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

First and Second Year

Module Year Term Prerequisites
MATH0002 Economics 1 - Combined Studies 1 1  
MATH0003 Analysis 1 1 1  
MATH0005 Algebra 1 1 1  
MATH0008 Applied Mathematics 1 1  
MATH0010 Mathematical Methods 1 1 1  
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
MATH0051 Analysis 4 2 2 MATH0004 Analysis 2
MATH0052 Geometry and Groups 2 2 MATH0013 Analysis 3 - Complex Analysis, MATH0006 Algebra 2, MATH0014 Algebra 3: Further Linear Algebra
MATH0053 Algebra 4 2 2 MATH0006 Algebra 2
MATH0055 Mathematics of Electromagnetism and Special Relativity 2 2 MATH0016 Mathematical Methods 3
MATH0056 Mathematical Methods 4 2 2 MATH0013 Analysis 3 - Complex Analysis, MATH0016 Mathematical Methods 3
MATH0057 Probability and Statistics 2 2 MATH0011 Mathematical Methods 2
MATH0058 Computational Methods 2 2 MATH0010 Mathematical Methods 1, MATH0006 Algebra 2, Some programming knowledge (e.g. Python) desirable
MATH0034 Number Theory 2 2 MATH0006 Algebra 2

Algebra

Module Year Term Prerequisites
MATH0014 Algebra 3: Further Linear Algebra 2 1 MATH0006 Algebra 2
MATH0053 Algebra 4 2 2 MATH0006 Algebra 2
MATH0021 Commutative Algebra 3 1 MATH0053 Algebra 4
MATH0022 Galois Theory 3 1 MATH0053 Algebra 4
MATH0036 Elliptic Curves 3 1 MATH0034 Number Theory, MATH0053 Algebra 4
MATH0023 Algebraic Topology 3 1 MATH0014 Algebra 3: Further Linear Algebra
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
MATH0029 Graph Theory and Combinatorics 3 2 MATH0057 Probability and Statistics
MATH0083 Prime Numbers and their Distribution 3 or 4 1 MATH0013 Analysis 3 - Complex Analysis, MATH0051 Analysis 4, MATH0034 Number Theory
MATH0075 Lie Groups and Lie Algebras 3 or 4 1 MATH0014 Algebra 3: Further Linear Algebra
MATH0073 Representation Theory 3 or 4 2 MATH0053 Algebra 4, MATH0021 Commutative Algebra (recommended)
MATH0104 Modular Forms 3 or 4 2 MATH0013 Analysis 3 - Complex Analysis, MATH0014 Algebra 3: Further Linear Algebra, MATH0034 Number Theory
MATH0076 Algebraic Geometry 4 1 MATH0021 Commutative Algebra, MATH0022 Galois Theory

Analysis

Module Year Term Prerequisites
MATH0051 Analysis 4 2 2 MATH0004 Analysis 2
MATH0052 Geometry and Groups 2 2 MATH0013 Analysis 3 - Complex Analysis, MATH0006 Algebra 2, MATH0014 Algebra 3: Further Linear Algebra
MATH0017 Measure Theory 3 1 MATH0051 Analysis 4
MATH0019 Multivariable Analysis 3 1 MATH0051 Analysis 4
MATH0020 Differential Geometry 3 1 MATH0011 Mathematical Methods 2
MATH0018 Functional Analysis 3 2 MATH0051 Analysis 4
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, MATH0052 Geometry and Groups (recommended)
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
MATH0071 Spectral Theory 4 1 MATH0018 Functional Analysis, MATH0019 Multivariable Analysis, MATH0017 Measure Theory (recommended)
MATH0072 Riemannian Geometry 4 1 MATH0019 Multivariable Analysis, MATH0020 Differential Geometry

Applied Mathematics

Module Year Term Prerequisites
MATH0056 Mathematical Methods 4 2 2 MATH0013 Analysis 3 - Complex Analysis, MATH0016 Mathematical Methods 3
MATH0055 Mathematics of Electromagnetism and Special Relativity 2 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
MATH0080 Waves and Wave Scattering 3 or 4 2 MATH0056 Mathematical Methods 4
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
MATH0028 Combinatorial Optimisation 3 1 MATH0014 Algebra 3: Further Linear Algebra
MATH0026 Biomathematics 3 1 MATH0011 Mathematical Methods 2
MATH0030 Mathematical Ecology 3 1 MATH0010 Mathematical Methods 1
MATH0032 Introduction to Mathematica 3 1  
MATH0033 Numerical Methods 3 1 MATH0006 Algebra 2, MATH0011 Mathematical Methods 2, MATH0058 Computational Methods
MATH0031 Financial Mathematics 3 2 MATH0016 Mathematical Methods 3, MATH0057 Probability and Statistics
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)
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 MATH0011 Mathematical Methods 2
MATH0088 Quantitative and Computational Finance 4 2 MATH0016 Mathematical Methods 3, MATH0031 Financial Mathematics