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MX4545: NUMBER THEORY (2020-2021)

Last modified: 05 Aug 2021 13:04

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 Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
  • Dr Ehud Meir

Qualification Prerequisites

  • Programme Level 4

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

What other courses must be taken with this course?


What courses cannot be taken with this course?


Are there a limited number of places available?


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, algebraic integers in quadratic number fields.


  • Polynomial Congruences.
  • Quadratic Residues and Quadratic Reciprocity.
  • Bertrand’s postulate.
  • Algebraic number fields.
  • Algebraic integers.
  • Quadratic number fields and their rings of algebraic integers.
  • Cyclotomic number fields and their rings of algebraic integers.
  • The factorisation of ideals in rings of algebraic integers.

In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

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

Teaching Breakdown

  • 1 during University weeks 25 - 29, 31 - 34, 38 - 39
  • 1 Tutorial during University weeks 26 - 29, 31 - 34, 38 - 39

More Information about Week Numbers

In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

3 x standard course assessments - 30%, 30% and 40%

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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