MST30010

Learning Outcomes:

Upon successful completion of this module a student should have the following skills:

1. Solid understanding of the main concepts and results indicated within the contents of this module.
2. The ability to apply counting arguments involving Lagrange's theorem and the class equation to deduce statements on the structure of groups.
3. The ability to compare group (via homomorphisms between them).
4. The ability to use the isomorphism theorems to identify groups.
5. The ability to build combinatorial and arithmetic arguments relying on fundamentals of group theory.

Indicative Module Content:

Basics of groups, subgroups, cyclic groups, cosets, Lagrange's theorem, normal subgroups and quotient groups, the centre of a group, homomorphisms, the isomorphism theorems, the subgroup correspondence theorem, group actions, orbits, Cayley's theorem, inner automorphisms, conjugacy, the class equation, Cauchy's theorem and p-groups.

Student Effort Hours:

Approaches to Teaching and Learning:

Requirements, Exclusions and Recommendations

Students should have completed a course in abstract algebra prior to taking this module (for example, MST20010). This course should contain at least an introduction to groups, subgroups, cosets, and permutation groups.

All questions about eligibility (in particular if you think the meet the requirements but have not passed MST20010) should be addressed to the module coordinator.

Module Requisites and Incompatibles

Assessment Strategy

Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Self-assessment activities

How will my Feedback be Delivered?

Self-assessment activities are tentative and will be based on the following model: Students will be asked to grade their own responses to select assignments, based on a detailed solution sheet. They will prepare a detailed report on their weaknesses on key aspects of the module. Based on the accuracy of this report, their homework grades will be positively updated. The other two feedback strategies to employed (Feedback individually to students, post-assessment and Group/class feedback, post-assessment) are self-explanatory.