MATH 403 Irrationality and Transcendence (Not offered 2006-2007; to be offered 2007-2008) (Q)
The study of the nature of numbers is one of the most ancient and fundamental
pursuits in all of mathematics. In this course we explore the worlds of irrational
and transcendental number theory. A number is algebraic if it is the solution to a
nontrivial polynomial equation with integer coefficients. Numbers that are not
algebraic are called transcendental. While these issues are ancient, it was not until 1844 that it was shown that transcendental numbers exist. Since then many
modern techniques have been developed to shed some insight into these enigmatic numbers. These techniques beautifully weave ideas from algebra and
analysis together. Here we will provide all the necessary ideas from algebraic
number theory and from complex analysis. Mathematics 302 and Mathematics
313 are not pre-requisites.
Format: lecture/discussion. Evaluation will be based primarily on projects,
homework assignments, and exams.
Prerequisites: Mathematics 301 or 305, and Mathematics 312 or 315 or 317, or
permission of instructor. No enrollment limit (expected: 15).