Random Matrix Theory (MAST90103)
Graduate courseworkPoints: 12.5On Campus (Parkville)
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
Random matrix theory is a diverse topic in mathematics. It draws together ideas from linear algebra, multivariate calculus, analysis, probability theory and mathematical physics, amongst other topics. It also enjoys a wide number of applications, ranging from wireless communication in engineering, to quantum chaos in physics, to the Reimann zeta function zeros in pure mathematics. A self contained development of random matrix theory will be undertaken in this course from a mathematical physics viewpoint. Topics to be covered include Jacobians for matrix transformation, matrix ensembles and their eigenvalue probability density functions, equilibrium measures, global and local statistical quantities, determinantal point processes, products of random matrices and Dyson Brownian motion.
Intended learning outcomes
After completing this subject students should:
- have learned what are the objectives of random matrix theory from the viewpoint of mathematical physics, and other areas of mathematics such as probability theory and mathematical statistics;
- appreciate the application of matrix Jacobians, diffusion equations, equilibrium measures and loop equations in the analysis of random matrices;
- understand the concepts of joint eigenvalue probability density functions, correlation functions, and spacing distributions, and their relevance to random matrix theory;
- be familiar with the uses of transforms to study global properties and orthogonal polynomials to study local statistical quantities;
- have the ability to pursue further studies in these 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
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30021 | Complex Analysis |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
Corequisites
None
Non-allowed subjects
None
Recommended background knowledge
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20004 | Probability |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
| MAST30031 | Methods of Mathematical Physics | Semester 2 (On Campus - Parkville) |
12.5 |
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
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
| Description | Timing | Percentage |
|---|---|---|
2 written assignments totalling 50 pages (approximately the equivalent of 1000 words) due near the mid and end of the semester
| Second half of the teaching period | 40% |
Written examination
| During the examination period | 60% |
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator Mario Kieburg Mode of delivery On Campus (Parkville) Contact hours 36 hours consisting of 3 one hour lectures per week Total time commitment 170 hours Teaching period 2 March 2020 to 7 June 2020 Last self-enrol date 13 March 2020 Census date 30 April 2020 Last date to withdraw without fail 5 June 2020 Assessment period ends 3 July 2020 Semester 1 contact information
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (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.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022