Overview
MATH5605 is a Honours and Postgraduate coursework Mathematics course. It is a core course for all Pure Mathematics Honours students. See the course overview below.
Units of credit: 6
Cycle of offering: Term 2
Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.
More information: The Course outline will be made available closer to the start of term - please visit this website: www.unsw.edu.au/course-outlines
This course outline contains information about course objectives, assessment, course materials and the syllabus.
Important additional information as of 2023
UNSW Plagiarism Policy
The University requires all students to be aware of its policy on plagiarism.
For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.
If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.
The Online Handbook entry contains contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)
If you are currently enrolled in MATH5605, you can log into UNSW Moodle for this course.
Course overview
This course can be thought of as a continuation of Higher Analysis MATH3611. Functional analysis a central pillar of modern analysis, and we will cover its foundations.
The main emphasis will be on the study of the properties of bounded linear maps between topological linear spaces of various kinds. This provides the basic tools for the development of such areas as quantum mechanics, harmonic analysis and stochastic calculus. It also has a very close relation to measure and integration theory (MATH5825).
Detailed course schedule
- Normed linear spaces, bounded operators, Banach spaces.
- Functionals and Hahn-Banach theorems.
- The Baire-category theorem, the principle of uniform boundedness, the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem.
- Hilbert space theory; orthonormality, the Riesz representation theorem, projections, convexity.
- Operators on Hilbert spaces, normal and selfadjoint operators, spectrum and resolvent, Spectral mapping theorem.
- Compact operators, their spectral data, the spectral theorem.