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 Lagrange's theorem and group actions to deduce statements on the structure of groups.
3. The ability to compare groups and rings (via homomorphisms between them).
4. The ability to use basic algebraic tools in the context of matrix rings, polynomials rings, and the group of invertible matrices.
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, conjugacy. Rings, ideals, maximal ideals, quotient rings, matrix rings, polynomial rings.

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?

Feedback will be given during classtime as students work collaboratively on group assignments. Optional quizzes may be given online through Brightspace with feedback.