Math 341, Linear Algebra - Fall 2007

Nigel Boston

Contact Information

303 Van Vleck Hall.

Telephone: 263-4753.

E-mail: boston@math.wisc.edu

Homepage

Office Hours: T 2:30-3:30, W 9:30-10:30, R 11-12, or by appointment.

Text

Linear Algebra, Gateway to Mathematics, by Robert Messer

Course Overview

Background and Goals: This course is part of a group of transitional courses for math majors. These courses are meant to provide instruction on how to write and understand proofs, while covering similar topics as Math 340. It is also recommended for those students in the sciences and engineering who want to have a more theoretical understanding of linear algebra. After completing Math 341, students should be prepared to take proof-based courses at the 5XX level. This course is designated a "writing-intensive" course.

Alternatives: Math 340 for less theoretical students, Math 375 for Honors students as part of the calculus sequence.

Content coverage:

Definition, examples and basic facts in vector spaces
Linear systems
Linear combination, linear independence, basis and dimension, coordinates
Inner product spaces
Matrix algebra and inverse
Linear transformation, kernel, change of basis, isomorphism
Determinants
Eigenvalues and eigenvectors

Grading Policy

Homework will be set every Thursday and due the following Thursday. You are encouraged to discuss the exercises with your classmates but the work you hand in should be your own. You will be expected to read the sections of the book to be covered in advance of class. Homeworks will consist of some with answers at the back of the book and others that will be graded.

Since this is a writing-intensive course, writing of proofs will be assigned for homework and two homeworks will be handed back for rewriting. There will be a midterm during the semester. I do not intend to give make-up exams.

Homeworks will count for 35% of the final grade, the midterm for 25%, and the final exam for 40%.

The midterm will be held on Tuesday, October 23, in class. The final will be on Tuesday, December 18, at 12:25pm (in the usual room, B119 Van Vleck).

Sections

Main Lecture: TR 1-2:15 B119 VV.

Course Schedule

Tues, Sept 4: Course logistics, overview and motivation. Introduced sets and vector spaces. 1.1-1.3.
Thurs, Sept 6: More properties of vector spaces, subtraction and cancellation, Euclidean spaces. 1.3-1.5.
Tues, Sept 11: Matrices and function spaces. 1.6-1.7.
Thurs, Sept 13: Suspaces and lines and planes. 1.8-1.9.
Tues, Sept 18: Introduction to Gaussian elimination. 2.1-2.2.
Thurs, Sept 20: More on Gaussian elimination. 2.2.
Tues, Sept 25: Solving linear systems and applications. 2.3-2.4.
Thurs, Sept 27: More on applications, linear combinations. 2.4-3.1.
Tues, Oct 2: Spanning and linear independence. 3.2-3.3.
Thurs, Oct 4: More linear independence, basis. 3.3-3.4.
Tues, Oct 9: Dimension. 3.5.
Thurs, Oct 11: Coordinates. 3.6.
Tues, Oct 16: Inner Product Spaces. 4.1.
Thurs, Oct 18: Review for midterm.
Tues, Oct 23: Midterm.
Thurs, Oct 25: Geometry in Euclidean Spaces, Cauchy-Schwarz. 4.2-4.3.
Tues, Oct 30: Returned midterm, orthogonality. 4.4.
Thurs, Nov 1: Fourier analysis, matrix algebra. 4.5-5.1.
Tues, Nov 6: Matrix inverses. 5.2.
Thurs, Nov 8: Linear functions, compositions and inverses, matrix of a linear function. 6.1-6.3.
Tues, Nov 13: Matrices of compositions and inverses, change of basis. 6.4-6.5.
Thurs, Nov 15: Image and kernel, rank and nullity. 6.6-6.7.
Tues, Nov 20: Isomorphism. 6.8.
Tues, Nov 27: Induction, determinants. 7.1-7.2.
Thurs, Nov 29: Properties of determinants, Cramer's rule. 7.3-7.4.
Tues, Dec 4: More Cramer's rule. 7.4.
Thurs, Dec 6: Eigenvalues, eigenvectors, similarity. 8.1-8.2.
Tues, Dec 11: Diagonalization and begin review. 8.3.
Thurs, Dec 13: Review.

Homework Assignments

Due Thurs, Sept 13: 1.1, 1,7; 1.2 7,9; 1.3 5,6; 1.4 11.
Due Thurs, Sept 20: 1.5, 14,15: 1.6 8; 1.7 1,8; 1.8 19.
Due Thurs, Sept 27: 2.1 1a,c 2a,c 3a,c; 2.2 5b,d.
Due Thurs, Oct 4: 2.3 3, 6a,b, 9; 2.4 4, 6, 8; 2 review 13.
Due Thurs, Oct 11: 3.1 2,12; 3.2 4,12; 3.3 6,12; 3.4 8.
Due Thurs, Oct 18: 3.4 13; 3.5 5,14,20; 3.6 3,6.
Due Thurs, Oct 25: Revise for midterm on Oct 23, i.e. no set HW.
Due Thurs, Nov 1: 4.1 11,18; 4.2 5,14; 4.3 6,10.
Due Thurs, Nov 8: 4.4 6,17; 4.5 6,8; 5.1 5,7.
Due Thurs, Nov 15: 5.2 3; 6.1 3,18; 6.2 4,13; 6.3 2.
Due Thurs, Nov 29: writing assignment - rewrite midterm solutions and 3.5 14 and 4.5 8 in your own words.
Due Thurs, Dec 6: 6.4 5; 6.5 2; 6.6 9; 6.7 3; 6.8 9; 7.1 9.
Due Thurs, Dec 13: 7.2 2,7; 7.3 9; 7.4 7; 8.1 8; 8.2 4.