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Functional Analysis (MAST90020)
Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)
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About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Overview
Availability | Semester 1 - Dual-Delivery |
---|---|
Fees | Look up fees |
Functional analysis is a fundamental area of pure mathematics, with countless applications to the theory of differential equations, engineering, and physics.
The students will be exposed to the theory of Banach spaces, the concept of dual spaces, the weak-star topology, the Hahn-Banach theorem, the axiom of choice and Zorn's lemma, Krein-Milman, operators on Hilbert space, the Peter-Weyl theorem for compact topological groups, the spectral theorem for infinite dimensional normal operators, and connections with harmonic analysis.
Intended learning outcomes
After completing this subject, students will understand the fundamentals of functional analysis and the concepts associated with the dual of a linear space. They will also have an understanding of how these are used in mathematical applications in pure mathematics such as representation theory. They will have the ability to pursue further studies in this and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 31 January 2024
Eligibility and requirements
Prerequisites
All of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20022 | Group Theory and Linear Algebra | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
MAST30026 | Metric and Hilbert Spaces | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
Or equivalent
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 31 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Four equally weighted (10% each) homework assignments due evenly throughout the semester of up to 40 pages total
| Throughout the teaching period | 40% |
One written examination
| 60% |
Last updated: 31 January 2024
Dates & times
- Semester 1
Coordinator Jesse Gell-Redman Mode of delivery Dual-Delivery (Parkville) Contact hours 36 hours comprising; 3 x 1-hour lectures per week Total time commitment 170 hours Teaching period 28 February 2022 to 29 May 2022 Last self-enrol date 11 March 2022 Census date 31 March 2022 Last date to withdraw without fail 6 May 2022 Assessment period ends 24 June 2022
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
A. Bressan, Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations, Graduate Studies in Mathematics Vol. 143, American Mathematical Society, 2013
Recommended texts and other resources
R.J. Zimmer. Essential Results in Functional Analysis. Univ of Chicargo Press, 1990.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Ph.D.- Engineering Course Master of Science (Mathematics and Statistics) Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 31 January 2024