Click on the course title to view notes and other information (where applicable).

Basic courses

• Advanced Computational Methods in Statistics (STATS)
  Tutor: Dr N. Kantas, Imperial (2020-2021)
  (See 'Advanced Courses' for an advanced version of this course.)

• Algebraic Curves (PURE)
  Tutor: Professor Nicholas Shepherd-Barron, KCL (2015-2016)

• Algebraic Geometry (PURE)
  Tutor: Dr Ivan Tomasic, QMUL (2012-2013 / 2013-2014 / 2014-2015)  Abstract [PDF 35KB]

• Algebraic Number Theory (PURE)
  Tutor: Dr Manuel Breuning, KCL (2007-2008 / 2008-2009) Abstract [PDF 43KB]

• Algebraic Topology (PURE)
  Tutor: Professor Luke Hodgkin, KCL (2009-2010 / 2010-2011 / 2011-2012) Abstract [PDF 19KB]

• Analytical Methods (APPLIED)
  Tutors:
  Dr Helen Wilson, UCL Maths (2007-2008 / 2008-2009 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015)
  Professor Rod Halburd, UCL Maths (2018-2019)
  Dr Nick Ovenden, UCL Maths (2009-2010 / 2015-2016 / 2016-2017 / 2017-2018 / 2019-2020 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025)  

• An Introduction to the Finite Classical Groups (PURE)                                                                                Tutor: Dr Nick Gill, Open University (2024-2025)

• Applied Bayesian Methods (STATS)
  Tutors:
  Dr Shaun Seaman, UCL Stats (2007-2008 / 2008-2009 / 2009-2010)
  Dr Jing-hao Xue, UCL Stats (2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015 / 2015-2016 / 2017-2018 / 2018-2019)
  Dr Petros Dellaportas, UCL Stats (2016-2017 / 2019-2020 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025) Applied Bayesian Methods Abstract [PDF 17KB]

• Applications of Complex Analysis (APPLIED)
  Tutor: Professor Rod Halburd, UCL (2021-2022 / 2022-2023)  Applications of Complex Analysis Abstract [PDF 7KB]

• Applications of Differential Geometry to Mathematical Physics (APPLIED)
  Tutors: Professor Andy Hone, Kent, and Dr Steffen Krusch, Kent (2016-2017 / 2018-2019 / 2024-2025)

• Applied Computational Methods (APPLIED)
  Tutors:
  Professor Norbert Heuer, Brunel (2007-08)
  Professor Sergey Mikhailov, Brunel (2008-09)  Abstract [DOC 28KB]

• Bio-Mathematics (APPLIED) [PDF 2,622KB] Abstract [PDF 19KB]                                                                                              Tutor: Dr Stephen Baigent, UCL Maths (2007-2008 / 2008-2009 / 2009-2010 / 2010-2011 / 2011-2012)

   (See 'Advanced Courses' for an advanced version of this course.)                                                                                                    Tutor: Professor Cho-Ho Chu, QMUL (2007-2008 / 2008-2009 / 2009-2010 / 2012-2013)

• Class Field Theory (PURE)
  Tutor: Dr Mahesh Kakde, KCL (2016-2017 / 2017-2018)

• Complex Systems Dynamics (APPLIED)
  Tutors:
  Dr Hannah Fry, UCL Maths (2011-2012 / 2013-2014)
  Dr Vasiliki Evdoridou, OU (2018-2019)

• Differential Geometry & Mathematical Physics (APPLIED)
  Tutors: Dr Steffen Krusch / Prof. Andrew Hone, University of Kent (2022-2023)

• Dynamical Functional Equations and their Applications
  Tutor: Dr Ben Mestel, OU (2019-2020) 

• Dynamical Systems (APPLIED)
  Tutors:
  Professor David Arrowsmith, QMUL (2007-2008) with Dr Rainer Klages, QMUL (2008-2009)
  Dr Rainer Klages, QMUL (2009-2010)
  Dr Wolfram Just, QMUL (2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015)
  Professor Franco Vivaldi, QMUL (2015-2016 / 2016-2017 / 2017-2018 / 2018-2019)

• Elliptic Operators and Index Theorem (Part 1) (PURE) (See Part 2 under Advanced Courses)
  Tutor: Professor Michael Singer, UCL Maths (2017-2018)

• Exact Solution Methods for Differential Equations (APPLIED)
  Tutor: Professor Rod Halburd, UCL Maths (2017-2018)

• Finite Elements (APPLIED)
  Tutor: Dr Matthias Maischak, Brunel (2013-2014 / 2014-2015)

• Finite Simple Groups (PURE)
  Tutor: Professor Robert Wilson, QMUL (2007-2008 / 2008-2009 / 2009-2010) 

• Fundamental Theory of Statistical Inference (STATS)
  Tutor: Professor Alastair Young, Imperial (2007-2008 / 2008-2009 / 2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015 / 2015-2016 / 2016-2017 / 2017-2018 / 2018-2019 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025)
  FTSI Abstract [PDF 32KB]

• Galois Representation (PURE)
  Tutor: Professor F. Diamond, KCL (2016-2017 / 2018-2019)

• Geometric Group Theory (PURE)
  Tutor: Professor Ian Chiswell, QMUL (2010-2011 / 2011-2012) 

• Geometric Measure Theory (PURE)
  Tutor: Dr Toby O'Neil, OU (2016-2017)

• Graph Theory  (PURE)
  Tutors:
  Professors Graham Brightwell and Jan van den Heuvel, LSE (2007-2008) with Dr Jozef Skokan (2008-2009 / 2009-2010 / 2010-2011)
  Professor Jan van den Heuvel and Dr Jozef Skokan (2011-2012 / 2012-2013 / 2013-2014)
  Professor Jan ven den Heuvel and Dr Peter Allen (2014-2015 / 2015-2016)
  Dr Peter Allen, LSE (2016-2017 / 2017-2018 / 2018-2019 / 2019-2020)
  Professor J. Boettcher, LSE (2021-2022)
  Professor Jan van den Heuvel / Dr Yani Pehova (2022-2023)
  Professor Peter Allen, LSE (2023-2024 / 2024-2025)

• Homological Algebra
  Tutor:  Professor Markus Linckelmann, QMUL (2019-2020 / 2022-2023 / 2023-2024)

• 1617 Internal Fluid Dynamics ABSTRACT [PDF 887KB] Notes
  Tutor: Professor Frank Smith, UCL Maths (2012-2013)

• Introduction to Applied Topology
  Tutor: Dr Primoz Skraba, QMUL (2019-2020) 

• Introduction to Boundary Integral Equations (APPLIED)
  Tutor: Dr Timo Beckte, UCL (2016-2017)

• Introduction to Elliptic Operators and the Index Theorem (PURE)
  Tutor: Professor Michael Singer, UCL (2016-2017)

• Introduction to Harmonic Analysis
  Tutor: Professor Sasha Sodin, QMUL (2019-2020 / 2021-2022)

• Introduction to Random Topology

• Kaehler and HyperKaehler Geometry 
  Tutor: Professor Michael Singer, UCL (2018-2019)

• Lagrangian Torus Fibrations (PURE) 
  Tutor: Dr Jonny Evans, UCL (2018-2019)

• Lie Group Actions on Manifolds (PURE)
  Tutor: Professor Jurgen Berndt, KCL (2016-2017)

• Mathematical Aspects of Quantum Computing (PURE)
  Tutor: Professor Shahn Majid, QMUL (2021-2022 / 2022-2023) Mathematical Aspects of Quantum Computing Abstract [PDF 8KB]

• Mathematical Biology
  Tutor: Dr Philip Pearce, UCL (2023-2024 / 2024-2025) Mathematical Biology Abstract [PDF 194KB]

• Maximum Entropy Models of Complex Networks (APPLIED)
  Tutor: Professor Ginestra Bianconi, QMUL (2019-2020 / 2021-2022)

• Measure and Category Measure and Category (PURE) [PDF 381KB]
  Tutor: Professor Marianna Csornyei, UCL Maths (2007-2008 / 2008-2009)

• Measure Theory
  Tutor: Dr Robert Simon, LSE (2018-2019 / 2019-2020 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025)

• Measure-thereotic Probabilty (STATS)
  Tutors:
  Professor Nick Bingham, Imperial (2007-2008 / 2008-2009 / 2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015 / 2015-2016 / 2016-2017 / 2017-2018 / 2018-2019)
  Professor Alexander Gnedin, QMUL (2019-2020 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025)

• Minimal Surfaces (PURE)
  Dr Giuseppe Tinaglia, KCL (2015-2016)

• Models (APPLIED)
  Tutor: Dr Oliver Kerr, City (2007-2008 / 2008-2009 / 2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015 / 2015-2016 / 2016-2017 / 2017-2018 / 2018-2019 / 2019-2020 / 2021-2022)

• Morse theory, topology and robotics (Basic)
  Tutor: Professor Michael Farber, QMUL (2022-2023 / 2023-2024 / 2024-2025) Morse theory, topology and robotics Abstract [PDF 115KB]

• Orthogonal Polynomials and Special Functions
  Tutor: Dr Ana Loureiro, Kent (2023-2024)  Orthogonal Polynomials and Special Functions Abstract [PDF 38KB]

• P-adic analysis (PURE)
  Tutor: Dr Shu Sasaki, KCL (2010-2011/2011-2012)

• P-adic numbers p-adic numbers (PURE) [PDF 258KB]
  Tutor: Dr Manuel Breuning, KCL (2009-2010)

• Potential Theory (PURE) [PDF 350KB] Abstract [PDF 36KB]
  Tutor: Professor Boris Khoruzenko, QMUL (2010-2011 / 2011-2012)

• Pseudo-differential operators and applications to PDEs 
  Tutor: Dr Claudia Garetto, QMUL (2022-2023 / 2023-2024) Pseudo-differential operators and applications to PDEs Abstract [PDF 12KB]                                                                          Tutor: Professor Michael Ruzhansky, QMUL (2024-2025)                             

• Representation Theory (PURE)
  Tutors:
  Dr Anton Cox, City (2012-2013)
  Dr M Linckelmann, City (2013-2014 / 2014-2015)
  Dr Matthew Fayers, QMUL (2015-2016 / 2016-2017 / 2017-2018)
  Dr John Bray, QMUL (2018-2019)                                                                                                                                                  (An advanced version of this course has also been offered, please see 'Advanced Courses'.)

• Representation Theory of Compact Lie Groups
  Tutor: Professor Michael Singer, UCL (2019-2020)

• Representation Theory of Finite Groups
  Tutor: Dr Yusra Naqvi, UCL (2023-2024) Representation Theory of Finite Groups 2023-2024 Course Abstract [PDF 61KB] 

• Representation Theory of p-adic Groups
  Tutor: Dr James Newton, KCL (2019-2020)

• Riemann Surfaces (PURE)
  Tutors: Dr John Armstrong, KCL (2012-2013)
  Dr Giuseppe Tinaglia, KCL (2013-2014) Abstract [PDF 55KB]

• Statistical Modelling and Estimation (STATS)
  Tutors: Professor Steven Gilmore, QMUL (2007-2008/2008-09)
  Dr Heiko Grossmann, QMUL (2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015) Abstract [PDF 20KB]

• Stochastic Processes (STATS)
  Tutors:
  Professor Valerie Isham, UCL Stats (2007-2008 / 2008-2009)
  Dr James Nelson, UCL Stats (2009-2010 / 2010-2011 / 2011-2012 / 2013-2014 / 2014-2015 / 2015-2016 / 2016-2017)
  Dr Codina Cotar, UCL Stats (2012-2013)
  Professor Maria De Iorio, UCL Statistics (2017-2018)
  Dr Ardo van den Hout, UCL Statistics (2018-2019 / 2019-2020)
  Dr Terry Soo, UCL (2021-2022 / 2022-2023 / 2023-2024 / 2024-2025)

• Symmetry Methods for Differential Equations (STATS)
  Tutor: Professor Peter Clarkson, Kent (2015-2016 / 2018-2019 / 2022-2023 / 2024-2025) Abstract [PDF 66KB]

• Theory or Linear Models (STATS)
  Tutor: Professor Steven Gilmour, KCL (2018-2019 / 2019-2020)                                                                                                        Tutor: Dr Kalliopi Mylona, KCL (2021-2022 / 2022-2023 / 2024-2025)

• Theory of Minimal Surfaces (PURE)
  Tutor: Dr Giuseppe Tianglia, KCL (2014-2015)

• Time Series Analysis
  Tutor: Dr Yining Chen, LSE Statistics (2022-2023 / 2023-2024 / 2024-2025) Time Series Analysis Abstract [PDF 20KB]

• Variational and Computational Methods for PDEs (APPLIED) [PDF 283KB]                                                                              Tutor: Professor Sergey Mikhailov, Brunel (2009-2010 / 2010-2011 / 2020-2021)

• Wave Scattering and Resonances (APPLIED)
  Tutor: Dr Dmitry Savin, Brunel (2012-2013 / 2013-2014 / 2015-2016 / 2017-2018 / 2019-2020)
  
  

 

Advanced courses

• Ads/CFT Correspondence (APPLIED) 
  Tutor: Dr Bogdan Stefanski, City (2009-2010)

• Advanced Computational Methods (APPLIED)
  Tutor: Dr Matthias Maischak, Brunel (2008-2009)

• Advanced Computational Methods in Statistics (STATS)
  Tutors:
  Dr Axel Gandy, Imperial (2008-2009 / 2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2013-2014 / 2014-2015 / 2015-2016)
  Dr Nikolas Kantas, Imperial (2016-2017 / 2017-2018 / 2018-2019 / 2019-2020 / 2022-2023 / 2023-2024)
  Dr Deniz Akyildiz, Imperial (2024-2025)

• Algebraic Statistics
  Tutor: Professor Henry Wynn, LSE (2008-2009) Abstract [PDF 35KB]

• Algebraic cycles of with applications to motives
  Tutor:  Dr Owen Patashnick, KCL (2023-2024)  Abstract [PDF 92KB]

• An Introduction to Ergodic Theory and Topological Dynamics
  Tutor: Dr R. Yassawi, OU (2021-2022) Abstract [PDF 92KB]

• An Introduction to Birational Geometry
  Tutor: Professor Paolo Cascini, Imperial (2021-2022)

• Aperiodic Order
  Tutor: Professor Uwe Grimm, OU (2014-2015)

• Applications of Differential Geometry to Mathematical Physics (2008-2009 / 2010-2011 / 2012-13)
  Tutors: Professor Andrew Hone, and Dr Steffen Krusch and G Brown, Kent Abstract [PDF 41KB]

• Asymptotic Analysis and Statistical Applications 
  Tutor: Dr Heather Battey, Imperial (2018-2019 / 2019-2020 / 2021-2022 / 2022-2023)

• Arithmetic Statistics (PURE)
  Tutor: Dr Christopher Keyes, KCL (2024-2025)

• Bayesian Adaptative Methods for Clinical Trials [DOC 20KB]
  Tutor: Dr Leonardo Bottolo, Imperial (2013-2014)

• Bayesian Hierarchical Models (STATS)
  Tutor: Dr Leondardo Bottolo, Imperial (2014-2015)

• Beilinson's Conjectures
  Tutor: Dr Oli Gregory, Imperial (2023-2024) Abstract [PDF 90KB]

• Big Data and Statistical Methods (STATS) 
  Tutor: Dr Mark Briers, Imperial (2018-2019)

• Birational Geometry (PURE)
  Tutor: Dr Calum Spicer, KCL (2022-2023 / 2023-2024 / 2024-2025) Birational Geometry Abstract [PDF 64KB]

• Black Holes
  Tutor: Dr Rod Halburd, UCL (2023-2024) Abstract [PDF 106KB]

• Boundary Integral Elements (APPLIED)
  Tutor: Dr Timo Betcke, UCL (2014-2015)

• Calibrated Geometry and Geometric Flows 
  Tutor: Dr J. Lotay, UCL (2016-2017)

• Calibrated Submanifolds 
  Tutor: Dr. Lorenzo Foscolo, UCL (2022-2023)

• The Classical Moment Problem (PURE)                                                                                                                                              Tutor: Professor A. Sodin, QMUL (2017-2018)

• Cohomology of Groups (PURE)                                                                                                                                                          Tutor: Professor Brita Nucinkis, RHUL (2017-2018 / 2019-2020)

• Combinatorial optimisation: packing, partitioning, and covering
  Tutor: Dr Ahmad Abdi, LSE Maths (2022-2023)

• Complex Analysis
  Tutor: Professor Rod Halburd, UCL Maths  (2011-2012 / 2013-2014 / 2015-2016)                                                        Abstract [PDF 67KB]

• Constant Mean Curvature
  Tutor: Dr Giuseppi Tinaglia, KCL (2011-2012)

• The Cremona Group (PURE)                                                                                                                                                                Tutor: Professor Nicholas Shepherd-Barron, KCL (2017-2018)

• Cryptography and Mathematics 
  Tutor: Professor Norman Biggs, LSE (2008-2009 / 2010-2011) Abstract [DOC 57KB]

• C* Algebras (PURE) (See 'Basic Courses' for a basic version of this course.)                                                                             Tutor: Dr Xin Li, QMUL (2017-2018 / 2018-2019)

• Design of Experiments (STATS)
  Tutor: Dr Steven Gilmour, Dr Kalliopi Mylona and Dr Vasiliki Koutra, KCL (2024-2025)                                                                    

• Differential Equations with Delay and Applications to Mathematical Biology (APPLIED)
  Tutor: Dr Jacques Furter, Brunel (2014-2015 / 2016-2017) Abstract [PDF 19KB]

• Distribution and Fourier Transforms 
  Tutor: Professor Yuri Safarov, KCL (2011-2012 / 2013-2014)                                                                                                Abstract [PDF 46KB]

• Dynamical Functional Equations and their Applications (APPLIED)
  Tutor: Dr Ben Mestel, OU (2016-2017)

• Dynamical Systems in Cosmology (APPLIED)
  Tutor: Dr Christian Boehmer, UCL Maths (2014-2015 / 2016-2017)

• Elements of Functional Data Analysis
  Tutor: Dr A. Duncan, Imperial (2021-2022)

•  Elliptic Operators and Index Theorem (PART 2) (PURE) (see Part 1 under Basic Courses)                                                     Tutors:                                                                                                                                                                                                Professor Simon Scott, KCL (2017-2018)
  Professor Qiwei Yao, LSE 

• Enumerative Combinatorics                                                                                                                                                                Tutors:                                                                                                                                                                                          Prof Peter Cameron, St Andrews (2013-2014)                                                                                                                                  Dr A. Fink, QMUL (2015-2016)

• Environmental Flows (2009-2010, 2013-2014) [PDF 428KB]                                                                                                              Tutor: Dr Mike Davey, Met Office (2009-2010 / 2013-2014)  Abstract [DOC 13KB]         

• Euler and the History of Mathematics
  Tutors: Professor Jeremy Gray and Dr June Barrow-Green, OU (2014-2015)

• Euler Systems and Iwasawa Theory (2018-2019)
  Tutors: Prof. Sarah Zerbes, UCL (2018-2019)

• Examples of Moduli Spaces in Algebraic Geometry
  Tutor: Professor Nicholas Shepherd-Barron

• Explicit Inertial Langlands Correspondence for GL (2) (PURE)
  Tutor: Dr Lassina Dembélé, KCL (2024-2025)

• Factor Models in Time Series (STATS)
  Tutor: Dr Matteo Barigozzi, LSE (2014-2015 / 2015-2016)

• Finite Classical Groups 
  Tutor: Dr Nick Gill, Open University (2013-2014)

• Foliations and 3-dimensional manifolds
  Tutor: Dr Mehdi Yazdi, KCL (2022-2023)

• Fundamentals of Differential Algebra
  Tutor: Dr Markus Rosenkranz, Kent  (2012-2013) Abstract [PDF 101KB]

• Galois Cohomology
  Tutor: Dr N. Dogra, KCL (2021-2022)  Galois Cohomology Abstract [PDF 18KB]

• Geometry of Modular Curves (PURE)
  Tutor: Professor Sarah Zerbes, UCL (2015-2016 / 2016-2017)

• Gowers norms and the Mobius function
  Tutor: Dr Aled Walker, KCL (2022-2023 / 2023-2024) Gowers norms and the Mobius function Abstract [PDF 100KB]

• Graph Algorithms and Models (PURE)
  Tutor: Dr Vincenzo Nicosia, QMUL (2017-2018 / 2018-2019)

• Groups of Finite Cohomological Dimension
  Tutor: Prof. F. Johnson, UCL (2021-2022)

• Higher-order networks 
  Tutor: Prof. Ginestra Bianconi, QMUL (2022-2023)

• High Dimensional Statistics (STATS)
  Tutor: Dr Yanbo Tang, Imperial (2024-2025)

• Hiperbolic Conversion Laws
  Tutor: Dr M. Scherecker, UCL (2021-2022)

• History of Geometry in the 19th Century                                                                                                                                Tutors: Professor Jeremy Gray and Dr June Barrow-Green, OU (2013-2014)

• History of Mathematics                                                                                                                                                                      Tutor: Professor June Barrow-Green, OU (2017-2018)

• Holomorphic Dynamics and Hyperbolic Geometry (2012-2013) [PDF 968KB]  Abstract [PDF 71KB]
  Tutor: Professor Shaun Bullet, QMUL (2012-2013)

• Homological Algebra (PURE)
  Tutor: Professor Markus Linckelmann, City (2016-2017)

• Hyperkshler Manifolds
  Tutor: Dr N. Kurnosov, UCL (2021-2022)

• Industrial Mathematics
  Tutors: Drs Robert Leese and John Allwright, Smith Institute/KTN (2009-2010)

• Integrability
  Tutor: Dr Benjamin Doyon, KCL  (2012-2013)

• Interfacial Fluid Mechanics (APPLIED)
  Tutor: Dr M. Pradas, Open University (2015-2016)

• Internal Fluid Dynamics (APPLIED)
  Tutor: Professor Frank Smith, UCL (2016-2017)

• Introduction to Aperiodic Order (APPLIED) 
  Tutor: Professor Uwe Grimm, OU (2018-2019)

• Introduction to Geometric Analysis on Manifolds
  Tutor: Professor Ovidiu Munteanu, UCL (2019-2020)

• Introduction to the Modern Theory of Scattering
  Tutor: Dr Jeffrey Galkowski, UCL (2019-2020 / 2022-2023)

• Introduction to Random Matrix Theory (PURE)
  Tutor: Dr Igor Smolyarenko, Brunel (2008-2009 / 2010-2011 / 2012-2013 / 2014-2015 / 2016-2017 / 2022-2023) 

• Introduction to Random Topology
  Tutor: Dr Omer Bobrowski, QMUL (2023-2024)                                                          Introduction to Random Topology Abstract [PDF 108KB]

• Introduction to Spectral Geometry*
  Tutor: Dr Jean Lagacé, KCL (2023-2024) Introduction to Spectral Geometry Abstract [PDF 92KB]

• Introduction to Spherical and Euclidean Buildings (PURE)
  Tutor: Dr Jeroen Schillewaert, Imperial (2014-2015)

• Introduction to Semiparametric Modelling 
  Tutor: Dr Clifford Lam, LSE (2011-2012)

• Introduction to the Spectral Theory of Hankel and Toeplitz Operators (PURE)
  Tutor: Dr Alexander Pushnitski, KCL (2014-2015)

• Invariant Theory of Finite Groups
  Tutors: Dr Jim Shank and Professor Peter Fleischmann, Kent (2009-2010)                                                                 Abstract [PDF 20KB]

• Inverse Problems
  Tutors:                                                                                                                                                                                                Professor Yaroslav Kurylev, UCL Maths and Professor Simon Arridge, UCL Maths (2009-2010 / 2013-2014)                                  Dr B. Jin, UCL Computer Science (2015-2016) Abstract [PDF 26KB]

• Kernel methods in machine learning and statistics (STATS)
  Tutors: Dr Nikolas Nusken / Dr Marina Riabiz, KCL (2022-2023 / 2023-2024)                                                                                  Tutor: Dr Nikolas Nusken, KCL (2024-2025)     

• Lie Group Actions on Manifolds (PURE)
  Tutor: Professor J. Berndt, Kings (2015-2016)

• Likelihood and Asymptotic Theory for Statistical Inference                                                                                                            Tutor: Dr Nancy Reid, Toronto and UCL Stats (2012-2013)                                                                                            Abstract [PDF 70KB]

• Mathematical Methods of Quantum Mechanics (APPLIED)                                                                                                                Tutor: Professor Rod Halburd, UCL (2024-2025)

• Mathematical Topics in General Relativity (APPLIED)                                                                                                                        Tutor: Dr Juan Antonio Valiente-Kroon, QMUL (2013-2014 / 2015-2016 / 2016-2017 / 2017-2018 / 2018-2019 / 2019-2020 / 2021-2022 / 2022-2023 / 2023-2024 / 2024-2025) 

• Mechanics of Solids and Fracture (2008-2009)                                                                                                                                  Tutor: Professor Sergey Mikhailov, Brunel                                                                                                                            Abstract [DOC 27KB]

• Medical Modelling (APPLIED)
  Tutor: Dr Nick Ovenden, UCL Maths (2008-2009 / 2010-2011 / 2014-2015) Abstract [DOC 26KB]
  Tutor: Dr John Curtis, UCL Maths (2017-2018)

• Minimal and Constant Mean Curvature Surfaces (PURE)                                                                                                                  Tutor: Dr Jean Legacé and Dr Stephen Lynch, KCL (2024-2025)

• Model Theory
  Tutor: Dr Ivan Tomasic, QMUL (2009-2010 / 2018-2019)

• Modular Forms (PURE)
  Tutor: Professor Fred Diamond, KCL (2012-2013), with Dr Sameer Murthy (2014-2015)

• Modular Forms and representation of GL2
  Tutor: Dr Robert Rockwood, KCL (2023-2024)                                                                                                               Abstract [PDF 67KB]

• Modular Group and Automorphic Forms                                                                                                                                         Tutor: Dr William Harvey, KCL (2008-2009 / 2010-2011)

• Multi Deck Theory
  Tutor: Dr Sergei Timoshin, UCL (2013-2014 / 2015-2016)

• Noncommutative Geometry 
  Tutor: Professor Shahn Majid, QMUL (2008-2009 / 2010-2011)

• Non-Linear Free Surfaces
  Tutor: Professor Jean-Marc Vanden-Broeck, UCL (2010-2011 / 2012-2013 / 2015-2016 / 2018-2019 / 2022-2023)
  Tutors: Dr Joaquin Rodrigues Jacinto, UCL Maths and Dr Chris Williams, Imperial (2017-2018)

• Non-Linear Free Surface Flows with Gravity and Surface Tension (APPLIED)
  Tutor: Professor Jean-Marc Vanden-Broeck, UCL  (2024-2025) 

• Numerical Analysis of the Helmholtz Equation
  Tutor: Professor Jeffrey Galkowski, UCL (2023-2024)                                                                                                              Abstract [PDF 11KB]

• Numerical Methods for Elliptic Partial Differential Equations (APPLIED)
  Tutor: Professor Stephen Langdon, Brunel (2024-2025) 

• Numerical Relativity (APPLIED)
  Tutor: Dr Katy Clough, QMUL (2024-2025) 

• Objective Bayesian Analysis
  Tutors:                                                                                                                                                                                                Dr Cristiano Villa, Kent (2016-2017)
  Dr Ana Loureiro, Kent (2017-2018)

• Orthogonal Polynomials and Special Functions
  Tutor: Dr Ana Loureiro, Kent (2019-2020 / 2021-2022)

• Painlevé equations and the Painlevé property
  Tutor: Professor Rod Halburd, UCL (2022-2023)
  Painlevé equations and the Painlevé property Abstract [PDF 82KB]

• Principles and Design Patterns in Data Scientific Software Engineering
  Tutor: Dr F. Kiraly, UCL (2021-2022)
  Principles and Design Patterns in Data Scientific Software Engineering Abstract [PDF 52KB]

• Probabilistic Analysis of Algorithms
  Tutor: Professor Alexander Marynych, Kyiv University, visiting QMUL (2023-2024) Probabilistic Analysis of Algorithms Abstract [PDF 75KB]

• The Probabilistic Method (2009-2010 / 2012-2013)
  Tutor: Dr John Talbot, UCL Maths 

• Quantum Ergodicity and Number Theory 
  Tutor: Prof Yiannis Petridis, UCL and Dr Steve Lester, QMUL (2018-2019)

• Reductive Groups
  Tutor: Professor N. Shepherd-Barron, KCL (2021-2022)

• Regression Diagnostics and the Forward Search
  Tutor: Professor Anthony Atkins LSE (2008-2009)

• REML Estimation and Linear Mixed Models                                                                                                                                      Tutors: Dr Robert Thompson and Dr Sue Whelan, QMUL (2008-2009 / 2010-2011)

• Representation Theory (2008-2009/2010-2011as an advanced course, 2012-2014 as a basic course)
  Tutors:                                                                                                                                                                                               Dr Anton Cox, City (2008-2012)                                                                                                                                                         Dr M Linckelmann, City (2013-2014) 

• Riemannian Holonomy
  Tutor: Dr Lorenzo Foscolo, UCL (2019-2020 / 2021-2022)

• Selective Inference
  Tutor: Dr Daniel Garcia Rasines, Imperial (2022-2023 / 2023-2024)

• Semiclassical Analysis
  Tutor: Dr. Galkowski, UCL (2021-2022)

• Solids Mechanics inc. Elastic Wave Propagation 
  Tutor: Professor Julius Kaplunov, Brunel (2011-2012)

• Spectral Theory 
  Tutor: Professor Leonid Parnovski, UCL Maths (2009-2010)

• Spectral Theory for Operatives and Matrices                                                                                                                                    Tutor: Professor Brian Davies, KCL (2012-2013)                                                                                                             Abstract [PDF 42KB]

• Statistics in Molecular Genetics (2009-2010) [PDF 721KB]
  Tutors: Dr Alexandra Lewin, Dr Lachlan Coin, Dr Maria de Iorio, Dr Sylvia Richardson and Professor David Balding, LSE, Imperial and UCL (2009-2010)

• Statistics in Practise
  Tutors: Dr Niall Adams, Imperial (2009-2010) 

• Statistical Mechanics
  Tutor:                                                                                                                                                                                                  Professor Christian Beck, QMUL (2009-2010)                                                                                                                                    Dr O. Bandtlow, QMUL, and Dr A. Baule (QMUL) (2015-2016)

• Statistical Pattern Recognition (STATS)
  Tutor: Dr Giovanni Montana, Imperial (2014-2015 / 2015-2016)

• Stochastic Finance (2008-2009) [PDF 7,802KB]
  Tutor: Professor Panos Vassiliou, UCL Stats (2008-2009)

• Symmetry Methods 
  Tutor: Professor Peter Clarkson, Kent (2010-2011 / 2012-2014 / 2018-2019)

• Symmetries, Conservation Laws and the Variational Complex (APPLIED)
  Tutor: Dr Jing Ping Wang, Kent (2014-2015)

• Syzygies and Homological Algebra
  Tutor: Professor Francis Johnson, UCL Maths (2009-2010)

• The Hardy-Littlewood Method (PURE)
  Tutor: Professor Igor Wigman and Dr Steve Lester, KCL (2024-2025)     

• The Mathematical Theory of Compressible Viscous Flows
  Tutor: Dr Ewelina Zatorska, UCL Maths (2019-2020)

• Topics in Probabilistic Number Theory
  Tutor: Dr Steve Lester and Professor Igor Wigman (2023-2024)                                                                                             Abstract [PDF 67KB]

• Topics in the Design of Experiments
  Tutors:                                                                                                                                                                                                Dr Barbara Bogacka, QMUL (2009-2010) and Dr Steve Coad, QMUL (2018-2019/2019-2020).
  Dr Steve Coad (2021-2022)

• Topological Arakelov Theory 
  Tutor: Professor Francis Johnson, UCL Maths (2011-2012)

• Topology, Geometry and Dynamics on Higher-order Networks (APPLIED)                                                                                      Tutor: Professor Ginestra Bianconi, QMUL (2024-2025)                                                                                                                  

• Toric Varieties
  Tutor: Tim Magee, KCL (2022-2023)

• Tropical Geometry (PURE)
  Tutor: Dr M. Manjunath, QMUL (2015-2016) 

• Value of L-functions
  Tutors: Dr Luis Garcia, UCL (2019-2020)
  
  

You can also consult a list of our past intensive courses.