This unit will be first offered in 2022.
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|
|Faculty/School||College of Sciences and Engineering
School of Natural Sciences
|Available as student elective?||No|
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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.
Special approval is required for enrolment into TNE Program units.
* 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 (see withdrawal dates explained for more information).
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.
You cannot enrol in this unit as well as the following:
1 x 180 minute lecture weekly, 1 x 60 minute tutorial weekly
AT1 - Assignments - weekly (20%)
AT2 - Mid-semester test (20%)
AT3 - Exam (3-hours) (60%)
|Timetable||View the lecture timetable | View the full unit timetable|
The University reserves the right to amend or remove courses and unit availabilities, as appropriate.