Mathematics 115

Fall, 2012
TuTh 12:40-2PM, 4 Evans Hall

Professor Kenneth A. Ribet
Telephone: 510 642 0648
Fax: (510) 642-8204
Office hours (885 Evans Hall)
photo of Ribet at National Academy
of Sciences garden party, taken by Arthur Jaffe


This course is elementary in the sense that no specific course is needed as a prerequisite. On the other hand, the ability to read and write proofs is pretty much essential. Math 55 and Math 113 provide helpful background. As we encounter objects that can be regarded as groups, rings, fields, homomorphisms,..., I will mention the connection to Math 113 in class.


An Introduction to the Theory of Numbers, Fifth Edition by Ivan Niven, H. S. Zuckerman and Hugh L. Montomery. Although the current edition was published 20 years ago, this book remains one of the definitive introductions to the subject. It is renowned for its interesting, and sometimes challenging, problems. Please see Montgomery's home page for the book and especially his lists of typos and errors in the book. Note that there are multiple lists because the book has been reprinted several times.

This book is not cheap, but it should be easy to find used copies: “Niven & Zuckerman” (as the book is widely known) has been used repeatedly at Berkeley.

Chapter-by-Chapter Description


Sage is a free open-source mathematics software system that does number theory calculations that will illustrate and illuminate the material of the course. Even before the semester begins, you can become familiar with sage by taking the tour and then experimenting with the software. When I taught Math 116 last semester, I projected a sage notebook from my laptop for a substantial fraction of each lecture period. Don't be surprised if I continue in that direction this semester. I will try to assign interesting homework problems that require sage for calculations.

You can download the software for your Windows, Linux or MacOS X box. Alternatively, you can run sage online at after you create an account for yourself.


Please do not plan travel on the dates of these exams. If you believe that you have a conflicting obligation because of an intercollegiate sport or other extracurricular activity, please read these guidelines immediately.

For practice exams, you might consult the web pages for my previous Math 115 courses

and for a recent course by Martin Olsson. You may also consult Richard Borcherds's Math 115 page for Fall, 2003.


Course grades will be based on a composite numerical score that is intended to weight the course components roughly as follows: midterm exams 15% each, homework 25%, final exam 45%.

When I taught this course in 2011, there were 33 registered students. Grades were distributed as follows: 11 As, 14 Bs, 4 Cs, 4 D/F. This rough distribution ignores +'s and -'s. Some students took the course P/NP. Their letter grades were converted to P or NP when I entered the final grades.

For this course (Fall, 2012), there were 36 registered students. They received 17 As, 13 Bs, 3Cs and 3Fs. The students with the a P/NP grading option had their grades converted when final grades were entered.

You can look at the course evaluations that my Math 115 students wrote in December, 2011 as well as the evaluations for this course. I encourage suggestions and comments about my teaching style and the evolution of the course. You can make them anonymously in various ways (e.g., by slipping a note under my office door) or just present them in email or a face-to-face conversation.


  1. Assignment due August 30, 2012: §1.2, problems 1, 2 and 3: all parts, using sage; also problems 4b, 5, 7, 15, 25, 27, 28, 47
  2. Assignment due September 6, 2012: §1.3, problems 2, 8, 10, 11, 13, 16, 17, 26, 28, 31
  3. Assignment due September 13, 2012:
  4. Assignment due September 20, 2012:
  5. Assignment due September 29, 2012: §2.3, problems 4, 8, 13, 14, 17, 18, 26, 27, 29, 30, 39
  6. Assignment due October 4, 2012:
  7. Assignment due October 11, 2012:
  8. Assignment due October 18, 2012:
  9. Assignment due October 25, 2012:
  10. Assignment due November 1, 2012:
  11. Assignment due November 8, 2012
  12. Assignment due November 15, 2012:
  13. Assignment due November 27, 2012:
  14. Assignment due December 6, 2012:

Some web resources related to the course


The calendar that follows (at least if you're logged into gmail!) attempts to call your attention to "events" of interest to math 115 students: class meetings, office hours, exams, optional class get-togethers (coffee, lunch, breakfast), and special lectures for undergraduates.

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