2009 March 19 / jj|d|a|v|i|s|@|c|a|r|l|e|t|o|n|.|e|d|u
Carleton College Math 232, Winter 2009, Prof. Joshua R. Davis
In my view, linear algebra is the most important math course. We begin with a simple idea — solving systems of linear equations — but it turns out that this idea pervades mathematics! Just about every higher math course uses linear algebra, and just about every mathematician uses it every day. Others who use math (e.g. physicists, computer scientists) also do a lot of linear algebra. The subject has numerous practical applications — web search engines, error-correcting communications protocols, cryptography, computer graphics, relativity, quantum mechanics, balancing chemical reactions, structural geology, and more. Because so many people use linear algebra, it can be seen from many different viewpoints — matrix/tensor algebra, intersecting hyperplanes, abstract vector spaces, etc. So there is a lot to say about the simple idea of solving systems of linear equations.
The basic course materials are
Our class meets in CMC 206 during period 2A (MW 9:50AM-11:00AM, F 9:40AM-10:40AM). Here's how you get in contact with me:
Dr. Joshua R. Davis (call me Josh if you like)
E-mail: jj|d|a|v|i|s|@|c|a|r|l|e|t|o|n|.|e|d|u
Office: CMC 327, x4482
Office hours: Sun 12-1, Tue 10-11, Wed 3-4, and Thu 3-4. You can also make an appointment; simply pick a free time from my weekly schedule and e-mail me. You can also talk to me after class.
Final grades (A, B, C, etc.) are assigned according to an approximate curving process. By this I mean that there are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades. The following elements contribute to the final grade.
You are encouraged to work with others on all assignments. Work together to figure out the problems, and then write them up separately, in your own words. You may not copy someone else's work or allow them to copy yours.
Homework is graded for correctness and for presentation. Depending on time constraints, perhaps only a subset of the work is graded; in order to ensure full credit, do all of the assigned problems. Make your paper easy to grade. The problems must be answered in the order they were assigned. Do not write them in multiple columns; just use one column, going down the page. Clearly write each problem's number on the left side of the page. If your paper is messy or disorganized from revisions or erasures, then you may need to recopy it.
How much work should you show? The answer is simple: Write your solutions as if the intended audience is your fellow students. By doing so, you show enough detail that your grader can ascertain whether you yourself understand the material. Your solutions should also be self-explanatory; the grader should not have to refer to the book, to determine whether your solution is correct. In short, if a classmate were to read one of your solutions, then she or he should be able to understand what the problem was and how you solved it.
Staple your week's worth of solutions into a single packet, in the order they were assigned. Packets that are not stapled are unacceptable. I will not accept packets that are not stapled. Staple your packet. Your packet? Staple it.
During the term, you have one free pass to hand in an assignment late. Here is how you activate it. Instead of handing in your assignment, send me e-mail declaring that you are using your late pass and proposing a new due date. If the due date is extended only a couple of days, then no explanation is necessary; if you need longer, then convince me. Use your free pass wisely. Otherwise, no late assignments are accepted, except in extreme circumstances that are truly beyond the student's control.
If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class, so that we can make arrangements. You may want to visit the dean's Disability Services/Resources page first.
Problems marked in bold must be handed in. Do the other problems, but do not hand them in. Remember that this quantity of problems is the minimum that I recommend to pass the course.
| Day | Topic | Reading | Problems | Due Day |
|---|---|---|---|---|
| 01 M 1/05 | solving linear systems | 1.1 | 1.1 #02, 04, 10, 15, 18, 19, 22, 28, 29, 37, 40 | 04 |
| 02 W 1/07 | row reduction | 1.2 | 1.2 #09, 10, 18, 24, 29, 32, 34, 36, 42 | 04 |
| 03 F 1/09 | matrix algebra I | 1.3 | 1.3 #04, 05, 07, 14, 18, 24, 28, 29, 30, 47, 48, 51, 54, 58 | 07 |
| 04 M 1/12 | linear transformations | 2.1 | 2.1 #02, 03, 05, 07, 18, 20, 32, 35, 37, 44, 48 | 07 |
| 05 W 1/14 | geometry of transformations | 2.2 | 2.2 #03, 05, 14, 16, 24, 27, 29, 33, 40, 42 | 07 |
| 06 F 1/16 | inverse transformations | 2.3 | 2.3 #04, 19, 28, 34, 40, 41, 45, 54 | 10 |
| 07 M 1/19 | matrix algebra II | 2.4 | 2.4 #07, 11, 12, 16, 23, 28, 35ab, 39, 44, 57, 72, 84, 86 | 10 |
| 08 W 1/21 | image, kernel | 3.1 | 3.1 #05, 06, 18, 20, 33, 35, 36, 43, 44, 45, 48 | 10 |
| 09 F 1/23 | span, independence | 3.2 | 3.2 #06, 15, 19, 24, 30, 36, 37, 39, 42, 46, 53, 54 | 13 |
| 10 M 1/26 | basis, dimension | 3.3 | 3.3 #16, 23, 32, 35, 43, 44, 47, 52, 61, 62, 63 | 13 |
| 11 W 1/28 | EXAM 1 (DAYS 01-08, SECTIONS 1.1-3.1) | |||
| 12 F 1/30 | coordinates | 3.4 | 3.4 #08, 17, 25, 29, 40, 49, 52, 57, 61, 66, 73, 74, 76 | 16 |
| 13 M 2/02 | vector spaces | 4.1 | 4.1 #03, 06, 19, 22, 26, 39, 44, 45, 47, 54 | 16 |
| 14 W 2/04 | linear transformations | 4.2 | 4.2 #09, 17, 26, 33, 48, 55, 62, 72, 74, 77, 78, 81 | 16 |
| 15 F 2/06 | matrices for transformations | 4.3 | 4.3 #02, 05, 15, 16, 19, 54, 59, 70 | 18 |
| -- M 2/09 | MIDTERM BREAK | |||
| 16 W 2/11 | orthonormality | 5.1 | 5.1 #06, 12, 15, 18, 27, 37, 42, 45 | 18 |
| 17 F 2/13 | Gram-Schmidt | 5.2 (omit QR) | 5.2 #14, 29, 33 | 21 |
| 18 M 2/16 | orthogonal transformations | 5.3 | 5.3 #06, 09, 10, 15, 16, 27, 30, 31, 38, 42, 52, 53 | 21 |
| 19 W 2/18 | least squares | 5.4 | 5.4 #04, 07, 09, 20, 30, 36, 39 | 21 |
| 20 F 2/20 | inner products | 5.5 | 5.5 #01, 06, 09, 18, 20, 26 | 24 |
| 21 M 2/23 | determinants | 6.1 | EXAM 2 IN PROGRESS | |
| properties of determinants | 6.2 | EXAM 2 IN PROGRESS | ||
| 22 W 2/25 | geometry of determinants | 6.3 (until Cramer) | 6.1 #07, 28, 38, 43, 44, 49 6.2 #05, 23, 37, 41 6.3 #04, 14, 18, 19, 20, 46 | 24 |
| intro to eigenstuff | 7.1 | 7.1 #01, 02, 03, 04, 05, 06, 07, 08, 18, 19, 34 | 24 | |
| 23 F 2/27 | computing eigenvalues | 7.2 | 7.2 #12, 22, 29, 34, 43 | 27 |
| 24 M 3/02 | computing eigenvectors | 7.3 | 7.3 #09, 20, 28, 31, 37, 38, 44, 46ab | 27 |
| 25 W 3/04 | diagonalization | 7.4 | 7.4 #16, 26, 59 232.jordan.pdf #01, 02, 03 | 27 |
| 26 F 3/06 | complex eigenvalues | 7.5 | 7.5 #19, 25, 32, 36 | 28 |
| 27 M 3/09 | spectral theorem | 8.1 | 8.1 #11, 12, 23, 24, 36 | never |
| 28 W 3/11 | Hamming code | |||
| -- Sa 3/14 | FINAL EXAM (3:30-6:00) | |||