General Information
| Meeting Time |
Tues.-Thurs., 11:00 - 12:15 |
| Location | 380-380X (basement, Math building 380)
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| Professor |
Ben Brubaker (brubaker@math.stanford.edu)
Office: 382-F (2nd floor, Math building 380)
Office Phone: 3-4507
Office Hours: Tu We 2-3:30, or by appointment. |
Course
Assistant |
Andy Schultz (aschultz@math.stanford.edu)
Office: 380-G (Basement, Math building)
Office Hours: Monday 1:30-3:30 |
| Textbook | A Course in Number Theory and Cryptography, by N. Koblitz |
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Grade
Breakdown | 2 Midterms -- 20 % each, Final Project -- 30%, Homework -- 30% |
Course
Content | We'll try to make it through many of the topics in Koblitz' book. The first several weeks will focus more on number theory tools which demonstrate the vulnerability of simple cryptosystems. Then we'll develop the basic theory of finite fields for two weeks. In the second half of the course, we'll introduce public key cryptography and survey examples including RSA and elliptic curve cryptosystems. We will do some minor programming using PARI throughout (see below for a description of PARI). |
| Prerequisites |
There aren't any specific prerequisites for this course. We will build up to most of the more difficult concepts together in lecture. Some familiarity with proofs and abstract mathematical thinking is useful, but can be developed over the course of the quarter.
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PARI
PARI is a computer algebra system written especially for number theory computations. It is FREE, and can be downloaded at the following main site:
PARI/GP Main Page (click on the "Download" link on the left margin)
Here are some instructions for downloading the files from the above site using UNIX:
Unix Installation Instructions
If you have a Windows-based computer, then the installation should be automatic upon downloading the appropriate file from the PARI/GP page (though I haven't tried it). For Mac users, it may be easiest to download the program Fink and Fink Commander from the web first. These programs fetch all of the appropriate files for you and then compile them on your hard drive. You can then run PARI from the terminal window (in OS X).
Here is some additional documentation:
Announcements & Dates
- Important Dates
- Sunday, April 17: Add deadline
- Wednesday, April 20: Exam 1 (7-8:30 pm) ROOM 380C
- Sunday, April 24: Drop deadline
- Wednesday, May 25: Exam 2 (7-8:30)
- Wednesday, June 8th: Final Projects Due (Noon Sharp)
Further Reading:
Good Textbooks on Number Theory
- Joseph Silverman, A Friendly Introduction to Number Theory -- friendly indeed, and very well written. Expands on basic concepts you might find to be too terse in Koblitz.
- Ireland and Rosen, A Classical Introduction to Modern Number Theory -- Another Springer GTM series book, but starts off very slow and builds to very sophisticated math. The number of chapters you can read and understand in this book is a very good measure of your understanding of algebraic number theory.
- Davenport, Multiplicative Number Theory -- Classic, but sadly another Springer graduate text. If you are interested in how multiplicative functions can be studied using infinite series, called Dirichlet series, then this is a great introduction.
Articles from the AMS (American Math. Society)
Web links
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