2008 June 4 / E-Mail Me

Carleton College Math 232, Spring 2008, 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

- Schedule, with reading assignments and homework exercises
*Linear Algebra With Applications*, 3rd edition, by Bretscher. This is currently the standard Carleton linear algebra textbook. Other editions of the text are not acceptable.- Sometimes we'll do exercises using the mathematics software
*Mathematica*. Here are some instructions and notebooks. Remember to right-click (or control-click) on a notebook link to save the notebook to your computer; then open the file in*Mathematica*.- Getting Started With
*Mathematica* - 232.visualtransf.nb is for visualizing linear transformations.
- 232.graphs.nb is for analyzing graphs. It also makes a first pass at describing how Google's PageRank algorithm works.
- 232.coordchange.nb shows how to construct new rock deformations from old ones.
- 232.hamming.nb describes the (7, 4) Hamming code.

- Getting Started With
- 2008s232.exam1q.pdf is a bunch of sample questions to help you study.
- 2008s232.exam1.pdf is our Exam 1. Percentiles: 75th = 87, 50th = 76, 25th = 73.5.
- 2008s232.exam1a.pdf is the answer key to our Exam 1.
- 232.jordan.pdf describes Jordan decomposition.
- 2008s232.exam2.pdf is our Exam 2. Percentiles: 75th = 81, 50th = 76.5, 25th = 65.
- 2008s232.exam2a.pdf is the answer key to our Exam 2.
- 2008s232.exam3.pdf is our Final Exam. Percentiles: 75th = 89, 50th = 82, 25th = 65.

Our class meets in CMC 319 during period 4A (MW 12:30PM-1:40PM, F 1:10PM-2:10PM). Here's how you get in contact with me:

Dr. Joshua R. Davis (call me Josh if you like)

E-mail: See here

Office: CMC 221, x4366

Office hours: Mon 1:40-2:40, Wed 3:30-4:30, Thu 8:30-9:30, and Thu 1:10-2:10. 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.

- Participation: Each class session covers one or two sections of the textbook, which
*you are expected to read before class*. Class will be conducted on the assumption that you have already read and thought about the sections. Attendance is mandatory; furthermore, you are expected to participate actively in group work, discussion, individual exercises, etc. Class participation influences final term grades in borderline cases. You are also required to attend office hours at least once before the first exam. - Homework: In this course, most of your learning will take place while doing homework. The homework problems are listed on the schedule. They will be collected once a week. I strongly encourage you to do the homework promptly, rather than waiting for the night before it is due. I may also assign several small writing assignments. Altogether, homework counts for 25% of your grade.
- Exam 1: This is an in-class exam worth 25% of your grade.
- Exam 2: This is a take-home exam worth 25% of your grade.
- Final Exam: Self-scheduled final exams are not allowed. The final exam is entirely cumulative and worth 25% of your 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. *Staple* each week's assignment into a single packet.

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.

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.

I want all of my students to work hard, learn a lot of math, and earn a good grade. Here are my recommendations:

- Don't wait until an exam to study. Keep up with the work throughout the term, always going back to understand problems you've missed. The material in a math class tends to build up quickly. If you don't understand one day's material, then you won't understand the next day's either, and you soon fall behind. If you sense yourself slipping, come talk to me immediately.
- Your greatest resource is your fellow students. Work together as much as possible.
- Do as many problems as possible. This is the best way to study math, because doing problems forces you to learn about the concepts actively.