Prime Numbers and their Distribution (MATH0083)

Key information

Faculty: Faculty of Mathematical and Physical Sciences
Teaching department: Mathematics
Credit value: 15

Restrictions: This module is normally taken by fourth (or third) year students on single or combined honours mathematics degrees, who have taken MATH0014 Algebra 3, MATH0051 Analysis 4 and MATH0034 Number Theory.
Timetable

Alternative credit options

There are no alternative credit options available for this module.

Description

Prime numbers have fascinated humans for millennia, and one of their cardinal mysteries is their irregular distribution on the number line. One of the great theorems is mathematics is the Prime Number Theorem, which gives an asymptotic estimate for the number of primes less than a given bound. A simple yet detailed proof of the Prime Number Theorem is the capstone goal of this course.

For a detailed investigation on prime numbers, we will need to build up some tools. The main objects of study in this course are functions of number-theoretic origin, i.e. arithmetic functions. A good deal of the course will be spent building up techniques for estimating sums of arithmetic functions and showing their equivalence with Dirichlet series. The latter allows us to bring to bear powerful techniques from real and complex analysis on the study of arithmetic functions. These tools will lead us to clear proofs of Dirichlet's theorem on primes in arithmetic progressions and the Prime Number Theorem.

Module deliveries for 2024/25 academic year

Intended teaching term: Term 1 听听听 Undergraduate (FHEQ Level 7)

Teaching and assessment

Mode of study: In person
Methods of assessment: 40% Exam

60% Coursework
Mark scheme: Numeric Marks

Other information

Number of students on module in previous year: 26
Module leader: Dr Ian Petrow
Who to contact for more information: math.ugteaching@ucl.ac.uk

Last updated

This module description was last updated on 8th April 2024.

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Important information

The catalogue has been updated with key information about the modules that will run during the 2024/25 academic session. Current and prospective students can browse through the catalogue to consider possible module choices for the coming year.

Please note,听information in the catalogue is听subject to change as teaching and assessment arrangements for 2024/25 may need to be adjusted in line with the University's Feedback and Assessment principles and operating model.

Centrally managed exam durations will be provided on students' individual exam timetables. Arrangements for locally managed exams and in-class activity will be confirmed by the teaching department for the module.

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