Mathematics 3360

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Mathematics 3360, Spring 2009

Applicable Algebra

Announcements

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

Lectures

Lec 1: MWF 9:05AM - 9:55AM, Malott 207
Lec 2: MWF 10:10AM - 11:00AM Malott 207

L. Billera
office: Malott 501, 5-6369
email: billera AT math DOT cornell DOT edu
office hours: Monday, 3:45-4:45; Wednesday 4:00-5:00; or by appointment

Teaching assistants

Margarita Amchislavska
office: 120 Malott Hall
email: margo1729 AT math DOT cornell DOT edu
office hours: Wednesday, 2:00-4:00, Malott 218

Mingzhong Cai
office: 120 Malott Hall
email: yiyang AT math DOT cornell DOT edu
office hours: Tuesday-Thursday, 1:45-2:45, Malott 218


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. 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., 1995.

The author has provided a list of errata.

Note: There is a recently released 3rd edition to Childs' textbook. We will be using the old 2nd edition.

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 evening exams (prelims) and a final.

Prelim 1: Tuesday, February 17, 7:30 - 9:00 PM, Goldwin Smith G64.
Prelim 2: Thursday, April 9, 7:30 - 9:00 PM, Rockefeller 203. (Note change from original date and room.)
Final exam: Mon, May 11, 2:00 - 4:30 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.

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 23
Assignment 2, due Friday, January 30
Assignment 3, due Friday, February 6
Assignment 4, due Friday, February 13
Assignment 5, due Friday, February 27
Assignment 6, due Friday, March 6
Assignment 7, due Friday, March 13
Assignment 8, due Friday, March 27
Assignment 9, due Friday, April 3
Assignment 10, due Friday, April 17
Assignment 11, due Friday, April 24
Assignment 12, due Friday, May 1
Assignment 13, due never

  • Homework solutions will be posted some time after they are due.

    Handouts

    Extra help and other useful links

    Last modified: April 27, 2009