MATH3325 Analysis 3 Honours: Functional analysis, Spectral theory and Applications
Later Year Course
| Offered By | Department of Maths |
|---|---|
| Academic Career | Undergraduate |
| Course Subject | Mathematics |
| Offered in | Second Semester, 2010 and Second Semester, 2011 |
| Unit Value | 6 units |
| Course Description |
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: Measure theory- functions of bounded variation over R, absolute continuity and integration, examples of more general measures (Radon, Hausdorff, probability measures), Fubini-Tonelli theorem, Radon-Nikodym theorem. Banach spaces and linear operators - classical function and sequence spaces, Hahn-Banach theorem, closed graph and open mapping theorems, and uniform boundedness principles, sequential version of Banach-Alaoglu theorem, spectrum of an operator and analysis of the compact self-adjoint case, Fredholm alternative theorem. Note: This is an HPC. It emphasises mathematical rigour and proof and continues the development of modern analysis from an abstract viewpoint. |
| Learning Outcomes |
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 contexts2. 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 |
| Indicative Assessment |
Assessment will be based on:
|
| Workload |
36 lectures, tutorials by arrangement |
| Areas of Interest | Mathematics |
| Requisite Statement |
A mark of 60 or more in MATH3320. |
| Incompatibility |
with MATH3022. |
| Consent Required | Please contact MATHSadmin@maths.anu.edu.au for consent to enrol in this course |
| Science Group | C |
| Academic Contact | Andrew Hassell |
The information published on the Study at ANU 2010 website applies to the 2010 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2009 website.
