2006 april 21 / e-mail me

Math 104-01, Spring 2006 Schedule

The textbook is Linear Algebra: A Geometric Approach, by Shifrin and Adams.

Lecture Topic Problems
1-2 vectors 1.1: 3ace, 4, 5, 7, 15, 17, 18, 20, 21
3-4 dot product 1.2: 1aeg, 2aeg, 3, 7, 10, 15, 17, 19
hyperplanes 1.3: 1abd, 3abc, 5, 7, 10a, 11
5-7 linear systems, Gaussian elimination 1.4: 1, 3abcdef, 4bc, 6, 7, 8
existence of solutions, rank 1.5: 1, 2ab, 3ab, 4a, 5b, 6, 8, 10, 12, 14
8-10 applications 1.6: 3, 5, 7, 8, 10, 11a, 12b
matrix operations 2.1: 1, 2acf, 6, 7abc, 8, 9, 10abd, 11, 12, 13, 15, 19
11-13 inverse matrices 2.2: 1abd, 2abd, 4acd, 8, 10, 12, 13, 14, 19
transpose 2.3: 1ajk, 2, 3, 4, 5, 6, 7, 9, 13abc, 16, 17a
14 IN-CLASS EXAM
15-16 subspaces of Rⁿ 3.1: 1abceg, 2acd, 4, 6, 8bd, 9, 10, 12, 13ab, 16, 20
17-19 interlude: 3D computer graphics 3D graphics handout; see also OpenGL Red Book Appendix G
linear independence 3.2: 1, 2, 3ab, 4, 5, 6, 7, 11, 12, 13, 14
20-22 basis and dimension 3.3: 1, 2abc, 3, 4ac, 6, 7, 10, 13, 14
four fundamental subspaces 3.4: 1abd, 4, 5, 7, 11, 12, 15, 16 and 3.5: 2
23-25 abstract vector spaces 3.6: 1, 2acd, 3acf, 4, 6ab, 8, 11a, 12, 13bc, 14ab
interlude: norms, relativity
26-28 projection 4.1: 1ab, 3, 4, 6, 8, 9, 11, 13
TAKE-HOME EXAM
orthogonal bases 4.2: 2c, 3, 6, 7ab, 8a, 9a, 11, 12ab
29-31 interlude: Fourier analysis
linear transformations 4.3: 1, 3ac, 6, 7, 9, 10, 11, 13, 15, 17, 20
interlude: isomorphisms isomorphism handout
32-34 change of basis 4.4: 1b, 3, 4, 8, 12, 14, 15, 16, 17, 22
determinants 5.2: 1abc, 2, 4, 5, 7, 9a, 11, 12
35-37 cofactors, Cramer's rule 5.3: 1, 2, 3, 5, 7, 8acf, 12a
characteristic polynomial 6.1: 1adegjp, 2, 4, 8, 10, 11, 13ab, 14a
38-40 diagonalizability 6.2:
complex eigenvalues, Jordan canonical form 7.1:
TAKE-HOME EXAM
41-42 interlude: error-correcting codes see also Wikipedia: Hamming code

Lecture	Topic	Problems
1-2	vectors	1.1: 3ace, 4, 5, 7, 15, 17, 18, 20, 21
3-4	dot product	1.2: 1aeg, 2aeg, 3, 7, 10, 15, 17, 19
	hyperplanes	1.3: 1abd, 3abc, 5, 7, 10a, 11
5-7	linear systems, Gaussian elimination	1.4: 1, 3abcdef, 4bc, 6, 7, 8
	existence of solutions, rank	1.5: 1, 2ab, 3ab, 4a, 5b, 6, 8, 10, 12, 14
8-10	applications	1.6: 3, 5, 7, 8, 10, 11a, 12b
	matrix operations	2.1: 1, 2acf, 6, 7abc, 8, 9, 10abd, 11, 12, 13, 15, 19
11-13	inverse matrices	2.2: 1abd, 2abd, 4acd, 8, 10, 12, 13, 14, 19
	transpose	2.3: 1ajk, 2, 3, 4, 5, 6, 7, 9, 13abc, 16, 17a
14	IN-CLASS EXAM
15-16	subspaces of Rⁿ	3.1: 1abceg, 2acd, 4, 6, 8bd, 9, 10, 12, 13ab, 16, 20
17-19	interlude: 3D computer graphics	3D graphics handout; see also OpenGL Red Book Appendix G
	linear independence	3.2: 1, 2, 3ab, 4, 5, 6, 7, 11, 12, 13, 14
20-22	basis and dimension	3.3: 1, 2abc, 3, 4ac, 6, 7, 10, 13, 14
	four fundamental subspaces	3.4: 1abd, 4, 5, 7, 11, 12, 15, 16 and 3.5: 2
23-25	abstract vector spaces	3.6: 1, 2acd, 3acf, 4, 6ab, 8, 11a, 12, 13bc, 14ab
	interlude: norms, relativity
26-28	projection	4.1: 1ab, 3, 4, 6, 8, 9, 11, 13
	TAKE-HOME EXAM
	orthogonal bases	4.2: 2c, 3, 6, 7ab, 8a, 9a, 11, 12ab
29-31	interlude: Fourier analysis
	linear transformations	4.3: 1, 3ac, 6, 7, 9, 10, 11, 13, 15, 17, 20
	interlude: isomorphisms	isomorphism handout
32-34	change of basis	4.4: 1b, 3, 4, 8, 12, 14, 15, 16, 17, 22
	determinants	5.2: 1abc, 2, 4, 5, 7, 9a, 11, 12
35-37	cofactors, Cramer's rule	5.3: 1, 2, 3, 5, 7, 8acf, 12a
	characteristic polynomial	6.1: 1adegjp, 2, 4, 8, 10, 11, 13ab, 14a
38-40	diagonalizability	6.2:
	complex eigenvalues, Jordan canonical form	7.1:
	TAKE-HOME EXAM
41-42	interlude: error-correcting codes	see also Wikipedia: Hamming code