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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