Group Theory and Functional Analysis unit (KMA322)

Introduction

This third year, second-semester unit covers some of the fundamental abstract structures, processes and relationships that underpin all of mathematics. The first half of the unit focuses on the central role groups play in modern algebra together with their application to the understanding of structure and symmetry in various scientific contexts. In the second half of the unit, we introduce the topological concepts essential to the study of continuity and convergence in infinite dimensional metric spaces. Applying these ideas, we develop the theory of normed and inner product spaces, and see how they are key to the study of differential and integral equations, quantum mechanics, numerical analysis, and many more areas. This unit is one of the options for students completing the Mathematics major of the BSc.

Summary

Unit name	Group Theory and Functional Analysis
Unit code	KMA322
Credit points	12.5
College/School	Sciences and Engineering School of Natural Sciences
Discipline	Mathematics
Coordinator	Associate Professor Jeremy Sumner
Available as an elective?	Yes
Delivered By	University of Tasmania
Level	Advanced

Availability

Specific information on 2027 unit availability will be available in August

Learning Outcomes

• Apply the fundamental concepts of group theory and functional analysis, through formulating mathematical proofs;
• Identify and develop solutions to applied problems in physics and the other sciences, using group theory and functional analysis;
• Apply logic, reasoning and a variety of communication skills to present mathematical ideas and results in a clear and precise way;
• Explain the fundamental connection between groups and symmetries, and the application of group theory to a broad range of mathematical and scientific contexts;
• Synthesise the necessary topological concepts that enable infinite processes to be carried out such as continuity and convergence;
• Analyse the structural development of basic topological spaces from metric to (infinite-dimensional) normed and inner-product spaces, and implement the properties of such spaces in a broad range of contexts.

Fee Information

2027 fee information will be available in August.

Requisites

Prerequisites

KMA321

Mutual Exclusions

You cannot enrol in this unit as well as the following:

KMA351|KMA352

Teaching

Teaching Pattern	3 x 1-hr lecture weekly, 1 x 2-hr tutorial weekly
Assessment	Quiz #1 (15%)|Quiz #2 (15%)|Weekly Assignments (30%)|Examination (40%)
Timetable	View the lecture timetable | View the full unit timetable

Textbooks

Required	Required readings will be listed in the unit outline prior to the start of classes.

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