The official UCL Maths module information is at this link. There is a graphical version of this pathways document.

Information on modules from other UCL departments can be found at the following links:

You may also find the UCL Module Catalogue useful.

Please note that the year column in the table below is for BSc and MSci Mathematics degrees only. Students on other degrees may take modules in different years. Check the degree structure document for your course for details.

First and Second Year

Module Year Term Prerequisites
MATH0003 Analysis 1 1 1  
MATH0005 Algebra 1 1 1  
MATH0008 Applied Mathematics 1 1  
MATH0010 Mathematical Methods 1 1 1  
MATH0110 Analysis for Joint Honours 1 1  
MATH0002 Economics 1 - Combined Studies 1 1 and 2  
MATH0004 Analysis 2 1 2 MATH0003 Analysis 1
MATH0006 Algebra 2 1 2 MATH0005 Algebra 1
MATH0007 Algebra for Joint Honours Students 1 2  
MATH0009 Newtonian Mechanics 1 2 MATH0008 Applied Mathematics, MATH0010 Mathematical Methods 1
MATH0011 Mathematical Methods 2 1 2 MATH0010 Mathematical Methods 1
MATH0013 Analysis 3 - Complex Analysis 2 1 MATH0003 Analysis 1, MATH0004 Analysis 2 (recommended)
MATH0014 Algebra 3: Further Linear Algebra 2 1 MATH0006 Algebra 2
MATH0015 Fluid Mechanics 2 1 MATH0011 Mathematical Methods 2, MATH0009 Newtonian Mechanics
MATH0016 Mathematical Methods 3 2 1 MATH0011 Mathematical Methods 2
STAT0001 Economics 2 - Combined Studies 2 1 and 2 MATH0002 Economics 1 - Combined Studies
MATH0051 Analysis 4 2 or 3 2 MATH0004 Analysis 2
MATH0053 Algebra 4 2 or 3 2 MATH0006 Algebra 2
MATH0055 Mathematics of Electromagnetism and Special Relativity 2 or 3 2 MATH0016 Mathematical Methods 3
MATH0056 Mathematical Methods 4 2 or 3 2 MATH0013 Analysis 3 - Complex Analysis, MATH0016 Mathematical Methods 3
MATH0057 Probability and Statistics 2 or 3 2 MATH0011 Mathematical Methods 2
MATH0058 Computational Methods 2 or 3 2 MATH0010 Mathematical Methods 1, MATH0006 Algebra 2, Some programming knowledge (e.g. Python) desirable
MATH0034 Number Theory 2 or 3 2 MATH0006 Algebra 2

Algebra

Module Year Term Prerequisites
MATH0014 Algebra 3: Further Linear Algebra 2 1 MATH0006 Algebra 2
MATH0053 Algebra 4 2 or 3 2 MATH0006 Algebra 2
MATH0022 Galois Theory 3 1 MATH0053 Algebra 4
MATH0023 Algebraic Topology 3 1 MATH0014 Algebra 3: Further Linear Algebra
MATH0029 Graph Theory and Combinatorics 3 1 MATH0057 Probability and Statistics (recommended)
MATH0109 Theorem Proving in Lean 3 1 Familiarity with the notion of proving theorems (for example, at least one of MATH0034, MATH0051, or MATH0053). Good coding skills are also desirable.
MATH0021 Homological Algebra 3 2 MATH0053 Algebra 4
MATH0036 Elliptic Curves 3 2 MATH0034 Number Theory, MATH0053 Algebra 4
MATH0035 Algebraic Number Theory 3 2 MATH0034 Number Theory, MATH0053 Algebra 4, MATH0022 Galois Theory (recommended)
MATH0038 History of Mathematics 3 2  
MATH0037 Logic 3 2 MATH0006 Algebra 2
MATH0108 Commutative Rings and Algebra 3 2 MATH0053 Algebra 4
MATH0073 Representation Theory 3 or 4 1 MATH0053 Algebra 4, MATH0021 Homological Algebra (recommended)
MATH0083 Prime Numbers and their Distribution 3 or 4 1 MATH0013 Analysis 3 - Complex Analysis, MATH0051 Analysis 4, MATH0034 Number Theory
MATH0104 Modular Forms 3 or 4 1 MATH0013 Analysis 3 - Complex Analysis, MATH0014 Algebra 3: Further Linear Algebra, MATH0034 Number Theory (recommended)
MATH0075 Lie Groups and Lie Algebras 3 or 4 2 MATH0014 Algebra 3: Further Linear Algebra
MATH0076 Algebraic Geometry 4 1 MATH0021 Homological Algebra, MATH0022 Galois Theory
MATH0061 Further Topics in Algebraic Number Theory 4 2 MATH0035 Algebraic Number Theory, MATH0022 Galois Theory

Analysis

Module Year Term Prerequisites
MATH0051 Analysis 4 2 or 3 2 MATH0004 Analysis 2
MATH0017 Measure Theory 3 1 MATH0051 Analysis 4
MATH0019 Multivariable Analysis 3 1 MATH0051 Analysis 4
MATH0018 Functional Analysis 3 2 MATH0051 Analysis 4
MATH0020 Differential Geometry 3 2 MATH0011 Mathematical Methods 2
MATH0070 Linear Partial Differential Equations 3 or 4 1 MATH0013 Analysis 3 - Complex Analysis, MATH0016 Mathematical Methods 3, MATH0051 Analysis 4
MATH0074 Topology and Groups 3 or 4 1 MATH0013 Analysis 3 - Complex Analysis, MATH0051 Analysis 4
MATH0069 Probability 3 or 4 2 MATH0017 Measure Theory
MATH0092 Variational Methods for Partial Differential Equations 3 or 4 2 MATH0051 Analysis 4
MATH0090 Elliptic Partial Differential Equations 3 or 4 2 MATH0070 Linear Partial Differential Equations (recommended), MATH0051 Analysis 4, MATH0018 Functional Analysis, MATH0019 Multivariable Analysis
MATH0107 Probabilistic Method in Combinatorics 3 or 4 2 MATH0029 Graph Theory and Combinatorics (recommended), MATH0028 Combinatorial Optimisation (recommended), MATH0057 Probability and Statistics (recommended)
MATH0071 Spectral Theory 4 1 MATH0018 Functional Analysis, MATH0019 Multivariable Analysis, MATH0017 Measure Theory (recommended)

Applied Mathematics

Module Year Term Prerequisites
MATH0056 Mathematical Methods 4 2 or 3 2 MATH0013 Analysis 3 - Complex Analysis, MATH0016 Mathematical Methods 3
MATH0055 Mathematics of Electromagnetism and Special Relativity 2 or 3 2 MATH0016 Mathematical Methods 3
MATH0025 Mathematics for General Relativity 3 1 MATH0016 Mathematical Methods 3
MATH0027 Methods 5 3 2 MATH0056 Mathematical Methods 4
MATH0054 Analytical Dynamics 3 2 MATH0011 Mathematical Methods 2, MATH0009 Newtonian Mechanics
MATH0024 Geophysical Fluids 3 2 MATH0015 Fluid Mechanics, MATH0016 Mathematical Methods 3
MATH0077 Real Fluids 3 or 4 1 MATH0015 Fluid Mechanics, MATH0016 Mathematical Methods 3, MATH0056 Mathematical Methods 4
MATH0118 Mathematics for Quantum Mechanics 3 or 4 1 MATH0056 Mathematical Methods 4, MATH0014 Algebra 3: Further Linear Algebra
MATH0080 Waves and Wave Scattering 3 or 4 2 MATH0056 Mathematical Methods 4
MATH0115 Solid Mechanics 3 or 4 2 MATH0015 Fluid Mechanics, MATH0056 Mathematical Methods 4
MATH0119 Dynamical Systems 3 or 4 2 MATH0017 Measure Theory, MATH0019 Multivariable Analysis (recommended), MATH0020 Differential Geometry (recommended)
MATH0106 Industrial and Geological Fluids 4 1 MATH0015 Fluid Mechanics, MATH0077 Real Fluids (recommended)
MATH0078 Asymptotic Approximation Methods 4 2 MATH0077 Real Fluids
MATH0079 Cosmology 4 2 MATH0025 Mathematics for General Relativity

Modelling, Computation and Finance

Module Year Term Prerequisites
MATH0026 Biomathematics 3 1 MATH0011 Mathematical Methods 2
MATH0030 Mathematical Ecology 3 1 MATH0010 Mathematical Methods 1
MATH0033 Numerical Methods 3 1 MATH0006 Algebra 2, MATH0011 Mathematical Methods 2, MATH0058 Computational Methods
MATH0028 Combinatorial Optimisation 3 2 MATH0014 Algebra 3: Further Linear Algebra
MATH0031 Financial Mathematics 3 2 MATH0016 Mathematical Methods 3, MATH0057 Probability and Statistics
MATH0114 Mathematics for Machine Learning and Artificial Intelligence 3 2 MATH0003 Analysis 1, MATH0004 Analysis 2, MATH0005 Algebra 1, MATH0006 Algebra 2, MATH0011 Mathematical Methods 2, MATH0014 Algebra 3: Further Linear Algebra, MATH0057 Probability and Statistics (recommended)
MATH0102 Applied Stochastic Methods 3 or 4 2 MATH0010 Mathematical Methods 1, MATH0011 Mathematical Methods 2, MATH0056 Mathematical Methods 4 (recommended), MATH0031 Financial Mathematics (recommended), MATH0065 Advanced Modelling Techniques (recommended), MATH0057 Probability and Statistics (recommended)
MATH0117 Spatial Mathematical Biology 3 or 4 2 MATH0030 Mathematical Ecology, MATH0016 Mathematical Methods 3
MATH0065 Advanced Modelling Techniques 4 1 MATH0010 Mathematical Methods 1, MATH0011 Mathematical Methods 2, MATH0013 Analysis 3 - Complex Analysis
MATH0086 Computational and Simulation Methods 4 1 MATH0056 Mathematical Methods 4, MATH0058 Computational Methods (recommended)
MATH0082 Evolutionary Games and Population Genetics 4 2 MATH0008 Applied Mathematics, MATH0010 Mathematical Methods 1, MATH0003 Analysis 1
MATH0088 Quantitative and Computational Finance 4 2 MATH0016 Mathematical Methods 3, MATH0031 Financial Mathematics (recommended)