• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Classification Advanced
Specialist
• Course subject Mathematics
• Academic career PGRD
• Course convener
• AsPr John Urbas
• Dr Andrew Hassell
• Mode of delivery In Person
• Offered in Second Semester 2015
Analysis 3: Functional Analysis, Spectral theory and Applications (MATH6214)

This course is intended both for continuing mathematics students 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
• 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: Graduate students attend joint classes with undergraduates but will be assessed separately.

## 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:

• Three assignments (30% total; LO 1-4)
• Essay paper (20%; LO 1-4)
• Take home exam (50%; 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.

## Workload

36 lectures, tutorials by arrangement

## Requisite and Incompatibility

You will need to contact the Department of Mathematics to request a permission code to enrol in this course.

## 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. 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:
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
2015 \$3096
International fee paying students
Year Fee
2015 \$4146
Note: Please note that fee information is for current year only.

## 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.

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
1791 20 Jul 2015 07 Aug 2015 31 Aug 2015 30 Oct 2015 In Person N/A

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions