Component
Integrated Master in Mathematics: Mathematics options

# Final Year, Component 02

Options from list
MA220-7-AU
Number Theory
(15 CREDITS)

Number theory encompasses some of the most classical and important topics in mathematics, stemming from the study of integers, Diophantine equations, prime numbers and modular arithmetic. As well as introducing each of these, in this module it will be demonstrated how techniques from a range of mathematical disciplines such as algebra and geometry can be brought to bear.

MA301-7-SP
Group Theory
(15 CREDITS)

" Group theory is the study of symmetries, which are actions that preserve structure (such as rotations of the cube). These permeate science at large, playing an important role in physics (particularly particle physics and astrophysics), chemistry (molecules and crystals), cryptography and even music! In this module you will learn advanced constructions and techniques in modern group theory, with special emphasis on the study of finite groups.

MA305-7-AU
Nonlinear Programming
(15 CREDITS)

How do you apply an algorithm or numerical method to a problem? What are the advantages? And the limitations? Understand the theory and application of nonlinear programming. Learn the principles of good modelling and know how to design algorithms and numerical methods. Critically assess issues regarding computational algorithms.

MA307-7-AU
Advanced Ordinary Differential Equations and Dynamical Systems
(15 CREDITS)

The subject of Ordinary Differential Equations (ODEs) is a very important and fascinating branch of mathematics. These equations describe many phenomena, for instance in physics, biology, engineering, chemistry, finance and neuroscience and elsewhere. This module will introduce you to advanced topics in ODEs and dynamical systems.

MA314-7-SP
Graph Theory
(15 CREDITS)

Examine key definitions, proofs and proof techniques in graph theory. Gain experience of problems connected with chromatic number. Understand external graph theory, Ramsey theory and the theory of random graphs.

MA315-7-SP
Cryptography and Codes
(15 CREDITS)

How do standard coding techniques in computer security work? And how does RSA cryptography work? Examine the principles of cryptography and the mathematical principles of discrete coding. Analyse the concepts of error detection and correction. Understand the algebra and number theory used in modern cryptography and coding schemes.

MA316-7-AU
Commutative Algebra
(15 CREDITS)

" Commutative algebra is the cornerstone established by Hilbert to give a formal backing to intuitive arguments in geometry. This module will provide you with a solid foundation of commutative rings and module theory, and will develop foundational notions used in other areas such as number theory, algebraic geometry and homological algebra. Examples will be key, and many will be made visual thanks to Hilbert’s Nullstellensatz.

MA323-7-SP
Partial Differential Equations
(15 CREDITS)

This module will cover partial differential equations (PDEs), which can describe a wide array of physical processes and phenomena. You will learn the properties of first and second order PDEs, the concepts behind them and the methods for solving such equations.

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