Courses & Units

Group Theory and Functional Analysis KMA322

This unit will be first offered in 2022.

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	College of Sciences and Engineering School of Natural Sciences
Discipline	Mathematics
Coordinator	Associate Professor Jeremy Sumner
Available as an elective?	Yes
Delivered By	University of Tasmania

Availability

Location	Study period	Attendance options		Available to
Hobart	Semester 2	On-Campus		International	Domestic

Key

: On-campus
: Off-Campus
: International students
: Domestic students

Note

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Units are offered in attending mode unless otherwise indicated (that is attendance is required at the campus identified). A unit identified as offered by distance, that is there is no requirement for attendance, is identified with a nominal enrolment campus. A unit offered to both attending students and by distance from the same campus is identified as having both modes of study.

Key Dates

Study Period	Start date	Census date	WW date	End date
Semester 2	22/7/2024	16/8/2024	9/9/2024	27/10/2024

* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (refer to How do I withdraw from a unit? for more information).

Unit census dates currently displaying for 2024 are indicative and subject to change. Finalised census dates for 2024 will be available from the 1st October 2023. Note census date cutoff is 11.59pm AEST (AEDT during October to March).

About Census Dates

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

The 2024 Commonwealth Supported Place (CSP) rates are still being finalised by the Government and we will update the domestic fee information as soon as we have more details.

Requisites

Prerequisites

KMA321

Mutual Exclusions

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

KMA351|KMA352

Teaching

Teaching Pattern	1 x 3-hr workshop weekly (39 hours total), 1 x 1-hr tutorial weekly (13 hours total).
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.
Links	Booktopia textbook finder

The University reserves the right to amend or remove courses and unit availabilities, as appropriate.