units
MTH3160
Faculty of Science
This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.
6 points, SCA Band 2, 0.125 EFTSL
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
Faculty
Organisational Unit
School of Mathematical Sciences
Coordinator(s)
Dr Zihua Guo and Dr Julie Clutterbuck
Offered
- Second semester 2016 (Day)
Synopsis
In this unit we develop the theory of Banach spaces. Topics covered include a basic introduction to normed spaces, topology in Banach spaces, dual spaces, continuous linear mappings between Banach spaces, weak convergence and weak compactness in separable Banach spaces, Hilbert spaces and the Riesz representation theorem. Applications of these theories may include the contraction mapping theorem and its usage to prove the Cauchy-Lipschitz theorem (existence and uniqueness of solution to ordinary differential equations).
Outcomes
On completion of this unit students will be able to:
- Understand the basic topological properties of normed spaces, and their applications to problems in other areas of mathematics;
- Understand and appreciate some important basic theorems in analysis and their applications, such as the contracion mapping theorem and the Riesz representation theorem;
- Recognise the conditions for existence and uniqueness of solutions to the initial value problem for systems of ordinary differential equations;
- Communicate mathematical ideas and work in teams as appropriate for the discipline of mathematics.
Assessment
Projects (two): 20%
Weekly assignments (10): 10%
Final examination (three hours): 70%
Workload requirements
Three 1-hour lectures and one 1-hour support class per week
See also Unit timetable information
Chief examiner(s)
This unit applies to the following area(s) of study
Prerequisites
On our site
Authorised by: Manager, Curriculum and Publications.
Maintained by: Curriculumn and Publications.
Last updated: 18 September 2017.
Copyright © 2024 Monash University. ABN 12 377 614 012 -
Accessibility -
Caution -
Privacy
Monash University CRICOS Provider Number: 00008C, Monash College CRICOS Provider
Number: 01857J
We acknowledge and pay respects to the Elders and Traditional Owners of the land on which our Australian campuses stand. Information for Indigenous Australians