Instructor: Prof. Daniel Ruberman
Email: ruberman@brandeis.edu
Office: Goldsmith 310
Phone: 7363074
Class schedule: Mon., Weds.12, Thurs. 13 Goldsmith 101.
Office hours (for the first two weeks): Monday 1112, Wednesday 1112, Thursday 1011, and by appointment. My schedule for fall 2004.
Textbook: Linear Algebra (3d edition) by Fraleigh and Beauregard.
Class home page (this page!): www.brandeis.edu/~ruberman/math21af04/math21af04.html
My home page: people.brandeis.edu/~ruberman/
There are two other linear algebra courses at Brandeis, Math 15 and Math 22a, and choosing correctly is important. Roughly speaking, the topics in covered in Math 22 are similar to those in this course, but the treatment is more theoretical and somewhat faster paced. The two courses have the same schedule, to simplify changing between them. Math 15 is a much less theoretical course than either 21 or 22 (you won't do very many proofs) and also covers less ground. You are strongly advised to discuss your placement with me and/or Professor Schwarz (Math 22), or one of the department's undergraduate advisors, Professors Monsky and Levine.
Sometimes I will write up some additional material, which you can download by clicking on the title.
Title 
Reading on functions 
Functions and linear transformations 
Classwork on reflections/rotations 
Dynamics of Cats/Mice 
Mathematica graphs 
No.  Date due  Sections to read  Problems  Solutions 

1

Thursday Sept. 9 
1.1

2, (3), 6, (11), 12, (13), 16, (23), 24, 26, 28, (31), 34, (35), 36, (41), 42.


2  Wednesday Sept. 15 
1.2

(1), 4, (7), 8, (13), 16, 22, (31), 34, 42c, 43, 45  
3

Thursday
Sept. 23 
1.3
1.4 
(7), 14, 18, 20, (23), 24, 32, (35), 40, 42, 43 (3), 6, (7), (15), 16, (21), 24 (more next HW) 

4

Monday
Oct. 4 
1.4
1.5 
(25), 28, (39), 40, 42, (43), 48, 53 4, 6, (7),(9), 12, 14, 16, 24, 26, 30, 35. 

5

Wednesday Oct. 13 
1.6

(1), 2, 10, 18, (19), (23), 24, 26, (31), 32, 44, 45.  
6

Thursday Oct. 21 
2.1
2.2 
(9), 10, 12, 20, 26, (27), 30 [Your proof might start: "Suppose there is a linear relation a w_{1} + b w_{2} +c w_{3} = 0 ...."] (31), 36. 2, (3), (9), 10, 12, 14, (15), 18, (19), 20. 

*

Monday Oct. 25  Reading on functions 


**

Wednesday Oct. 27  Review 1.6  Subspace/Basis Problems  
7

Thursday Oct. 28 
2.3
3.4 (pp. 218221) 
2, (3), (5), 6, 8, 16, (17), (19), 20, (25), 28, 31. 37, 39, 46. (For these problems, pretend that the linear transformation T goes from R^{n} to R^{m}. 

8

Thursday Nov. 4  4.1 4.2 
8, (9), (15), 16, (21), 22, (25), 28, (37), 53, 54, (56; optional but you should do it!) (7), 8, 1519, 31, 32 

9

Thursday Nov. 11  4.3 4.4 5.1 
4, 6, 14 (use exercise 35 of section 1.5), (15), 36 (think about how we find inverses). (5), 8, (11), 18, (19), (21), 22, (23). (3), 4, 8, (13), 24, (25) [more on HW 10]. 

10

Thursday Nov. 18  5.1
5.2 
27, 30, 32, 36.
(5), 6, 10, (11), 14, (15), 16, 21, 25. 

11

Thursday Dec. 2  6.1
6.2 
(3), 6, 8 [ie find a basis for the orthogonal complement], (11), (17), 22, 24, 26, 28.
(3), 6, 9, 10, 12, 16, (19), 20, 22, 27, 29, 30, 31. 

12

Thursday Dec . 9  6.3
8.1 8.3 (to mid p.435) 
(3), (9), 10, 12, 14, (15), 20, 21, 22, 23, 25.
(3), 4 [just find A], (5), 10, (13), 16. (3), 6, 8, (11), 12. 


That's  all  folks! 