Instructor: Willard Miller
Office: Vincent Hall 513
Office Hours: 11:15-12:05 MW, 9:05-9:55 F, or by appointment
Phone: 612-624-7379
miller@ima.umn.edu, miller@math.umn.edu

Prerequisites: Previous exposure to linear algebra: determinants and Cramer's rule.

Textbook: G. Strang , Linear Algebra and Its Applications, 3rd Ed., Brooks/Cole (Thomson Learning), 1988.

Class Description: A foundation course in linear algebra, with applications. Topics include: linear transformations, vector spaces, matrix calculus, solutions of systems of linear equations, determinants, orthogonality, LDU decompositions, SVD decompositions, canonical forms. Applications include: Gram-Schmidt process, least-squares approximations, the Fast Fourier transform (FFT), etc. This material is basic, both for the understanding of the theory of linear algebra and for numerical computation.

Software: MATLAB (by The Mathworks, Inc.) is ideal, but not required. No previous exposure is expected.

Policies:

1. Eight homework assignments [NO late homework will be accepted without good excuses].
2. Two Midterms plus the Final Exam [NO laptops. Standard calculator is OK. NO makeup tests without rigorous emergency reasons. Athletes please present "Proofs of Activities" in advance].
3. Grading Policy: Homework (20%), Two Midterms (40%), Final Exam (40%)

Content and Style: Will try to cover (inclusively) up to Chapter 6 (out of 7 chapters). Approximately two to three weeks for each chapter. Homework assignments are mainly from the textbook, which has many well designed exercise problems. The theory will predominate, but there will be considerable attention to applications in other fields.

Student Conduct: Statement on Scholastic Conduct: Each student should read the college bulletin for the definitions and possible penalties for scholastic dishonesty. Students suspected of cheating will be reported to the Scholastic Conduct Committee.

Paper Grader: Hazem Hamdan
Office: Vincent Hall 522
Office Hours: 12:20-1:20 MW,
Phone: 612-624-4143
hamdan@math.umn.edu,

Introduction to MATLAB (courtesy of Professor Peter Olver) Postscript file  PDF file

Math 4242, Section 10  Spring 2003    Tentative Syllabus 

		Week	Topic	Section	HW due
W	JAN 22	1	Introduction and Linear equations	1.1-1.2
F	JAN 24	1	Introduction to Gaussian Elimination	1.3
M	JAN 27	2	Matrix Notation and Multiplication	1.4
W	JAN 29	2	Triangular Factorization	1.5
F	JAN 31	2	Inverses and Transposes	1.6
M	FEB 3	3	Inverses and Transposes/Applications	1.6/1.7	1
W	FEB 5	3	Applications	1.7
F	FEB 7	3	Vector Spaces and Subspaces	2.1
M	FEB 10	4	m Equations in n Unknowns	2.2
W	FEB 12	4	Linear Independence, Basis, & Dimension	2.3	2
F	FEB 14	4	Row, Column, and Null Spaces	2.4
M	FEB 17	5	Row, Column, and Null Spaces	2.4
W	FEB 19	5	Linear Transformations	2.6
F	FEB 21	5	Orthogonal Subspaces	3.1
M	FEB 24	6	Orthogonal Subspaces	3.1	3
W	FEB 26	6	Inner products, Projections	3.2
F	FEB 28	6	Inner products, Projections	3.2
M	MAR 3	7	Least Squares Approximations	3.3
W	MAR 5	7	Orthogonal Bases, Gram-Schmidt Orthogonalization	3.4	4
F	MAR 7	7	Orthogonal Bases, Gram-Schmidt Orthogonalization	3.4
M	MAR 10	8	Fast Fourier Transform	3.5
W	MAR 12	8	Review	3.6
F	MAR 14	8	Midterm I: Chapters 1-3
			Spring Break
M	MAR 24	9	Properties of the Determinant	4.1-4.2
W	MAR 26	9	Formulas for the Determinant	4.3
F	MAR 28	9	Applications of Determinants	4.4
M	MAR 31	10	Introduction to Eigenvalues	5.1	5
W	APR 2	10	Matrix Diagonalization	5.2
F	APR 4	10	Powers of Matrices	5.3
M	APR 7	11	Powers of Matrices	5.3
W	APR 9	11	Matrix Exponential	5.4
F	APR 11	11	Matrix Exponential	5.4
M	APR 14	12	Complex Matrices	5.5	6
W	APR 16	12	Review
F	APR 18	12	Midterm II: Chapter 4, Sections 5.1-5.4
M	APR 21	13	Complex Matrices	5.5
W	APR 23	13	Similarity Transformations	5.6
F	APR 25	13	Similarity Transformations	5.6
M	APR 28	14	Extreme Values and Positive Definite Matrices	6.1	7
W	APR 30	14	Tests for Positive Definiteness	6.2
F	MAY 2	14	Tests for Positive Definiteness	6.2
M	MAY 5	15	Indefinite Matrices	6.3
W	MAY 7	15	The Singular Value Decomposition (SVD)	Appendix A	8
F	MAY 9	15	Review
TU	MAY 13		Final Exam, 8:00 -10:00 am, VH2

HW1 :  Due in class: Monday, February 3
1.2.3, 1.2.5 (page 10); 1.3.1, 1.3.5(page16); 1.4.1, 1.4.5, 1.4.22 (pages 27-30), 1.5.4, 1.5.5 (page 39)

HW2:  Due in class: Wednesday, February 12
1.5.9, 1.5.11(page 40); 1.6.3, 1.6.8, 1.6.19 (pages 49-51); 2.1.3, 2.1.5 (page 69),  2.2.3, 2.2.7 (pages 77-78);

HW3 Due in class: Monday, February 24
2.3.1, 2.3.5, 2.3.16 (pages 87-88); 2.4.3(page 99), 2.6.7, 2.6.8, 2.6.18(pages 125-126)

HW4 Due in class: Wednesday, March 5
3.1.1,3.1.5 (pages 141-142);  3.2.3, 3.2.8(page 151); 3.3.3,  3.3.5, 3.3.7, 3.3.12,  3.3.26 (pages 163-165).

HW5 Due in class: Monday, March 31
3.4.2,3.4.6, 3.4.13, 3.4.17(pages 180-181),4.2.1,4.2.4,4.2.6(page 219), 4.3.5, 4.3.6, 4.3.7(pages 228-229),4.4.5(page 238)

HW6  Due in class: Monday, April 14
 5.1.1,5.1.2,5.1.3(pages 251-252), 5.2.2, 5.2.7, 5.2.10(pages 260-261),5.3.1, 5.3.9(pages 272-273),5.4.1, 5.4.2(page 286)

Solutions to HW6      PDF

HW7 Due in class: Monday, April 28
5.5.1, 5.5.7, 5.5.8(pages 301-302),5.6.3,5.6.5 5.6.13(pages 315-316)

HW8 Due in class: Wednesday, May 7
6.1.2, 6.1.4(page 328), 6.2.1, 6.2.2,6.2.4,6.2.7,6.2.12(page 337),6.3.2, 6.3.11(pages 345-346)