Functional Analysis
Subject 620-628 (2009)
Note: This is an archived Handbook entry from 2009. Search for this in the current handbook
| Credit Points: | 12.50 | ||||||||||||
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| Level: | 9 (Graduate/Postgraduate) | ||||||||||||
| Dates & Locations: | This subject has the following teaching availabilities in 2009: Semester 2, - Taught on campus.
On-campus Timetable can be viewed here. For information about these dates, click here. | ||||||||||||
| 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: | It is recommended that students have completed a third year subject on measure and integral (equivalent to 620-312 [2008] Linear Analysis). | ||||||||||||
| Non Allowed Subjects: | None. | ||||||||||||
| Core Participation Requirements: | It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit. |
Coordinator
Assoc Prof Jerry Koliha| Subject Overview: |
Functional Analysis is the study of spaces of functions and various structures on these spaces, in particular norms. This subject has important applications to differential and integral equations in mathematics, engineering and physics. The syllabus will consist of the following: Bounded linear operators between Banach and Hilbert spaces. Operator topologies. Classical spectrum of an operator. Spectral theory. Compact, Fredholm and Browder operators. Self-adjoint, normal and unitary operators on a Hilbert space. C* and von Neumann algebras. |
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| Objectives: | After completing this subject, students will gain: - familiarity with the theory of bounded linear operators; - an understanding of the spectral theory of operators; - recognition of familiar spaces in terms of their more formal properties; - exposure to applications in the solutions of linear equations in abstract spaces - exposure to applications in physics; - the ability to pursue further studies in this and related areas. |
| Assessment: | Up to 40 pages of written assignments (20%: two assignments worth 10% each, due mid and late in semester), a 3 hour written examination (80%, in the examination period). |
| Prescribed Texts: | TBA |
| Recommended Texts: | TBA |
| Breadth Options: | This subject is not available as a breadth subject. |
| Fees Information: | Subject EFTSL, Level, Discipline & Census Date |
| Generic Skills: | At the completion of this subject, students should gain: - Problem-solving skills (especially through tutorial exercises and assignments) including engaging with unfamiliar problems and identifying relevant 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 the analysis; - Through interactions with other students, the ability to work in a team. |
| Related Majors/Minors/Specialisations: |
R05 RM Master of Science - Mathematics and Statistics |
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