Math 58. Number Theory

Fall 2012


Homework 8 is due Monday December 10, 2012 at the end of the class. The homework is here. Remember to choose one problem to present in class on Monday.

The source for most of the lectures on primality testing is Andrew Granville's excellent paper "It is easy to determine whether a given integer is prime".


Elementary Theory of Numbers by William J. Leveque.

The textbook is not mandatory.

Topics we will cover

Our goal in this class is to get a sample of the many topics in number theory. We will cover divisibility, congruences, Euclidean algorithm, Chinese Remainder Theorem, Pell equations among other topics.


The course grade will be based on:
Homework 25%,
Presentations 25%,
Midterm (take-home) 20%,
Final Exam (take-home) 30%.


There will be written homework due roughly every week. The most recent homework will be posted in the announcements and a copy of all homeworks can be accessed here. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.


For each written homework, the student must select a problem (and solution) to present in class. Each student will present a different problem, so I suggest the students to team up to decide which student presents which problem.


There will be one midterm and one final exam. Both will be take home exams. Dates to be announced later. On the midterm and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

Accommodations Statement

If you believe that you need accommodations for a disability, please contact Leslie Hempling in the Office of Student Disability Services, located in Parrish 130, or e-mail to set up an appointment to discuss your needs and the process for requesting accommodations. Leslie Hempling is responsible for reviewing and approving disability-related accommodation requests and, as appropriate, she will issue students with documented disabilities an Accommodation Authorization Letter. Since accommodations may require early planning and are not retroactive, please contact her as soon as possible. For details about the Student Disabilities Service and the accomodations process, visit

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Leslie Hempling in the Office Of Student Disability Services.

Last modified on November 30, 2012.