| Unit name | Random Matrix Theory |
|---|---|
| Unit code | MATH30033 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Professor. Mezzadri |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
Year 2 Theoretical Physics or MATH20015 Multivariable Calculus. |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Why is this unit important?
Random Matrix Theory is concerned with the study of the statistical properties of the spectra and of other invariants of matrices whose entries are random variables distributed according to certain probability laws. It is often used to study systems whose detailed mathematical description is either not known or too complicated to allow any kind of successful approach. It is remarkable and fascinating that predictions obtained with techniques from Random Matrix Theory have turned out to be accurate in a wide range of fields: statistical mechanics, quantum chaos, nuclear physics, number theory, combinatorics, machine learning, wireless telecommunications and structural dynamics, to name only few examples. In many cases, the underlying reasons of the connections between Random Matrix Theory and other areas of mathematics and physics are still not understood.
How does this unit fit into your programme of study
This unit complements other courses offered in the School of Mathematics and provides useful background to the level M/7 Quantum Chaos. It has relations to the level H/6 units Quantum Mechanics, Statistical Mechanics. The course will appeal to students from a broad range of backgrounds, in applied and pure mathematics as well as in statistics.
Content overview
The unit will place particular emphasis on the statistics of the eigenvalues of ensembles of unitary and Hermitian matrices, including the Wigner semicircle law for the density of the eigenvalues for the Gaussian Unitary Ensemble, the Gaudin-Mehta distribution and the Tracy-Widom distribution. It will also cover orthogonal polynomials techniques to compute spectral correlations. Different ensembles have distinct invariance properties, which in applications are used to model systems whose physical or mathematical behaviour depends only on their symmetries. In some cases the dimension of the matrices will be treated as a large asymptotic parameter. There will be a general discussion about how this relates to current research in various fields of mathematics and physics.
How will the students, personally, be different as a result of the unit
At the end of the unit the students will have improved their logical thinking and have increased the range and scope of their problem-solving techniques.
Learning Outcomes
After completing this unit successfully, the student should be able to:
The unit will be taught through a selection of lectures, online materials, independent activities such as problem sheets and other exercises, problem classes, support sessions and office hours.
Tasks which help you learn and prepare you for summative tasks (formative):
Guided asynchronous independent activities such as problem sheets and/or other exercises.
Tasks which count towards your unit mark (summative):
80% Timed examination 20% Coursework.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
When assessment does not go to plan
If you fail this unit and are required to resit. Reassessment is by a written examination in the August/September Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH30033).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
