production
Skip to Content

Log In

  1. University Home
  2. Catalogue of Courses
  3. Postgraduate
  4. 2014-2015
  5. Mathematical Sciences
  6. MX5509: Number Theory

MX5509: NUMBER THEORY (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

This course concerns the integers, and more generally the ring of algebraic integers in an algebraic number field.  The course begins with statements concerning the rational integers, for example we discuss the Legendre symbol and quadratic reciprocity. We also prove a result concerning the distribution of prime numbers. In the latter part of the course we study the ring of algebraic integers in an algebraic number field. One crucial result is the unique factorisation of a nonzero ideal as a product of primes, generalising classical prime factorisation in the integers.



Course Details

Study Type Postgraduate Level 5
Term Second Term Credit Points 20 credits (10 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr William Turner

What courses & programmes must have been taken before this course?

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Number Theory is the study of integers and has three main branches: Elementary, Analytical and Algebraic. This course consists of a selection of topics from these branches. The topics will include some of the following; the theory of quadratic congruences, continued fractions, pseudo-primes, primitive roots, Diophantine equations, the distribution of prime numbers, and algebraic integers in quadratic number fields.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

One 3-hour written examination (80%); one in-course assessment (20%).

Formative Assessment

There are no assessments for this course.

Feedback

None.

Course Learning Outcomes

None.
 

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.