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Measure Theory (MAST90012)
Graduate courseworkPoints: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Email: lreeves@unimelb.edu.au
Overview
Availability | Semester 1 |
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Fees | Look up fees |
Measure Theory formalises and generalises the notion of integration. It is fundamental to many areas of mathematics and probability and has applications in other fields such as physics and economics. Students will be introduced to Lebesgue measure and integration, signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative, conditional expectation, Borel sets and standard Borel spaces, product measures, and the Riesz representation theorem.
Intended learning outcomes
After completing this subject, students will understand the fundamentals of measure theory and be acquainted with the proofs of the fundamental theorems underlying the theory of integration. They will also have an understanding of how these underpin the use of mathematical concepts such as volume, area, and integration and they will develop a perspective on the broader impact of measure theory in ergodic theory and have the ability to pursue further studies in this and related areas.
Generic skills
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:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
Both of the following subjects, or equivalent:
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20022 | Group Theory and Linear Algebra | Semester 2 (On Campus - Parkville) |
12.5 |
MAST30026 | Metric and Hilbert Spaces | Semester 2 (On Campus - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Additional details
Up to 40 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3-hour written examination (60%, in the examination period).
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator Lawrence Reeves Mode of delivery On Campus (Parkville) Contact hours 36 hours comprising three 1-hour lectures per week Total time commitment 170 hours Teaching period 27 February 2017 to 28 May 2017 Last self-enrol date 10 March 2017 Census date 31 March 2017 Last date to withdraw without fail 5 May 2017 Assessment period ends 23 June 2017 Semester 1 contact information
Email: lreeves@unimelb.edu.au
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
W. Rudin. Real and Complex Analysis. McGraw – Hill. Third Edition. 1987.
P. Halmos. Measure Theory. Springer. 1974. - Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Course Ph.D.- Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022