Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

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

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

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).

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

- 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.

- 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.