# MSc in Mathematical Sciences (OMMS) 2019-20

The confirmed synopses for Part C 2019-20 will be available on the course management portal https://courses.maths.ox.ac.uk/ before the start of Michaelmas Term 2019. Please see the current edition of the *Examination Regulations* (https://www.admin.ox.ac.uk/examregs/) for the full regulations governing these examinations. The Examination Conventions for the course can be found at: https://www.maths.ox.ac.uk/members/students/postgraduate-courses/omms-pa....

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 on the MSc course are expected to offer a minimum of eight units, including the compulsory two-unit dissertation, with the students able to take an additional one or two units if they wished to do so. One unit is the equivalent of a 16 hour lecture course. Students are permitted to take courses from the "Mathematics Department Units" and "Statistics Department Units", as well as up to two courses from the "Computer Science Options". At least three of the units offered must be assessed by written examination/

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 (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)
- C5.1 Solid Mechanics (MT)
- C5.2 Elasticity and Plasticity (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)
- 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)

For the synopses of the above courses, please visit https://courses.maths.ox.ac.uk/overview/postgraduate#44964.

**Statistics Department Units **

- SC1 Stochastic Models in Mathematical Genetics (MT)
- SC2 Probability and Statistics for Network Analysis (MT)
- SC4 Advanced Topics in Statistical Machine Learning (HT)
- SC5 Advanced Simulation Methods (HT)
- SC7 Bayes Methods (HT)
- SC8 Topics in Computational Biology (HT)
- SC9 Probability on Graphs and Lattices (MT)
- SC10 Algorithmic Foundations of Learning (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 http://www.stats.ox.ac.uk/current_students/bammath/course_handbooks/.

**Computer Science Options **

The Computer Science units available are:

- CCS1 Categories, Proofs and Processes (MT)
- CCS2 Quantum Computer Science (MT)
- CCS3 Automata, Logic and Games (MT)

For full details of these units see the Department of Computer Science's website http://www.cs.ox.ac.uk/teaching/courses/.

Please note that these 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 into 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.

**Registration for Part C courses 2019-20**

Students will be asked to sign up for classes at the start of Michaelmas Term 2019. 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.