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:
Year information is for BSc and MSci Mathematics students only. Students on joint degrees may take modules in different years - check the degree structure document for your course for details.
First and Second Year
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) |
| 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 |
| MATH0109 Theorem Proving in Lean |
3 |
2 |
Familiarity with the notion of proving theorems (for example, at least one of MATH0034, MATH0051, MATH0052 or MATH0053) |
| 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 |
| MATH0104 Modular Forms |
3 or 4 |
1 |
MATH0013 Analysis 3 - Complex Analysis, MATH0014 Algebra 3: Further Linear Algebra, MATH0034 Number Theory (recommended) |
| MATH0073 Representation Theory |
3 or 4 |
2 |
MATH0053 Algebra 4, MATH0021 Homological Algebra (recommended) |
| 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 |
| MATH0052 Geometry and Groups |
2 or 3 |
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 |
| 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, 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 |
| 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) |
| MATH0072 Riemannian Geometry |
4 |
1 |
MATH0019 Multivariable Analysis, MATH0020 Differential Geometry |
Applied Mathematics
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 |
| MATH0032 Introduction to Mathematica |
3 |
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) |
| 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) |