MT4519 Number Theory

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

10.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr T D H Coleman

Dr T D H Coleman
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Tom Coleman; Dr Firdavs Rakhmonov

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

The aim of this module is to introduce students to some important topics in number theory. Topics to be covered may include: prime numbers, cryptography, continued fractions, Pell's equation, the Gaussian integers and writing numbers as sums of squares.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2505 AND ( PASS MT3501 OR PASS MT3502 OR PASS MT3503 OR PASS MT3504 OR PASS MT3505 )

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Extend a basic knowledge of modular arithmetic to more advanced topics such as primitive roots and quadratic residues, as well as stating and proving many results concerning these concepts
  • Understand the theory of finite and infinite continued fractions, and apply this knowledge to find good rational approximations of algebraic and transcendental numbers
  • Apply ideas from the above topics to analyse famous equations such as the sum of two/three/four squares, Pell¿s equations, and special cases of Fermat's Last Theorem
  • Analyse the role that number theory plays in many areas of mathematics (such as cryptography, analysis, abstract algebra) and vice versa