Functional Analysis

Subject MAST90020 (2011)

Note: This is an archived Handbook entry from 2011.

Credit Points: 12.50
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject is not offered in 2011.
Time Commitment: Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour practice class per week.
Total Time Commitment: 3 contact hours and 7 hours private study per week.
Prerequisites: None.
Corequisites: None.
Recommended Background Knowledge: Subjects in linear algebra (equivalent to 620-231 Group Theory and Linear Algebra) and metric spaces (equivalent to 620-329 Metric and Hilbert Spaces).
Non Allowed Subjects: None.
Core Participation Requirements:

For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.

The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

Contact

Email: ghjorth@unimelb.edu.au
Subject Overview:

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.
Objectives: 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.
Assessment: Up to 40 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3 hour written examination (60%, in the examination period).
Prescribed Texts: G. Pedersen. Analysis Now. Springer, 1988.
Recommended Texts: R.J. Zimmer. Essential Results in Functional Analysis. Univ of Chicargo Press, 1990.
Breadth Options:

This subject is not available as a breadth subject.
Fees Information: Subject EFTSL, Level, Discipline & Census Date
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.
Related Course(s): Master of Science (Mathematics and Statistics)

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