Department of Mathematical Sciences
Northern Illinois University

### MATH 423, Spring 2007 6:00-7:15 pm, M W, DU 310

INSTRUCTOR: 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.

TEXTS: Linear Algebra: An Introductory Approach, by C.W. Curtis
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.

SYLLABUS: I plan to cover at the following sections of Curtis: 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 Complex Numbers; Chapter 7, The Theory of a Single Linear Transformation; Chapter 8, Dual Vector Spaces and Multilinear Algebra (Section 26 only).

TENTATIVE SCHEDULE OF LECTURES:

```     Monday                   Wednesday                  M Tu  W Th  F
Holiday                  3 Vector spaces         JAN 15 16 17 18 19
4 Subspaces                4 Linear dependence         22 23 24 25 26
5 Bases                    5 Dimension                 29 30 31  1  2
7 Finite dimension       8,9 Systems of equations  FEB  5  6  7  8  9
10 Manifolds               11 Transformations           12 13 14 15 16
11 Transformations         13 Matrices                  19 20 21 22 23
13 Matrices                     EXAM I                  26 27 28  1  2
16 Determinants            17 Determinants          MAR  5  6  7  8  9
SPRING BREAK                             12 13 14 15 16
18,19 Determinants         15 Inner products            19 20 21 22 23
15 Inner products          15 Inner products            26 27 28 29 30
22 Eigenvalues             22 Eigenvectors          APR  2  3  4  5  6
23 Invariant subspaces     23 Invariant subspaces        9 10 11 12 13
Jordan canonical form           EXAM II                 17 17 18 19 20
Jordan form (notes)        Jordan form (notes)          23 24 25 26 27
26 Quotients               26 Dual spaces           MAY 30  1  2  3  4
FINAL EXAM   Monday, May 7, 6:00-7:50 pm              7  8  9 10 11
```