Department of Mathematical Sciences
Northern Illinois University

## 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

## SYLLABUS

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

GRADING: Grades will be based on 600 points: 300 points for two in-class exams, 100 points for homework, and 200 points for the final exam.
Exams are scheduled for February 28, April 18, and May 7.

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
```
Homework 2   |   Homework 4   |   Homework 5   |   Homework 7

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