- Code MATH3325
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
All activities that form part of this course will be delivered remotely in Sem 2 2020.
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 wokshops (5%; LO 1-4)
- Take home exam (40%; LO 1-4)
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
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WorkloadThree lectures per week, workshops by arrangement.
Requisite and Incompatibility
Tuition fees are for the academic year indicated at the top of the page.
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- 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.
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