Group Theory: An Introduction to Abstract Mathematics (U01459)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-1-GTh

Core first year course for Honours Degrees in Mathematics and/or Statistics. Syllabus summary: True and false mathematical statements. Functions between sets. Infinite sets, countable and uncountable. Numbers: primes, proof of the existence of infinitely many primes. Rational numbers, irrationality of the square root of 2. Modular arithmetic: elementary exercises in reasoning. Ideas of addition and multiplication mod n. Euclidean algorithm, congruence equations. Permutations: definition, construction of multiplication table for S3. Groups: the idea of a group, identity, inverses, subgroups. The above examples, invertible matrices, symmetries of geometrical figures. Theory of groups: definition of group. Uniqueness of inverses, etc., as examples of proof, associativity of multiplications assumed throughout. Cosets and Lagrange's theorem, Fermat's little theorem. The idea of isomorphism.

Entry Requirements

? Pre-requisites : H-Grade Mathematics or equivalent; prior attendance at MAT-1-PCa and MAT-1-SEq or their equivalent

? Prohibited combinations : MAT-1-mi2

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 1), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 1st year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Wednesday	12:10	13:00	Central
Lecture	Friday	12:10	13:00	Central

? Additional Class Information : Tutorials: Tu at 1110 and 1210.

Summary of Intended Learning Outcomes

1. Appreciation of and the ability to handle abstract arguments in set theory and group theory.
2. Ability to apply such arguments in number theory and geometry.