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Random Matrix Theory (MAST90103)
Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)
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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 - Dual-Delivery |
---|---|
Fees | Look up fees |
Random matrix theory is a diverse mathematical tool. It draws together ideas from linear algebra, multivariate calculus, analysis, probability theory, group and representation theory, differential geometry, combinatorics and mathematical physics. It also enjoys a wide number of applications, ranging from wireless communication in engineering, to time series analysis in statistics, quantum chaos and quantum field theory in physics, to the Riemann zeta function zeros and prime numbers in number theory. A self contained development of random matrix theory will be undertaken in this course from various viewpoints.
Topics to be covered include:
- Gaussian random matrix models and their application in likelihood analysis and modelling covariance matrices in time series analysis;
- eigenvalue densities and the concept of eigenvalue repulsion;
- classification of random matrices ensembles;
- derivation of Jacobians for matrix transformations such as diagonalisations;
- joint eigenvalue densities and correlation functions;
- orthogonal polynomials and the concept of determinantal point processes;
- supersymmetry and non-linear sigma-models;
- the log-gas picture;
- free probability theory and its application to matrix sums and products.
Intended learning outcomes
Upon completion of this subject, students should be able to:
- Identify the objectives of random matrix theory from the viewpoint of mathematical physics, and other areas of mathematics such as probability theory and mathematical statistics;
- Compute matrix Jacobians, apply the concepts of joint eigenvalue probability density functions, correlation functions, and spacing distributions, and understand their relevance to random matrix theory;
- Demonstrate comprehension of how the symmetry classification is related to matrix (Lie-)groups;
- Explain the basic ideas of the techniques of orthogonal polynomials, supersymmetry, loop equations, moment method and free convolutions in the analysis of random matrices; and
- Use integral transforms to study global and local statistical quantities.
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: 31 January 2024
Eligibility and requirements
Prerequisites
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST30021 | Complex Analysis |
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
|
12.5 |
Corequisites
None
Non-allowed subjects
None
Recommended background knowledge
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20004 | Probability |
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
|
12.5 |
MAST30031 | Methods of Mathematical Physics | Semester 2 (Dual-Delivery - 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: 31 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
1 written assignment – 20 hours of work required – early in the second half of the teaching period
| Second half of the teaching period | 20% |
1 written assignment – 20 hours of work required – late in the teaching period
| Late in the teaching period | 20% |
Written examination
| During the examination period | 60% |
Last updated: 31 January 2024
Dates & times
- Semester 1
Coordinator Mario Kieburg Mode of delivery Dual-Delivery (Parkville) Contact hours 36 hours consisting of 3 one hour lectures per week Total time commitment 170 hours Teaching period 28 February 2022 to 29 May 2022 Last self-enrol date 11 March 2022 Census date 31 March 2022 Last date to withdraw without fail 6 May 2022 Assessment period ends 24 June 2022 Semester 1 contact information
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
There are no specifically prescribed or recommended texts for this subject.
- 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.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 31 January 2024