Undergraduate Study

AMH2   Advanced Methods of Mathematical Physics

General Information

This page relates to the Applied Mathematics Honours course "Advanced Methods of Mathematical Physics".

Lecturer for this course: Nalini Joshi.

For general information on honours in the School of Mathematics and Statistics, refer to the relevant honours handbook.

Advanced Methods of Mathematical Physics

An Honours Course in Applied Mathematics

Nalini Joshi

Information Sheet

Further reading Assessments
Week 1
  • Mathematical appendices a, Ref [4];
  • Chapter 2, Ref [3].
  • Useful site for special functions: DLMF
Week 2
  • See Ref [5] for more details on Random Matrix Theory.
Week 3
  • Ref [1] has more details on how orthogonal polynomials arise in quantum field theory.
Week 4 Assignment 1 released. Revised on 29Aug19 to include the word "monic" in the first line. Revised on 31Aug19 to correct the interval of integration and remove the unnecessary x. The due date has been extended.
Week 5
Week 6
  • Further details of symmetry groups associated with Painlevé equations appear in Ref [6].
Assignment 1 was due on 14 September 2019. Solutions can be found here.
Week 7
Week 8 Assignment 2 was released.
Week 9
  • See Ref [2] for more information about Riemann-Hilbert problems.
Assignment 2 was due on 12 October 2019.
Week 10
Week 11
  • See Chapter 7 of Ref [3], specially Section 7.2, for examples of algebraic entropy in dynamical systems.
Lectures in Weeks 11 and 12 will be given by Dr Giorgio Gubbiotti.
Week 12 Assignment 2 was due on 12 October 2019. Solutions can be found here.
During 14-18 November 2019 The take-home exam was released at 11:59pm 14 November and was due at 10:00am on 18 November 2019.

Useful references:

  1. D. Bessis, C. Itzhykson, JB Zuber, Quantum field theory techniques in graphical enumeration, Advances in Applied Math, 1, 109-157, 1980.
  2. P. Deift, Orthogonal Polynomials and Random Matrices: a Riemann-Hilbert approach , Courant Institute of Mathematical Sciences and American Mathematical Society, 1998.
  3. J. Hietarinta, N. Joshi, F. Nijhoff, Discrete Systems and Integrability, Cambridge University Press, 2016.
  4. L. Landau, L. Lifshitz, Quantum Mechanics: Non-relativistic Theory, Pergamon Press, 3rd edn, 1977.
  5. M. Mehta, Random Matrices and the Statistical Theory of Energy Levels, Academic Press, 1967.
  6. M. Noumi, Painleve equations through symmetry, American Mathematical Society, 2004.



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