Postgraduate Courses

MSc in Mathematical Sciences

Schedule of units for course: MSc in Mathematical Sciences (OMMS) 2020-21

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

Mathematical and Theoretical Physics

• Michaelmas
  • Quantum Field Theory
  • Groups and Representations
  • Topological Quantum Theory
  • Radiative Processes and High Energy Astrophysics
  • An Introduction to LaTeX
  • Kinetic Theory
  • Quantum Processes in Hot Plasma
  • Advanced Quantum Theory
  • C7.5 General Relativity I
  • C5.5 Perturbation Methods
  • C6.1 Numerical Linear Algebra
  • C3.1 Algebraic Topology
  • C3.4 Algebraic Geometry
  • C3.3 Differentiable Manifolds
  • Advanced Philosophy of Physics
• Hilary
  • String Theory I
  • Cosmology
  • Soft Matter Physics
  • Galactic and Planetary Dynamics
  • Nonequilibrium Statistical Physics
  • Collisionless Plasma Physics
  • Advanced Fluid Dynamics
  • Symbolic, Numerical and Graphical Scientific Programming
  • Advanced Quantum Field Theory
  • C5.6 Applied Complex Variables
  • C3.2 Geometric Group Theory
  • C7.6 General Relativity II
  • C5.4 Networks
  • C7.4 Introduction to Quantum Information
  • Supersymmetry and Supergravity
  • Advanced Philosophy of Physics
  • High Energy Density Physics
  • Renormalisation Group
  • Astroparticle Physics
  • Geophysical Fluid Dynamics
  • C7.7 Random Matrix Theory
• Trinity
  • String Theory II
  • Conformal Field Theory
  • Quantum Matter: Superconductors, Superfluids, and Fermi Liquids
  • Topics in Soft and Active Matter Physics
  • Quantum Field Theory in Curved Space-Time
  • The Standard Model and Beyond I
  • The Standard Model and Beyond II
  • Advanced Topics in Plasma Physics
  • MTP Dissertation
  • Collisional Plasma Physics

MSc in Mathematical Modelling and Scientific Computing

• Michaelmas
  • C6.3 Approximation of Functions
  • B5.5 Further Mathematical Biology
  • B6.3 Integer Programming
  • C5.11 Mathematical Geoscience
  • C5.12 Mathematical Physiology
  • C5.5 Perturbation Methods
  • C5.1 Solid Mechanics
  • C8.1 Stochastic Differential Equations
  • C6.5 Theories of Deep Learning
  • C5.7 Topics in Fluid Mechanics
  • B5.3 Viscous Flow
  • B5.2 Applied Partial Differential Equations
  • Supplementary Applied Mathematics
  • B6.1 Numerical Solution of Differential Equations I
  • C6.1 Numerical Linear Algebra
  • Mathematical Modelling
  • Practical Numerical Analysis
  • Additional Skills
• Hilary
  • C5.6 Applied Complex Variables
  • C3.9 Computational Algebraic Topology
  • C5.2 Elasticity and Plasticity
  • C6.4 Finite Element Method for PDEs
  • C5.9 Mathematical Mechanical Biology
  • B8.3 Mathematical Models of Financial Derivatives
  • C5.4 Networks
  • B6.2 Numerical Solution of Differential Equations II
  • B5.1 Stochastic Modelling of Biological Processes
  • B5.4 Waves and Compressible Flow
  • Case Studies in Mathematical Modelling
  • Case Studies in Scientific Computing
  • B5.6 Nonlinear Systems
  • Further Partial Differential Equations
  • Further Mathematical Methods
  • C6.2 Continuous Optimisation
  • Advanced Topics in Statistical Machine Learning
• Trinity
  • C++ for Scientific Computing (course not running 19-20, materials for reference)
  • Python in Scientific Computing (course not running 19-20, materials for reference)
  • MMSC Dissertations

MSc in Mathematics and Foundations of Computer Science

• Michaelmas
  • C3.1 Algebraic Topology
  • C1.3 Analytic Topology
  • B2.1 Introduction to Representation Theory
  • C2.1 Lie Algebras
  • C1.1 Model Theory
  • B3.5 Topology and Groups
  • C3.4 Algebraic Geometry
  • C2.2 Homological Algebra
  • Categories, Proofs and Processes
  • Computer Aided Formal Verification
  • Foundations of Computer Science
  • B8.5 Graph Theory
  • Introduction to Cryptology
  • C8.3 Combinatorics
  • C3.8 Analytic Number Theory
  • C2.4 Infinite Groups
  • Computational Learning Theory
  • Quantum Computer Science
  • B6.3 Integer Programming
  • C3.10 Additive and Combinatorial Number Theory
  • C2.7 Category Theory
  • C3.3 Differentiable Manifolds
  • Automata, Logic and Games
• Hilary
  • Computational Game Theory
  • C3.7 Elliptic Curves
  • B3.4 Algebraic Number Theory
  • B2.2 Commutative Algebra
  • C1.2 Godel's Incompleteness Theorem
  • Lambda Calculus and Types
  • C1.4 Axiomatic Set Theory
  • C2.6 Introduction to Schemes
  • C2.5 Non-Commutative Rings
  • C3.2 Geometric Group Theory
  • C2.3 Representation Theory of Semisimple Lie Algebras
  • Analysing Logics using Tree Automata
  • Categorical Quantum Mechanics
  • C3.9 Computational Algebraic Topology
  • Distributional Models of Meaning
  • C5.4 Networks
  • C8.4 Probabilistic Combinatorics
  • Probability and Computing
  • C3.5 Lie Groups
  • B8.4 Information Theory
  • Computational Complexity
  • Applied Category Theory
  • C7.4 Introduction to Quantum Information
• Trinity
  • Concurrency
  • MFoCS Dissertations
  • Topological Groups

MSc in Mathematical Finance (28m)

• Michaelmas
  • Module 5: Advanced Modelling Topics 1
  • Module 6: Advanced Numerical Methods
  • Dissertations - MSc in Mathematical Finance
• Hilary
  • Module 7: Advanced Modelling Topics 2
  • Module 8: Quantitative Risk Management
  • Dissertations - MSc in Mathematical Finance
• Trinity
  • Dissertations - MSc in Mathematical Finance

Industrially Focused Mathematical Modelling

• Michaelmas
  • Core01: Mathematical Modelling
  • Core02: Scientific Computing
  • Core03: Modelling, analysis and computation of continuous real world problems
  • Core04: Computational Techniques
  • Core05: Mathematical Analytics
  • Core06: Optimisation
• Hilary
  • C3.5 Lie Groups
  • C3.9 Computational Algebraic Topology
  • C4.6 Fixed Point Methods for Nonlinear PDEs
  • C5.2 Elasticity and Plasticity
  • C5.4 Networks
  • C5.6 Applied Complex Variables
  • C5.9 Mathematical Mechanical Biology
  • C6.4 Finite Element Method for PDEs
  • C8.2 Stochastic Analysis and PDEs
  • C8.4 Probabilistic Combinatorics
  • ModCase: Modelling Case Studies
  • SciCase: Scientific Computing Case Studies

PDE CDT Programme

Graduate Courses

• Michaelmas
  • Scientific Computing for DPhil students I
• Hilary
  • Scientific Computing for DPhil students II

MSc in Mathematical and Computational Finance

• Michaelmas
  • Introduction to Partial Differential Equations
  • Introduction to Probability
  • Introduction to Statistics
  • Numerical Methods
  • Stochastic Calculus
  • Financial Derivatives
  • Statistics and Financial Data Analysis
  • Financial Computing with C++ Part I
  • Python
  • An Introduction to LaTeX
  • Financial Markets and Instruments
  • Markdown reports
• Hilary
  • Stochastic Volatility
  • Fixed Income and Credit
  • Asset Pricing
  • Market Microstructure and Algorithmic Trading
  • Deep Learning
  • Optimisation
  • Stochastic Control
  • Financial Computing with C++ II
  • Quantitative Risk Management
  • Advanced Monte Carlo Methods
  • Advanced Numerical Methods
• Trinity
  • Dissertation

CDT in Mathematics of Random Systems

• Michaelmas
  • C6.5 Theories of Deep Learning
  • Simulation Methods and Stochastic Algorithms
  • Foundations of Stochastic Analysis
  • Foundations of Data Science
  • Function Spaces and Distribution Theory
• Hilary
  • C4.9 Optimal Transport & Partial Differential Equations
  • C6.2 Continuous Optimisation
  • C7.7 Random Matrix Theory
  • C8.2 Stochastic Analysis and PDEs
  • C8.4 Probabilistic Combinatorics
  • C8.5 Introduction to Schramm-Loewner Evolution
  • C8.6 Limit Theorems and Large Deviations in Probability
  • Optimisation