Mathematics 115
Fall, 2000
3 Evans Hall, MWF 11:10-12

Professor Ken Ribet

photo of Ribet by Karl Rubin

885 Evans Hall

Regular office hours Tu 11-noon, Th 12-1, Fri 2-3
Office telephone: 642 0648
Fax number: 642 8204
Secretary: 642 5026

Exam week office hours:



Elementary Number Theory and its applications by Kenneth H. Rosen. photo of Ken Rosen You want the fourth edition. The publisher is Addison Wesley Longman. This book lists for $86 but can be had cheaper on-line. One place to shop is, which claims a price of $46.03 airshipped from a company in England! As you can infer from the publisher's web page for our book, a companion website has been created. When I taught this course last year, I used An Introduction to the Theory of Numbers by Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery as a text. For alternative possibilities, check out my guide to recent and classic books on number theory.

When you discover misprints in the textbook, please e-mail me with what you've found. I'm compiling a list, which I'll send to the author at the end of the semester.


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.'' It has been my intention to emphasize applications to cryptography in this course. Our textbook was recommended by a mathematician at another university who taught a course like this from a similar perspective.

It looks as if I will follow the book's table of contents, treating Chapters 1 and 2 pretty superficially. We should certainly be able to cover Chapter 8, which treats cryptology. By the end of the course, we should have covered the very important Chapter 11. If there's time, we'll talk about continued fractions as well (Chapter 12).


The exams are closed-book examinations. No calculators are allowed. On the other hand, arithmetic answers do not have to be simplified for full credit. Please bring your own blue books to the exams.

If you'd like to see some questions that I've given in exams for this course before, you can look at the Spring, 1998 and the Fall, 1999 questions. The first of these courses was taught in 50-minute MWF courses, while the second was taught in 80-minute TuTh courses. These documents, by the way, are in Adobe Acrobat format.


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.

Your homework score for the class is computed in such a way that your lowest score is ignored and your next lowest score is given only half its usual weight. There will be 14 assignments, each worth 20 points. Thus the maximum possible homework score will be 250.

  1. Assignment due September 6:
  2. Assignment due September 11:
  3. Assignment due September 18:
  4. Assignment due September 25:
  5. Assignment due October 4:
  6. Assignment due October 11
  7. Long and hard assignment due October 16:
  8. Assignment due October 23:
    (Note that the number-theoretic cryptography workshop begins at the MSRI on October 16.) Our grader, John Voight, will be lecturing on perfect numbers in class on Friday, October 27.
  9. Assignment due October 30:
  10. Assignment due November 8:
  11. Assignment due November 15:
    Note that office hours on November 16 will be 2-3PM instead of 12-1PM.
  12. Assignment due November 22:
  13. Assignment due December 1:
  14. Assignment due December 8:


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 two semesters ago. The final grade distribution in the class was as follows (I neglect +'s and -'s): 15 A's, 13 B's, 4 C's, and 2 D's. Grades were lower than this when I taught the course five semesters ago.

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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