Unit name | Analytic Number Theory |
---|---|
Unit code | MATHM0007 |
Credit points | 20 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Dr. Saha |
Open unit status | Not open |
Pre-requisites |
Complex Function Theory (Math 33000), Number Theory and Group Theory (Math 11511) |
Co-requisites |
MATH30200 Number Theory |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit aims
To gain an understanding and appreciation of analytic number theory, and some of its most important achievements. To be able to apply the techniques of complex analysis to study a range of specific problems in number theory.
General Description of the Unit
The study of prime numbers is one of the most ancient and beautiful topics in mathematics. After reviewing some basic results in elementary number theory and the theory of Dirichlet characters and L-functions, the main aim of this lecture course will be to show how the power of complex analysis can be used to shed light on irregularities in the sequence of primes. Significant attention will be paid to developing the theory of the Riemann zeta function. The course will build up to a proof of the Prime Number Theorem and a description of the Riemann Hypothesis, arguably the most important unsolved problem in modern mathematics.
Relation to Other Units
This is one of three Level 6 and Level 7 units which develop number theory in various directions. The others are Number Theory and Algebraic Number Theory.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
Learning Objectives
To gain an understanding and appreciation of Analytic Number Theory and some of its important applications. To be able to use the theory in specific examples.
Transferable Skills
Using an abstract framework to better understand how to attack a concrete problem.
Lectures and exercises.
100% Examination.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html