Mathematics 115
Fall, 1999
3 Evans Hall, TuTh 12:40-2

Professor Ken Ribet

885 Evans Hall

Office hours: M 10-11, W 11-12, Th 10:30-11:30
Office telephone: 642 0648
Fax number: 642 8204
Secretary: 642 5026


An Introduction to the Theory of Numbers by Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery. You want the fifth edition. Publisher is John Wiley & Sons, Inc. This is a classic number theory textbook (``Niven & Zuckerman''), updated by Hugh Montgomery. It is renowned for its excellent problems. If you think that you've spotted a misprint in the book, first consult Hugh Montgomery's list of errors. For alternative treatments, check out my guide to recent and classic books on number theory.

Some software that may be run on a PC under DOS is available by ftp to The README explains how to run the binary executable that you can download from the server. For more extensive documentation, pick up the files clint0.pdf, clint1.pdf, clint2.pdf, clint3.pdf, and clint4.pdf. Our book's author Hugh Montgomery wrote to me as follows:

In this set of programs is one that performs powering congruentially for integers up to 1018. I wrote the programs in Turbo Pascal almost 10 years ago. Recently I learned that the Borland Turbo Pascal compiler has a bug in it that causes programs compiled with it to crash on PCs running at clock speeds of (roughly) 300MHz or higher. I have installed a patch in my compiler that fixes this, but I haven't gotten around to recompiling the programs that are there.
You may prefer to use the program PARI/gp, which is now available for a variety of platforms. This program was developed by and for number theorists, and is used widely in research. As Monica Chew pointed out to me, browsable documentation is available from the HASSE Server in Munich.

While I'm at it, I might refer you to Prime Form, a primality-testing program that is available "for all 32-bit Windows operating systems and has been tested under Windows 95, 98, NT3.51, NT4.0, and Windows 2000."

According to the General Catalog, this course treats ``Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.''


Now that the course is over, you can download the questions for all three exams in a single document. If you're curious about the kind of exams that I have given in the past, you can check out the Spring, 1998 questions that I gave in this course. (The midterm exams were one hour long, by the way.) You can even look at the answers to the old first midterm, second midterm and final exam; these documents are in Adobe Acrobat format. I propose to follow the book in order, covering the first N chapters.


Homework will be assigned weekly. The grader for this course is John Voight. The assignment will be discussed in class on the day that it is due. Therefore, late homework cannot be accepted!

For numerical problems, the grader encourages you to use computer software as you see fit. Be sure, however, to include printouts that explain what you did.

  1. Assignment due September 2:
  2. Assignment due September 9:
  3. Assignment due September 16:
  4. Assignment due Tuesday, September 28:
  5. Assignment due Thursday, October 7:

  6. Assignment due Thursday, October 14: Author Hugh Montgomery suggests that Problem 3 in § 2.4 be worked out using the programs that he wrote for IBM compatibles some years ago. For documentation, see the parent directory.

  7. Assignment due Tuesday, October 26:
  8. Assignment due Tuesday, November 9:
  9. Assignment due Tuesday, November 16:
  10. Assignment due Thursday, December 2: [The problems in § 7.8 should be done by you in private after the lecture on December 2. They do not need to be submitted.] This is a long assignment, so please get started ASAP!

E-mail Messages

I maintain a mailing list of students in the class. My intention is to send mail to the entire class when I make significant changes to this Web page and when I have some news to communicate. You can retrieve the messages with news in them by clicking on the links below:


The final course grade will be computed by weighting the exams and homework roughly as follows: midterm exams, 15% each; homework, 20%; final exam, 50%. I reserve the right to change the mix at the end of the semester--one can often see only after the fact how successful a given exam has been. I last taught this course three semesters ago. The final grade distribution in the class was as follows (I neglect +'s and -'s): 9 A's, 14 B's, 3 C's, and one Pass.

Miscellaneous links related to number theory and/or this course

The campus maintains an official Web page for this course, but it's only a skeleton page.

Kenneth A. Ribet * , Math Department 3840, Berkeley CA 94720-3840

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