Number Theory and Cryptography

Fall 2003
Mathematics V3020 section 001
M, W 10:35-11:50 am
520 Mathematics Building
http://www.math.columbia.edu/~glass/fall03/

Darren Glass
Office: 516 Mathematics Building
Office Phone: (212) 854-5135
glass@math.columbia.edu

The best way to get in touch with me is by email. I am an email addict.

Announcements

Check this part of the website regularly for announcements.

Course Information

Content

Number Theory is, in my rather biased opinion, the most beautiful area of mathematics. It is one of the oldest area of mathematics, and in recent years a great number of applications to cryptography (and other things) have been found. Some of the topics will include: divisbility, modular arithmetic, prime numbers, public key cryptography, and quadratic reciprocity.

A list of what I have done each day can be found at this website

Textbook

A Friendly Introduction to Number Theory (Second Edition - Joseph Silverman. (available at Amazon and ADDALL as well as your local bookstore) will be our primary textbook. I will supplement it with other material, and will post those references here as we go along.

I often find it helpful to look at multiple books to get a variety of viewpoints on the same material. If you wish to do this, some of the books I reccomend are:

Office Hours and Other Help

Number Theory is not an easy subject, and it is almost certain that you will need help during the semester. Please do not hesitate to take advantage of the various forms of help that we provide. The Columbia Help Room is Mathematics 406. I will be there on Wednesdays from 3-4, but you may go there anytime it is open to have your questions answered.

The TA for this course is Alex Kontorovich (alexk@math.columbia.edu). He will be in the Columbia help room on Mondays and Wednesdays from 5-6 and Tuesdays from 10-11.

I will be in my office (516 Mathematics) on Mondays from 1:30-3 and by appointment.

Grading

25% - Midterm (Oct. 22 in-class)
35% - Final (TBA)
40% - Homework and Class Participation

Midterm

This exam will be in class, closed book, etc. The exam will be on October 22nd in class. I chose this date in part to avoid conflicting with any religious holidays, etc. If there is going to be a conflict you must let me know as soon as you do. No makeup exams will be given without prior arrangement.


Final

The final exam will be a three hour cumulative exam which is scheduled for Monday December 15th from 9am-noon. Please make any travel plans accordingly.

Homework

Homework will be assigned roughly once a week. You are encouraged to discuss homework with each other, but you must turn in your own work. If you aren't sure exactly where the boundary lies, please ask me rather than make assumptions. Late homework will be penalized unless prior permission has been obtained from the professor. All homework will be graded not only on correctness, but also on how well you communicate and explain your answers. Mathematics is a process, not a final answer, and your work should reflect that. For many of you, this will be the first course where you are writing proofs. Learning to do this well is a slow and difficult process. Some hints (written by Allison Pacelli) which you may find helpful are here. A more detailed introduction to writing for math courses can be found on Annalisa Crannell's webpage

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