MAT 311
Number Theory


Sorin Popescu (office: Math 3-109, tel. 632-8255, e-mail sorin at


Caner Koca (office: Math 3-118, e-mail caner at


TuTh 02:20pm-03:40pm, Lgt Engr Lab 154


Either MAT 312 (Applied algebra), or MAT 313 (Abstract Algebra) or MAT 318 (Classical Algebra) are mandatory prerequisites for this class. In general some basic algebra exposure is required and assumed, but I will try to keep prerequisites to a minimum.


We will be covering a number of elementary topics in number theory and some applications. Some theoretical aspects will be trated in detail while others will provide brief but insightful and motivating excursions into topics like Mersenne Primes, number sieves, RSA cryptography, elliptic curves, etc if time will permit.

There are many excellent undergraduate books on the subject. Here is a sample list (all of them available in our library), however we will mainly use this semester only the first two of them:

These are a mixture of classical texts (for example Dirichlet), modern efforts, more elementary (for example Kumanduri and Romero) and more advanced (for example Rosen, or Ireland and Rosen), algebraic (for example Andrews or Davernport) or analytic approaches (for example, Apostol). This course will concentrate only on elementary algebraic number theory, and applications.

Course description:

We will cover only parts of the textbook(s) (Davenport and Rosen) and the schedule may/will be adjusted based on students' preparation and progress.

TopicSections in textbookWeekNotes
Numbers, sequences, and sums. Induction. Fibonacci numbers. DivisibilityDavenport Chap. 11/23-1/28
Greatest Common Divisor, Euclidean algorithm, Fundamental theorem of arithmetic 1/30-2/4
Linear Diophantine equations / Congruences2/6-2/11
Fermat's little theorem / Euler's FormulaDavenport Chap. 22/13-2/18

Projects, Homework & Grading:

Homework and project (TBA) are an integral part of the course. Problems marked with an asterisk (*) are for extra credit. In addition to homework you will be required to hand in a research/scholarship/computing project. Projects with a nontrivial writing component may be used to satisfy the Mathematics Upper Division Writing Requirement.

Your grade will be based on the weekly homeworks (20%), project (25%), midterm (25%), and the final exam (30%). The two lowest homework grades will be dropped before calculating the average.

The midterm will be held in class on 03/23.

A review session will be held on 04/28 in Math P-131, 3:00-4:00pm. The final exam will be comprehensive.

Grades are now posted on the Solar system. Have a nice summer!


The following is a short list of web sites devoted to number theory or number theoretic related topics relevant for our class: A number of interesting local links that you are warmly encouraged to explore:

Math Learning Center

The Math Learning Center (MLC), located in Room S-240A of the Math Tower, is an important resource. It is staffed most days and some evenings by mathematics tutors (professors and advanced students). For more information and a schedule, consult the MLC web site.

Special needs

If you have a physical, psychiatric, medical or learning disability that may impact on your ability to carry out assigned course work, you may contact the Disabled Student Services (DSS) office (Humanities 133, 632-6748/TDD). DSS will review your concerns and determine, with you, what accommodations may be necessary and appropriate. I will take their findings into account in deciding what alterations in course work you require. All information on and documentation of a disability condition should be supplied to me in writing at the earliest possible time AND is strictly confidential. Please act early, since I will not be able to make any retroactive course changes.