Mathematics 336

Cornell University-->

Mathematics 336, Spring 2008

Applicable Algebra

Announcements

Course announcements will be posted here from time to time. Please check regularly.

Lecture

MWF 9:05-9:55A Malott 406

L. Billera
office: Malott 501, 5-6369
email: billera AT math DOT cornell DOT edu
office hours week of 5/12: Monday, May 12, 2:00-4:00; Wednesday, May 14, 9:45-11:45

Teaching assistant

Megan Owen
office: 657 Rhodes Hall
email: mao29 AT cornell DOT edu
office hours: Tuesday, May 6, 1-2 PM; Thursday, May 8, 1-2 PM; Monday, May 12, 11AM-Noon. Also, by appointment. All in 657 Rhodes Hall.


Course description

This is an introduction to abstract algebra (groups, rings, and fields) with emphasis on how these ideas are applied. Applications will include basic RSA cryptography and error-correcting codes. For a more theoretical treatment, see Math 432. The prerequisite is basic linear algebra as taught in Math 221, 223-4, 231 or 294.

See the schedule of lectures for the specific topics we will cover.

Text

Lindsay Childs, A Concrete Introduction to Higher Algebra, 2nd ed., Springer, 1995. The author has provided a list of errata. The text will be supplemented by the RSA paper on cryptography and by notes on error-correcting codes written by Sarah Spence.

The text and supplementary material are essential parts of the course. Please plan on reading them thoroughly; this is not the kind of course where you can simply look at the examples and try to imitate them when you do the homework.

Exams

There will be two in-class exams (prelims) and a final.

Prelim 1: Friday, February 22, in class.
Prelim 2: Friday, April 4, in class.
Final exam: Wednesday, May 14, 7:00-9:30 PM; Malott 406..

Homework

The homework is the most important part of the course. Most of your learning will take place while doing it.

There will be weekly homework assignments. These are due on Fridays (except for prelim weeks) and are to be turned in in class. We will not accept late homework except in very unusual circumstances. We will, however, drop the lowest homework grade.

You should start attempting the problems as soon as possible after the material is presented in lecture. Please don't save it all for the night before it is due.

Solutions should be written carefully, using good English, complete sentences, and adequate detail. Some of these solutions will be proofs. A good guideline here is that you should write proofs the way you would like to see them in your textbook.

Working together

We have no objection in principle to collaboration on the homework, provided that it is done in a way that maximizes the benefit of the homework to all people involved. (One person simply telling another how to do a problem totally defeats the purpose of the problem.) It is our opinion that you get maximum benefit from a homework problem if you work hard on it alone before combining your ideas with someone else's. In any case, the paper that you turn in with your name on it should represent your own solutions, written in your own words, regardless of whether you arrived at some of those solutions in collaboration with others.

In particular, you may not simply copy someone else's homework and turn it in as your own. This will be treated as a violation of Cornell's Academic Integrity Code. Similarly, copying solutions that you might find on the web or from some other source is illegal.

Academic integrity

We take academic integrity very seriously and will follow university procedures in all cases of suspected cheating. Details are spelled out in the Academic Integrity Code, cited in the previous paragraph. In an effort to prevent one common form of cheating, we will xerox a random sample of exam books before returning them.

Grading

At the end of the semester we will compute a weighted average of the numerical grades and convert this to a letter grade according to our judgment as to what is appropriate. The weighting scheme is approximately as follows: homework (20%), prelims (45%), and the final (35%). There is no pre-ordained curve. The grades for extra credit homework problems will be accumulated separately and used to make adjustments to the final grades.

We rarely give incompletes, and then only to people who have a passing grade on a substantial part of the course but have a good reason (usually medical) for being unable to complete the requirements.

Assignments

Assignment 1, due Friday, January 25
Assignment 2, due Friday, February 1
Assignment 3, due Friday, February 8
Assignment 4, due Friday, February 15
Assignment 5, due Friday, February 29
Assignment 6, due Friday, March 7
Assignment 7, due Friday, March 14
Assignment 8, due Friday, March 28
Assignment 9, due Friday, April 11
Assignment 10, due Friday, April 18
Assignment 11, due Friday, April 25
Assignment 12, due Friday, May 2
Assignment 13, due never

Partial Solutions

Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
Assignment 6
Assignment 7
Assignment 8
Assignment 9
Assignment 10
Assignment 11
Assignment 12

Handouts

Extra help and other useful links

Last modified: May 6, 2008