Metric and Hilbert Spaces
Subject MAST30026 (2014)
Note: This is an archived Handbook entry from 2014.
|Dates & Locations:|| |
This subject is not offered in 2014.
|Time Commitment:||Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week |
Total Time Commitment:
Estimated total time commitment of 120 hours
Study Period Commencement:
and one of
Study Period Commencement:
Semester 1, Semester 2
|Recommended Background Knowledge:|| |
|Non Allowed Subjects:||
Students who have completed either of the following may not enrol in this subject for credit.
|Core Participation Requirements:||
For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry.
Third Year Coordinator
This subject provides a basis for further studies in modern analysis, geometry, topology, differential equations and quantum mechanics.It introduces the idea of a metric space with a general distance function, and the resulting concepts of convergence, continuity, completeness, compactness and connectedness. The subject also introduces Hilbert spaces: infinite dimensional vector spaces (typically function spaces) equipped with an inner product that allows geometric ideas to be used to study these spaces and linear maps between them.
Topics include: metric and normed spaces, limits of sequences, open and closed sets, continuity, topological properties, compactness, connectedness; Cauchy sequences, completeness, contraction mapping theorem; Hilbert spaces, orthonormal systems, bounded linear operators and functionals, applications.
On completion of this subject, students should understand:
and should be able to:
Two or three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
|Prescribed Texts:|| |
J. J. Koliha, Metrics, Norms and Integrals: An introduction to Contemporary Analysis, World Scientific, 2008
L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, 2nd Ed, Academic Press, 1999
E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, 1989
|Breadth Options:|| |
This subject potentially can be taken as a breadth subject component for the following courses:
You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
Mathematical Physics |
Pure Mathematics (specialisation of Mathematics and Statistics major)
Science credit subjects* for pre-2008 BSc, BASc and combined degree science courses
Science-credited subjects - new generation B-SCI and B-ENG.
Selective subjects for B-BMED
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