MATH 303(F) Analytic Number Theory (Q)

The fundamental theorem of arithmetic says that every natural number beyond 1 is a product of prime numbers in a unique way, up to ordering. Analytic number theory is an area of number theory that employs powerful ideas from analysis to discover beautiful structure within the set of primes. In this course, we will investigate a number of elementary questions about arithmetic and the set of natural numbers. We will then move to the study of the distribution of prime numbers and prove the amazing Prime Number Theory. In addition, we will consider other classical summits of the subject including the Riemann zeta function, Riesel Numbers, Siepinski Numbers, Perfect Numbers, Carmichael Numbers as well as modern applications such as primality testing. We will also introduce some powerful tools from complex analysis that are at the heart of the subject.
Format: lecture. Evaluation will be based primarily on performance on homework, projects, and exams.
Prerequisites: Mathematics 301 or 305. No enrollment limit (excepted: 15).

Hour: LUCA