University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 10

Semester: 2

Availability restrictions: Not automatically available to General Degree students

Planned timetable: 10.00 am Mon (even weeks), Tue and Thu

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-requisite(s): Before taking this module you must pass MT2505 and ( pass MT3501 or pass MT3502 or pass MT3503 or pass MT3504 or pass MT3505 )

Learning and teaching methods and delivery

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

Scheduled learning hours: 35

Guided independent study hours: 115

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 100%


Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Dr C P Bleak
Module teaching staff: Dr Collin Bleak
Module coordinator email cb211@st-andrews.ac.uk

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