Department of Mathematical Sciences
Northern Illinois University

MATH 423, Summer 2006

12:30-1:45, M T W R, Davis 309

June 19 - August 10

Professor John Beachy, Watson 355, 753-6753, email:
Office hours: M T W 2:00-3:00; R 10:30-11:30


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.
MATH 240 summary (pdf format, 8 pages)     Abstract Algebra OnLine

TEXT: Linear Algebra: An Introductory Approach, by C.W. Curtis, (Springer Verlag, 1984, ISBN 0387909923))

GRADING: Grades will be based on 500 points: 400 points for four hour exams and 100 points for homework.

TENTATIVE SYLLABUS: I plan to cover the following sections.

Chapter 2, Vector Spaces and Systems of Linear Equations (2 weeks)
Chapter 3, Linear Transformations and Matrices (1 week)
Chapter 5, Determinants (1 week)
Chapter 4, Vector Spaces with an Inner Product (2 weeks)
Chapter 7, The Theory of a Single Linear Transformation (2 weeks)


EXAM I, Monday, July 3   |   Exam I, in .pdf format
    (postponed from Thursday), covering sections 2 - 10
Exam II, Monday, July 15,   |   Exam II
    covering sections 11 - 13 in detail (know the proofs)
    sections 16 - 19 in much less detail (know the statements of theorems, and how to use determinants)
Exam III, Monday, July 31,   |   Exam III
    covering sections 15 and 22 (plus notes)
Exam IV, Thursday, August 10,   |   Exam IV
    covering sections 22-25, as summarized in the class notes


6/20: Homework 1, due at 5:00 pm
6/27: Homework 2, due in class
7/10: Homework 3, due in class
7/13: Homework 4, due in class
7/24: Homework 5, due at 5:00 pm
7/27: Homework 6, due in class
8/8,9: Homework 7 and 8, due in class


Hefferon, Linear Algebra, and Solutions Manual
Matthews, Elementary Linear Algebra
Payne, A Second Semester of Linear Algebra


Introductory lecture
Row reduction of matrices
Vector spaces and subspaces
Sample Test 1 from 1998 (the last question about linear transformations is inappropriate)
Class notes on canonical forms
    (12 pages in Acrobat reader format; the first 5 have been revised a bit from the ones I handed out in class)