Part C Mathematics 2020-21


The confirmed synopses for Part C 2020-21 will be available on the course management portal before the start of Michaelmas Term 2020.

Honour School of Mathematics - Units

See the current edition of the Examination Regulations ( for the full regulations governing these examinations. Examination Conventions can be found at:

In the unlikely event that any course receives a very low registration we may offer this course as a reading course (this would include some lectures but fewer classes).

Students staying on to take Part C will take a minimum of eight units and a maximum of ten units. These 8-10 units must include a CCD Dissertation on a Mathematical Topic (which will count as a double Maths Department Unit) or a COD Dissertation on the History of Mathematics (which will count as a double unit from the "Other Units" list). One unit is the equivalent of a 16 hour lecture course. The equivalent of four units must be taken from the schedule of "Mathematics Department units" (which include the CCD dissertation and, if applicable, a dissertation offered by the Statistics department). Up to four units may be taken from the schedule of "Other Units" with not more than two from each category (Statistics options, Computer Science options, Other options).

Most Mathematics Department lecture courses are independently available as units, the exception being:

  • C7.1 Theoretical Physics - this is available as a double-unit only.

All the units described are "M-Level".

Mathematics Department Units

  • C1.1 Model Theory (MT)
  • C1.2 Godel's Incompleteness Theorem (HT)
  • C1.3 Analytic Topology (MT)
  • C1.4 Axiomatic Set Theory (HT)
  • C2.1 Lie Algebras (MT)
  • C2.2 Homological Algebra (MT)
  • C2.3 Representation Theory of Semisimple Lie Algebras (HT)
  • C2.4 Infinite Groups (MT)
  • C2.5 Non-Commutative Rings (HT)
  • C2.6 Introduction to Schemes (HT)
  • C2.7 Category Theory (MT)
  • C3.1 Algebraic Topology (MT)
  • C3.2 Geometric Group Theory (HT)
  • C3.3 Differentiable Manifolds (MT)
  • C3.4 Algebraic Geometry (MT)
  • C3.5 Lie Groups (HT)
  • C3.7 Elliptic Curves (HT)
  • C3.8 Analytic Number Theory (MT)
  • C3.9 Computational Algebraic Topology (HT)
  • C3.10 Additive and Combinatorial Number Theory (MT)
  • C3.11 Riemannian Geometry (HT)
  • C4.1 Further Functional Analysis (MT)
  • C4.3 Functional Analytic Methods for PDEs (MT)
  • C4.6 Fixed Point Methods for Nonlinear PDEs (HT)
  • C4.8 Complex Analysis: Conformal Maps and Geometry (MT)
  • C4.9 Optimal Transport & Partial Differential Equations (HT)
  • C5.1 Solid Mechanics (MT)
  • C5.2 Elasticity and Plasticity (HT)
  • C5.3 Statistical Mechanics (HT)
  • C5.4 Networks (HT)
  • C5.5 Perturbation Methods (MT)
  • C5.6 Applied Complex Variables (HT)
  • C5.7 Topics in Fluid Mechanics (MT)
  • C5.9 Mathematical Mechanical Biology (HT)
  • C5.11 Mathematical Geoscience (MT)
  • C5.12 Mathematical Physiology (MT)
  • C6.1 Numerical Linear Algebra (MT)
  • C6.2 Continuous Optimisation (HT)
  • C6.3 Approximation of Functions (MT)
  • C6.4 Finite Element Method for PDEs (HT)
  • C6.5 Theories of Deep Learning (MT)
  • C7.1 Theoretical Physics (MT/HT)
  • C7.4 Introduction to Quantum Information (HT)
  • C7.5 General Relativity I (MT)
  • C7.6 General Relativity II (HT)
  • C7.7 Random Matrix Theory Part C Course (HT)
  • C8.1 Stochastic Differential Equations (MT)
  • C8.2 Stochastic Analysis and PDEs (HT)
  • C8.3 Combinatorics (MT)
  • C8.4 Probabilistic Combinatorics (HT)
  • C8.5 Introduction to Schramm-Loewner Evolution (HT)
  • C8.6 Limit Theorems and Large Deviations in Probability (HT)
  • CCD Dissertations on a Mathematical Topic [double unit] (MT/HT)

The Guide to Mathematics Options at Part C can be found at

Other Units

  1. Statistics Options

    Students in Part C may take the units below, which are drawn from Part C of the Honour School of Mathematics and Statistics.

    The Statistics units available are as follows (please note these are all TBC):

    • Stochastic Models in Mathematical Genetics (MT)
    • Probability and Statistics for Network Analysis (MT)
    • Advanced Topics in Statistical Machine Learning (HT)
    • Advanced Simulation Methods (HT)
    • Bayes Methods (HT)
    • Topics in Computational Biology (HT)
    • Probability on Graphs and Lattices (MT)
    • Algorithmic Foundations of Learning (MT)
    • Graphical Models (MT)

    For full details of these units see the syllabus and synopses for Part C of the Honour School Mathematics and Statistics, which are available on the web at

  2. Computer Science Options

    Students in Part C may take the units below, which are drawn from Part C of the Honour School of Mathematics and Computing.

    Please note that these four courses will be examined by mini-project (as for MSc students). Mini-projects will be handed out to candidates on the last Monday or Friday of the term in which the subject is being taught, and you will have to hand it in to the Exam Schools by noon on Monday of Week 0 of the following term. The mini-project will be designed to be completed in about four to five days. It will include some questions that are more open-ended than those on a standard sit-down exam. The work you submit should be your own work, and include suitable references.

    Please note that the Computer Science courses in Part C are 50% bigger than those in earlier years, i.e. for each Computer Science course in the 3rd year undergraduates are expected to undertake about 10 hours of study per week, but 4th year courses will each require about 15 hours a week of study. Lecturers are providing this extra work in a variety of ways, e.g. some will give 16 lectures with extra reading, classes and/or practicals, whereas others will be giving 24 lectures, and others still will be doing something in between. Students will need to look at each synopsis for details on this.

    The Computer Science units available are:

    • CCS1 Categories, Proofs and Processes (MT)
    • CCS2 Quantum Processes and Computation (MT)
    • CCS3 Automata, Logic and Games (MT)

    For full details of these units see the Department of Computer Science's website

  3. Other Options

    • COD Dissertations on the History of Mathematics [double unit] (MT/HT)
    • Philosophy options - see below for details (double unit)

    Students in Part C may take the units below, which are drawn from Part C of the Honour School of Mathematics and Philosophy. Students interested in taking a Philosophy double unit are encouraged to contact their college tutors well in advance of term, to ensure that teaching arrangements can be made.

    The Philosophy units available are as follows:

    • There are no Philosophy units available in 2020/21

    For full details of these double units see the Faculty of Philosophy's website

Registration for Part C courses 2020-21

Students will be asked to register for the options they intend to take by the end of week 10, Trinity Term 2020. It is helpful if their registration is as accurate as possible as the data is used to make arrangements for teaching resources. Towards the start of the academic year students will be given the opportunity to make edits to their course registration. Students will then be asked to sign up for classes at the start of Michaelmas Term 2020. Further information about this will be sent via email before the start of term.

Every effort will be made when timetabling lectures to ensure that mathematics lectures do not clash. However, because of the large number of options in Part C this may sometimes be unavoidable. The timing of lectures for a course taught by another faculty will usually be set by that faculty and the Mathematical Institute has little control over the arrangements. In the event of clashes being necessary, then students will be notified of the clashes by email and in any case options will only be allowed to clash when the take-up of both options is unlikely or inadvisable.