Mathematics 115

Fall, 2011
TuTh 9:40-11AM, 3 Evans Hall

Professor Kenneth A. Ribet
Telephone: 510 642 0648
Fax: 510 642 8204
photo of Ribet giving a lecture
to high school students at the MSRI in Berkeley


This course is elementary in the sense that no other upper-division course is needed as a prerequisite. Although Math 53 and Math 54 are required of Math 115 students, Math 55 is much more relevant. If you know abstract algebra (Math 113), then you will find many arguments that are familiar from your study of groups and rings. Whenever appropriate, I will allude to connections with Math 113 for the benefit of those of you who have studied abstract algebra or will do so at some point.


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, most recently one year ago.


Sage is a free open-source mathematics software system that does number theory calculations that will illustrate and conceivably even illuminate the material of the course. I urge you to become familiar with sage by taking the tour and then experimenting with the software. I will try to assign interesting homework problems that require sage (or other software) for calculations. I will also bring sage into the classroom from time to time.

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

Chapter-by-Chapter Course Description

Some web resources related to the course


Homework assignments will be due on Thursdays, with possible perturbations because of midterm exams and the Thanksgiving holiday.
  1. Assignment due September 1, 2011. Assume in problem 19 that the set has at least two elements. The problem is visibly false for 1-element sets, even though the error hadn't been reported before.
  2. Assignment due September 8, 2011:
  3. Assignment due September 15, 2011:
  4. Assignment due September 22, 2011:
  5. Assignment due September 29, 2011:
  6. Assignment due October 6, 2011.
  7. Assignment due October 13, 2011:
  8. Assignment due October 20, 2011:
  9. Assignment due October 27, 2011:
  10. Assignment due November 3, 2011:
  11. Assignment due November 10, 2011.
  12. Assignment due November 17, 2011.
  13. Assignment due November 22, 2011 (spoiler).
  14. Assignment due December 1, 2011:


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 last taught this course five years ago, there were 47 registered students at the end of the semester. One of the students had effectively dropped the course well before the final exam. The remaining 46 grades were distributed as follows: 17 As, 16 Bs, 13 Cs.


The calendar that follows (if you're logged into gmail!) attempts to call your attention to "events" of interest to math 115 student: class meetings, office hours, exams, noteworthy lectures (such as the Serge Lang undergraduate lecture by Jordan Ellenberg, which will be held on December 1 at 4:10PM.)

Now that the semester is over

The grades were distributed as follows: 11 As, 14 Bs, 4 Cs, 4 D/F. This rough distribution ignores +'s and -'s and does not reflect that some grades were converted to P or NP.

If you're a bit bored, you might enjoy gazing back at the class photo that we took right before the class ended. If you are totally bored, you can look at the course evaluations that were written around the same time.

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