Topics in Pure Mathematics
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.
Students taking this module should typically have at least a B in Mathematics in Scottish Highers, AS-, or A-Level, or an equivalent qualification.
Propositions, negation, conjunction, disjunction, implication, equivalence. Truth tables
Basic definitions and examples, commutative (Abelian) groups, Cayley tables, order of a group. Permutations and Cycles. Cyclic groups and generators. Subgroups.
Constructive Proof, Disproof by Counterexample, Proof by Contradiction, Proof by Contrapositive, Proof by Induction.
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.
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.