Number Theory

Number theory is one of the oldest branches of mathematics, and has been studied since the time of the ancient Greeks. Some problems, such as the study of Diophantine equations (the study of solutions to polynomial equations in either whole or rational numbers), have been studied for thousands of years with intensive work and progress continuing to the present day. At ASU, graduate students can study both classical algebraic number theory and more modern areas such as arithmetic geometry (a blending of number theory with geometry).

Prerequisites

Students beginning graduate work in number theory should have a solid background in general undergraduate mathematics. In addition to the general departmental prerequisites, it is strongly recommended that the student have taken a course in abstract algebra, and ideally an introductory undergraduate number theory course.

Students with no background in number theory may start with Introduction to Number Theory. The basic graduate algebra sequence is strongly recommended. Graduate number theory courses are offered on a rotating basis. In the past few years, courses have been given in algebraic number theory and the theory of elliptic curves. There have also been working seminars in class field theory, Iwasawa theory, and modular forms.

Master's students in number theory usually take one qualifying examination in Real Analysis or Algebra. The second written examination can be either another qualifying examination, a master's level examination in number theory (based on the undergraduate course Introduction to Number Theory and one other course), or part of a comprehensive examination in number theory.

Ph.D. students in number theory will usually take their qualifying examinations in Real Analysis and Algebra, though other combinations are possible. The two part comprehensive examination in number theory will be based on graduate courses in number theory which may vary according to the specific area of the student's research interest.

For more information on specific aspects and content of this program, contact one of the Number Theory faculty:

http://math.asu.edu/research/numbers.html