• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr Scott Morrison
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2014
Analysis 3 Honours: Functional analysis, Spectral theory and Applications (MATH3325)

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.

## Learning Outcomes

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

## Indicative Assessment

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)

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

36 lectures, tutorials by arrangement

## Requisite and Incompatibility

To enrol in this course you must have successfully completed MATH3320 with a mark of 60 or above. You are not able to enrol in this course if you have previously completed MATH3022.

## Fees

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. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
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.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee
1994-2003 \$1650
2004 \$1926
2005 \$2298
2006 \$2520
2007 \$2520
2008 \$2916
2009 \$2916
2010 \$2916
2011 \$2946
2012 \$2946
2013 \$2946
2014 \$2946
International fee paying students
Year Fee
1994-2003 \$3390
2004 \$3450
2005 \$3450
2006 \$3618
2007 \$3618
2008 \$3618
2009 \$3618
2010 \$3750
2011 \$3756
2012 \$3756
2013 \$3756
2014 \$3762
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
7322 21 Jul 2014 01 Aug 2014 31 Aug 2014 30 Oct 2014 In Person N/A