Faculty of Science

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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.

Monash University

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences


Dr Zihua Guo and Dr Julie Clutterbuck



  • Second semester 2016 (Day)


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).


On completion of this unit students will be able to:

  1. Understand the basic topological properties of normed spaces, and their applications to problems in other areas of mathematics;

  1. Understand and appreciate some important basic theorems in analysis and their applications, such as the contracion mapping theorem and the Riesz representation theorem;

  1. Recognise the conditions for existence and uniqueness of solutions to the initial value problem for systems of ordinary differential equations;

  1. Communicate mathematical ideas and work in teams as appropriate for the discipline of mathematics.


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