MATH6214 Analysis 3: Functional Analysis, Spectral theory and Applications

Offered By	Department of Mathematics
Academic Career	Graduate Coursework
Course Subject	Mathematics
Offered in	Second Semester, 2011 and Second Semester, 2012
Unit Value	6 units
Course Description	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	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)
Workload	36 lectures, tutorials by arrangement
Course Classification(s)	AdvancedAdvanced courses are designed for students having reached 'first degree' level of assumed knowledge, which provide a deep understanding of contemporary issues; or 'second degree' and higher levels of knowledge; or for transition to research training programs. and SpecialistSpecialist courses are designed for students having reached 'first degree' level of assumed knowledge, which provide for the acquisition of specialist skills; or 'second degree' and higher level of knowledge; or for transition to research training programs; or knowledge associated with professional accreditation.
Eligibility	Bachelor degree; with third year Mathematics.
Requisite Statement	Third year Mathematics required.
Consent Required	Please contact MATHSadmin@maths.anu.edu.au for consent to enrol in this course.
Programs	Master of Mathematical Sciences and Master of Mathematical Sciences
Academic Contact	MATHSadmin@maths.anu.edu.au

The information published on the Study at ANU 2011 website applies to the 2011 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2010 website.