Handbook 1996 : Faculty of Science (Volume 4 page 212)
Mathematics subject : Next:618-311 | Prev:618-301 | Search | Help
Credit points: 15.0
Coordinator: Dr K Ecker
Prerequisite: Mathematics 618-301
Contact: 39 lectures (three a week)
Timetable: Second semester
Objectives:
On completion of this subject, students should:Comprehend:
- fundamental concepts about measures and Lebesgue integration with respect to a variety of measures;
- how basic concepts of linear algebra can be generalized to infinite dimensional situations using techniques from analysis;
- how these concepts arise in many branches of mathematics, as for example, in partial differential equations, operations research and probability, but also in areas of theoretical physics such as quantum mechanics.
Have developed:
- the ability to give rigorous mathematical arguments at an advanced level; to apply abstract concepts to solving problems in other areas of mathematics such as differential equations.
Appreciate:
- the necessity for a rigorous theoretical foundation of concepts used frequently in mathematics and physics.
Content:
Linear spaces and operators Normed and inner product spaces, Hilbert spaces, abstract Fourier series; linear functionals and operators; dual spaces. Measure and integration Introduction to measure and integration; dominated convergence and applications.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
Mathematics subject : Next:618-311 | Prev:618-301 | Search | Help
Handbook 1996 : Faculty of Science (Volume 4 page 212)
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.