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Measure Theory (MAST90012)
Graduate courseworkPoints: 12.5On Campus (Parkville)
To learn more, visit 2023 Course and subject delivery.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Overview
Availability | Semester 1 |
---|---|
Fees | Look up fees |
Measure Theory introduces the modern conceptual framework of analysis that has led to a transformation and generalisation of such basic objects as functions, and such notions as continuity, differentiability and integrability.
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 the core topics of Lebesgue's theory of integration, and abstract measure theory, in particular signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative. Additional topics may include rudiments of probability theory (conditional expectation, Borel sets and measures) and geometric analysis (rectifiable curves, Hausdorff measure and dimension).
Intended learning outcomes
On completion of 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;
- Understand how these underpin the use of mathematical concepts such as volume, area, and integration;
- 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;
- Ttime-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 31 January 2024
Eligibility and requirements
Prerequisites
All of
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 |
Or equivalent
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: 31 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Continuing assessesment taking up to 40 hours, and worth 40% of the mark, throughout the semester.
| Throughout the semester | 40% |
A written examination
| During the examination period | 60% |
Last updated: 31 January 2024
Dates & times
- Semester 1
Coordinator Brian Krummel Mode of delivery On Campus (Parkville) Contact hours Total time commitment 170 hours Teaching period 27 February 2023 to 28 May 2023 Last self-enrol date 10 March 2023 Census date 31 March 2023 Last date to withdraw without fail 5 May 2023 Assessment period ends 23 June 2023 Semester 1 contact information
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
Elias M. Stein & Rami Shakarchi, Real analysis : measure theory, integration, and Hilbert spaces Princeton lectures in Analysis, Vol III, Princeton University Press, 2005.
Terence Tao, An introduction to measure theory, Graduate Studies in Mathematics, AMS, 2011.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - 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.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 31 January 2024