- Code MATH3325
- Unit Value 6 units
This course is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.
Topics to be covered include:
Hilbert spaces - bounded linear operators, compact operators, the spectral theorem for compact self-adjoint operators; Fourier transform, applications to partial differential equations and the central limit theorem.
Measure theory - abstract measure theory, integration, Fubini-Tonelli theorem, Radon-Nikodym theorem, Hausdorff measure, fractals.
Banach spaces and linear operators - basic properties, Baire category theorem and its consequences (uniform boundedness principle, closed graph and open mapping theorems), Hahn-Banach theorem and dual spaces, sequential version of Banach-Alaoglu theorem, dual spaces of L^p spaces and spaces of continuous functions. Applications to Fourier series, fractals.
Note: This is an HPC. It emphasises mathematical rigour and proof and continues the development of modern analysis from an abstract viewpoint.
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, students will have the knowledge and skills to:
1. Explain the fundamental concepts of functional analysis and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of functional analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from functional analysis
4. Apply problem-solving using functional analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts
Assessment will be based on:
- Four assignments (40% total; LO 1-4)
- Essay paper (15%; LO 1-4)
- Attendance and participation in lectures and tutorials (5%; LO 1-4)
- Take home exam (40%; LO 1-4)
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36 lectures, tutorials by arrangement
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|1788||20 Jul 2015||07 Aug 2015||31 Aug 2015||30 Oct 2015||In Person||N/A|