Mathematics MMath (Honours)

#### First year

Students will take between one and three first-year modules in mathematics. There is one core compulsory module, 'Mathematics', that can be studied in either semester.


[Mathematics](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT1002): introduces the ideas and techniques required for further study of mathematics or applications to other sciences.

Students who do not possess at least a B at Advanced Higher or A-Level Mathematics will need to take 'Introductory Mathematics' in their first semester before taking the compulsory 'Mathematics' module. This option is popular for students on different degree routes who wish to study Mathematics.

[Introductory Mathematics](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT1001): designed for students who do not meet the entry requirements for the first-year 'Mathematics' module. Provides a secure base in elementary calculus.

First-year students can, in addition, take one or both of the optional modules in 'Pure and Applied Mathematics' and 'Statistics in Practice': 

[Mathematics and Statistics 1000-level modules](https://www.st-andrews.ac.uk/subjects/modules/search/?mod=false&profile=_default&query=!null&f.Module-prefix%7Cdomaincode=mt&collection=uosa-module-catalogue-v2&sort=metamodulecode&wildcard=1&form=simple&num.ranks=10&f.School%7Cdept=school%20of%20mathematics%20and%20statistics&f.Year%7CAllDocumentsFill=All%20modules)
#### Second year

Students will take the following compulsory modules in their second year:


[Analysis](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2502): introduces key concepts of real analysis: limit, continuity and differentiation.
[Multivariate Calculus](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2503): extends the techniques of calculus in a single variable to the setting of real functions of several variables.
[Combinatorics and Probability](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2504): introduces counting techniques for finite structures and the behaviour of random variables.
[Abstract Algebra](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2505): explores the key concepts of modern abstract algebra: groups, rings and fields.
[Linear Mathematics](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2501): introduces the theory of vector spaces, linear independence, linear transformations and diagonalisation.
[Vector Calculus](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2506): introduces the theory of scalar and vector fields and associated techniques for the modelling of problems arising in the physical world.
[Mathematical Modelling](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2507): investigates the translation of physical problems into mathematics.
[Statistical Inference](https://www.st-andrews.ac.uk/subjects/modules/catalogue/?meta_modulecode=MT2508): introduces techniques for drawing inferences about population characteristics from observed data.

[Mathematics and Statistics 2000-level modules](https://www.st-andrews.ac.uk/subjects/modules/search/?mod=false&profile=_default&query=!null&f.Level%7CMavLev=2000&f.Module-prefix%7Cdomaincode=mt&collection=uosa-module-catalogue-v2&sort=metamodulecode&wildcard=1&form=simple&num.ranks=10&f.School%7Cdept=school%20of%20mathematics%20and%20statistics&f.Year%7CAllDocumentsFill=All%20modules)
#### Honours

In the final three years, you choose from a wide variety of advanced options. Here is a sample of Honours modules which have been offered in previous years:


Bayesian Inference
Dynamical Systems
Fractal Geometry
Solar Theory
Techniques of Applied Mathematics
Topology

As an MMath student, you will also be able to take Masters-level modules. In the past, these have included:

Advanced Data Analysis
Advanced Group Theory
Ergodic Theory and Dynamical Systems
Estimating Animal Abundance and Biodiversity
Galois Theory
Geophysical Fluid Dynamics
Spatial Models and Pattern Formation in Mathematical Biology

In your third, fourth and fifth years, you will choose from a range of 3000-level, 4000-level and 5000-level modules. 

Here are the modules offered during the current session and in previous years:

[Mathematics and Statistics 3000-level modules](https://www.st-andrews.ac.uk/subjects/modules/search/?mod=false&profile=_default&query=!null&f.Module-prefix%7Cdomaincode=mt&f.Level%7CMavLev=3000&collection=uosa-module-catalogue-v2&sort=metamodulecode&wildcard=1&form=simple&num.ranks=10&f.School%7Cdept=school%20of%20mathematics%20and%20statistics&f.Year%7CAllDocumentsFill=All%20modules)
[Mathematics and Statistics 4000-level modules](https://www.st-andrews.ac.uk/subjects/modules/search/?mod=false&profile=_default&query=!null&f.Module-prefix%7Cdomaincode=mt&f.Level%7CMavLev=4000&collection=uosa-module-catalogue-v2&sort=metamodulecode&wildcard=1&form=simple&num.ranks=10&f.School%7Cdept=school%20of%20mathematics%20and%20statistics&f.Year%7CAllDocumentsFill=All%20modules)
[Mathematics and Statistics 5000-level modules](https://www.st-andrews.ac.uk/subjects/modules/search/?mod=false&profile=_default&query=!null&f.Module-prefix%7Cdomaincode=mt&f.Level%7CMavLev=5000&collection=uosa-module-catalogue-v2&sort=metamodulecode&wildcard=1&form=simple&num.ranks=10&f.School%7Cdept=school%20of%20mathematics%20and%20statistics&f.Year%7CAllDocumentsFill=All%20modules)

In your final year, you also undertake an advanced project on a topic chosen in consultation with the teaching staff of the School of Mathematics and Statistics. You will be required to investigate the topic in some depth, submit a report and give a presentation.