Math 21a: Applied Linear Algebra

Instructor: Prof. Daniel Ruberman
E-mail: ruberman@brandeis.edu
Office: Goldsmith 310
Phone: 736-3074
Class schedule: Mon., Weds.1-2, Thurs. 1-3 Goldsmith 101.
Office hours (for the first two weeks): Monday 11-12, Wednesday 11-12, Thursday 10-11, 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/

Syllabus

• Chapter 1: Vectors, Matrices, and Linear Systems.
• Chapter 2: Dimensions, Rank, and Linear transformations.
• Chapter 3: Vector spaces.
• Chapter 4: Determinants.
• Chapter 5: Eigenvalues and Eigenvectors.
• Chapter 6: Orthogonality
• Chapter 7: Change of Basis.
• Other topics (time permitting): Quadratic forms, Linear algebra with complex numbers.

Placement

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.

Exams, homework and grading

• There will be 2 midterm exams, 2-3 quizzes, and a 3-hour final exam. The schedule for the in-class exams and quizzes will be posted shortly.
• Homework will be assigned and collected weekly and will be graded and returned to you. You may discuss homework with others, or with me, but you must write up your solutions by yourself.
• Grading formula:
  Homework 10%
  Quizzes 15%
  Mid-term exams 40%
  Final exam 35%

Web links

• Homework assignments will be available from this page. Some of this will be in pdf format, for which you will need the free Acrobat Reader.

Homework assignments.

In addition to the even-numbered homework, which are to be handed in for grading, I have suggested some odd-numbered problems for you to do for practice. (The odd ones are in parentheses.) The solutions to these are in the back of the book, so they won't be graded; you can write the solutions on the same paper as the even ones if you find that to be convenient. Sometimes there will be some problems that I made up; you can find them by clicking the green button. Solutions will be posted after the problems are turned in, and are accessed by clicking the orange buttons.

Handouts

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 w1 + b w2 +c w3 = 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. 218-221)	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 Rn to Rm.
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, 15-19, 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!

Exam schedule and solution sheets

Event	Date	Review sheet	Review solutions	Text sections
Quiz 1	Wednesday, Sept 29	N/A		1.1- 1.4
Quiz 2	Monday, Dec. 6	N/A		Cumulative; emphasis on 6.1, 6.2.
Exam 1	Thursday, Oct. 14, 7-8:30 pm Room 122 Gerstenzang			1.1 - 1.6
Makeup quiz for problems 2 and 5	Thursday, Oct. 28, in class
Exam 2	Monday, Nov. 22, in two sessions. 4-6 pm Room TBA 7-9 pm Room TBA			2.1-5.2 details on review sheet
Final Review	Mon., Dec. 13, 12-1:30 Goldsmith 100
Final	Wednesday, Dec. 15 9:15-12:15 (block F) Room 122 Gerstenzang			Through 8.3

Academic Honesty

You are expected to be honest in all of your academic work. The University policy on academic honesty is distributed annually as a section of the Rights and Responsibilities handbook. Instances of alleged dishonesty will be forwarded to the Office of Campus Life for possible referral to the Student Judicial System. Potential sanctions include failure in the course and suspension from the University. If you have any questions about my expectations, please ask me.

Last updated: Dec. 11, 2004
URL: http://www.brandeis.edu/~ruberman/math21af04/math21af04.html