# Part C, Mathematics and Computer Science

Maths and Computer Science Part C students are required to take either six optional units from schedules C1 and C2 and a Mathematics Dissertation or five optional subjects and a Computer Science Project. Schedule C1 will contain Computer Science options and Schedule C2 will contain Mathematics options.

Each of the optional subjects will be examined by a sit-down paper, which is likely to be of two hours' duration, or by a mini-project (please note that most of the Computer Science options will be examined by mini-project).

Computer Science mini-projects will be handed out to candidates on the last Friday of the term in which the subject is being taught (expect those which are shared with MFoCS course which will be released on the last Monday) and must submitted by noon on Monday of week 0 of the following term. The mini-project will be designed to be completed in about three 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 entirely 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 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. Computer Science lecturers are providing this extra work in a variety of ways, e.g. some will give 16 lectures but will require you to undertake extra reading, classes and/or practicals, whereas others will be giving 24 lectures, and others still will be doing something in between. Please look at each synopsis for details on this.

#### Schedule C1

- Automata, Logic and Games 24 Lectures, Michaelmas Term 2019
- Categories, Proofs and Processes 20 Lectures, Michaelmas Term 2019
- Computational Learning Theory 24 Lectures, Michaelmas Term 2019
- Concurrent Algorithms and Data Structures approximately 20, Michaelmas Term 2019
- Physically Based Rendering 20 Lectures, Michaelmas Term 2019
- Probabilistic Model Checking 20 Lectures, Michaelmas Term 2019
- Quantum Computer Science 24 Lectures, Michaelmas Term 2019
- Advanced Security 19 Lectures, Hilary Term 2020
- Advanced Topics in Machine Learning Hilary Term 2020
- Categorical Quantum Mechanics 16 Lectures, Hilary Term 2020
- Computational Game Theory 20 Lectures, Hilary Term 2020
- Database Systems Implementation 22 Lectures, Hilary Term 2020
- Probability and Computing 20 Lectures, Hilary Term 2020
- Requirements 16 Lectures, Trinity Term 2020

#### Schedule C2

Any Maths Schedule C option may be taken, see here, but the following are recommended:

- C1.1 Model Theory
- C1.2 Godel's Incompleteness Theorems
- C1.3 Analytic Topology
- C1.4 Axiomatic Set Theory
- C2.1 Lie Algebras
- C2.2 Homological Algebra
- C2.3 Representation Theory of Semisimple Lie Algebras
- C2.4 Infinite Groups
- C2.5 Non Commutative Rings
- C2.6 Introduction to Schemes
- C2.7 Category Theory
- C3.1 Algebraic Topology
- C3.2 Geometric Group Theory
- C3.3 Differentiable Manifolds
- C3.4 Algebraic Geometry
- C3.5 Lie Groups
- C3.6 Modular Forms
- C3.7 Elliptic Curves
- C3.8 Analytic Number Theory
- C3.10 Additive and Combinatorial Number Theory
- C4.1 Functional Analysis
- C4.2 Linear Operators
- C6.1 Numerical Linear Algebra
- C8.1 Stochastic Differential Equations
- C8.3 Combinatorics
- C8.4 Probabilistic Combinatorics
- Computational Algebraic Topology