University Course Planner The University of Adelaide Australia

PURE MTH 7055 - Topology and Analysis

Career: Postgraduate Coursework
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

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Student Status

Domestic
International

What type of place are you studying in

Commonwealth supported
Full fee paying

Study Level

Undergraduate
Postgraduate Coursework
Non Award

Program of Study

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.

Units
EFTSL
Amount
3
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
4210 Tue 15/03/2022 Thu 24/03/2022 Fri 06/05/2022 Fri 10/06/2022


Class Details

Enrolment Class: Workshop
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.