Topics in Pure Mathematics

On this page
Credits

20

Module code

MA12002

About the module

This module is mandatory for Level 1 students on BSc and MMath Mathematics degrees and is optional for Level 1 students taking the BSc in Mathematics combined with any of Accountancy, Economics, Financial Economics or Psychology. The module is also suitable for students on non-mathematics degrees and recommended for students on physics and computing degrees. If you have questions about this module please contact our Undergraduate Admissions Tutor.

Prerequisites

Students taking this module should typically have at least a B in Mathematics in Scottish Highers, AS-, or A-Level, or an equivalent qualification.

Indicative Content

  • Logic

    Propositions, negation, conjunction, disjunction, implication, equivalence. Truth tables

  • Group Theory

    Basic definitions and examples, commutative (Abelian) groups, Cayley tables, order of a group. Permutations and Cycles. Cyclic groups and generators. Subgroups.

  • Proof

    Constructive Proof, Disproof by Counterexample, Proof by Contradiction, Proof by Contrapositive, Proof by Induction.

  • Number Theory

    Integers and Divisibility. Greatest Common Divisor and the Euclidean Algorithm, leading to prime factorisation and the Fundamental Theorem of Arithmetic, and continued fractions. Properties of Primes. Linear Diophantine Equations. Relations, equivalence relations and congruences (modular arithmetic). (Higher degree) Diophantine Equations.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via coursework (100%) consisting of tests.

Credit Rating

This module is a Scottish Higher Education Level 1 or SCQF level 7 module and is rated as 20 SCOTCAT credits or 10 ECTS credits.