an Inner Product

Chapter 6, Polynomials and Comples Numbers

Chapter 7, The Theory of a Single Linear Transformation

Chapter 8, Dual Vector Spaces and Multilinear Algebra (Section 26)

HANDOUTS: Syllabus (as handed out in class)   |   Schedule of lectures (tentative)

ASSIGMENTS:

Hmwk     Due    Curtis                   Kolman                        
 1       1/24   3 #10;     4 #2,6,7      3.2 #4,5,8  3.3 #13,15        
 2       1/31   4 #5,10;   5 #3 +1       3.4 #5,23   3.5 #3,6,16       
 3       2/07   6 #4,5;    7 #2,6,7      3.5 #14,23,29,31,32         
 4       2/14   10 #2,4,9  +1
 5       2/26   The problem set is listed below.
 6       3/21   19 #2,5,9,10     *** postponed till 3/26
 7       3/28   The problems set is given below.
 8       4/04   Curtis 15 #2,4,7,9  22 #3,5
 9       4/16   Class Notes p 8 #1-5  Kolman 7.1 #7b; 7.2 #11c; 7.4 #19

ONLINE REFERENCES:

Hefferon, Linear Algebra, and Solutions Manual

Matthews, Elementary Linear Algebra

Payne, A Second Semester of Linear Algebra

CLASS NOTES:

Introductory lecture

Row reduction of matrices

Vector spaces and subspaces

Sample Test 1 from 1998

Class notes on canonical forms