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.
|Unit name||Group Theory and Functional Analysis|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Associate Professor Jeremy Sumner|
|Available as an elective?||Yes|
|Delivered By||University of Tasmania|
|Location||Study period||Attendance options||Available to|
- International students
- Domestic students
|Study Period||Start date||Census date||WW date||End date|
* 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 2022 are indicative and subject to change. Finalised census dates for 2022 will be available from the 1st October 2021. Note census date cutoff is 11.59pm AEST (AEDT during October to March).
- 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.
|Field of Education||Commencing Student Contribution 1,3||Grandfathered Student Contribution 1,3||Approved Pathway Course Student Contribution 2,3||Domestic Full Fee 4|
1 Please refer to more information on student contribution amounts.
2 Please refer to more information on eligibility and Approved Pathway courses.
3 Please refer to more information on eligibility for HECS-HELP.
4 Please refer to more information on eligibility for FEE-HELP.
Please note: international students should refer to What is an indicative Fee? to get an indicative course cost.
You cannot enrol in this unit as well as the following:KMA351|KMA352
1 x 3-hr workshop weekly (39 hours total), 1 x 1-hr tutorial weekly (13 hours total).
|Assessment||Quiz #1 (15%)|Examination (40%)|Weekly Assignments (30%)|Quiz #2 (15%)|
|Timetable||View the lecture timetable | View the full unit timetable|
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.