PURE MTH 7055 - Topology and Analysis
Career: | Postgraduate Coursework |
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Units: | 3 |
Term: | 4210 |
Campus: | North Terrace |
Contact: | Up to 3 hours per week |
Available for Study Abroad and Exchange: | Yes |
Available for Non-Award Study: | No |
Assumed Knowledge: | MATHS 2100 |
Assessment: | Ongoing assessment, examination |
Syllabus: |
Solving equations is a crucial aspect of working in mathematics, physics, engineering, and many other fields. These equations might be straightforward algebraic statements, or complicated systems of differential equations, but there are some fundamental questions common to all of these settings: does a solution exist? If so, is it unique? And if we know of the existence of some specific solution, how do we determine it explicitly or as accurately as possible? This course develops the foundations required to rigorously establish the existence of solutions to various equations, thereby laying the basis for the study of such solutions. Through an understanding of the foundations of analysis, we obtain insight critical in numerous areas of application, such areas ranging across physics, engineering, economics and finance. Topics covered are: sets, functions, metric spaces and normed linear spaces, compactness, connectedness, and completeness. Banach fixed point theorem and applications, uniform continuity and convergence. General topological spaces, generating topologies, topological invariants, quotient spaces. Introduction to Hilbert spaces and bounded operators on Hilbert spaces. |
Course Fees
Study Abroad student tuition fees are available here
Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.
The fees displayed below for international students are for students commencing a program in 2024 only. International students who commenced a program in 2023 or prior can find their fee here.
EFTSL | |||
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0.125 |
Course Outline
A Course Outline which includes Learning Outcomes, Learning Resources, Learning & Teaching for this course may be accessed here
Critical Dates
Term | Last Day to Add Online | Census Date | Last Day to WNF | Last Day to WF |
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4210 | Tue 15/03/2022 | Thu 24/03/2022 | Fri 06/05/2022 | Fri 10/06/2022 |
Class Details
Enrolment Class: Workshop | |||||||
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Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
10591 | WR01 | 5 | 4 | 28 Feb - 4 Apr | Monday | 10am - 11am | Engineering & Mathematics, EM218, Teaching Room |
25 Apr - 30 May | Monday | 10am - 11am | Engineering & Mathematics, EM218, Teaching Room | Note: This class will be delivered both online and face to face. Please refer to MyUni for details once enrolled. | |||
Related Class: Tutorial | |||||||
Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
11480 | TU01 | 5 | 4 | 4 Mar - 8 Apr | Friday | 9am - 10am | Engineering & Mathematics, EMG07, Teaching Room |
29 Apr - 3 Jun | Friday | 9am - 10am | Engineering & Mathematics, EMG07, Teaching Room | Note: This class is only available for face-to-face (on-campus) students. | |||
11483 | TU02 | 5 | 5 | 28 Feb - 4 Apr | Monday | 5pm - 6pm | MyUni, OL, Online Class |
25 Apr - 30 May | Monday | 5pm - 6pm | MyUni, OL, Online Class | Note: This class is for offshore / interstate students only. Where this requirement is not met, students risk being removed from this class. Please refer to MyUni for details once enrolled. | |||
Related Class: Lecture | |||||||
Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
19397 | LEC0 | 5 | 4 | This class does not have any timetabled face-to-face sessions. Please check MyUni or contact your Course Coordinator for details. |