Syllabus for Number Theory (Math 5653), Spring 2013

MW 2-3:15 pm, Monroe 111.

Text: Elementary Number Theory, Gareth Jones and Josephine Jones, corrected edition.


If you are not comfortable with proofs, you will likely find this course very challenging. Prerequisites 3 and 4 should normally be satisfied if you took MATH 3354.

Course outline

The course will start with a brief review of very basic concepts and results in number theory (greatest common divisor, prime factorization, congruences) which should be familiar to you from Math 3354. This material corresponds roughly to the first 3 chapters of the book and will be covered in the first 3 classes. We will spend approximately 7 more weeks on the material discussed in the textbook -- the plan is to cover the majority of the remaining topics, including techniques for solving congruences, the structure of the group of units of Zn, quadratic reciprocity, Riemann Zeta function, representation of integers by sums of squares and Fermat's theorem. In the remaining 5 weeks (these will not necessarily be the last 5 weeks of classes) we will cover some more advanced topics, most likely taken from the following list (we will probably only have time for 2 or 3 of those).

  Continued fractions and Pell's equation
  Dirichlet' theorem on primes in arithmetic progressions
  Introduction to algebraic number fields
  Introduction to elliptic curves
  Introduction to $p$-adic numbers


The course grade will be based on homework, two midterms and the final, with weights distributed as follows:


The final will be given in-class on Mon, May 6th, 2-5pm. The format of the midterms is open at this point, but most likely one of them will be given in class (during our regular class time), while the other will be take-home. It is possible that one of the midterms will have both take-home and in-class parts. The midterm dates given below are tentative and may be changed later.

Make-up policy


Collaboration policy.


Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates: