MTH3141 · Algebra 1: Group theory

Overview

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups; cosets; normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorems; group actions; Sylow theorems and group presentations.

Areas of study: Applied mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Communicate the beauty and the power of pure mathematics;
2. Capture the mathematical notion of symmetry via group theory;
3. Apply the fundamental concepts of abstract algebra;
4. Explain the notion of proof in mathematics and be able to carry out basic proofs;
5. Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve abstract algebra problems;
6. Extend and deepen understanding of abstract algebra through advanced proofs, generalisations, and applications, demonstrating higher levels of rigour and independence.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.