University of Essex enjoy breaking away from tradition. In this module you will break from “classical physics” and gain a conceptual understanding in quantum physics. You will develop skills in solving quantum mechanical problems associated with atomic and molecular systems.

Group theory is the study of symmetries, which are the actions that rotate polyhedrons such as the cube and they permeate science at large, playing an important role in physics (such as the standard model of particle physics ), chemistry (molecules, crystals, materials science…), cryptography or 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.

In this module you will learn what underpins the algorithms used where variables are integer and apply these algorithms to solve integer and mixed integer problems with cutting-plane algorithms.

The subject of Ordinary Differential Equations (ODEs) is a very important and fascinating branch in mathematics. An abundance of phenomena in physics, biology, engineering, chemistry, finance and neuroscience to name a few, may be described and studied using such equations. The module will introduce you to advanced topics and theories in ODEs and dynamical systems.

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.

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. Analsye the concepts of error detection and correction. Understand the algebra and number theory used in modern cryptography and coding schemes.

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, as well as help developing foundational notions helpful in other areas such as number theory, algebraic geometry, and homological algebra. Examples will be key, many of them will be made ‘graphic’ thanks to Hilbert’s Nullstellensatz.

This module will enable you to expand your knowledge on multiple statistical methods. You will learn the concepts of decision theory and how to apply them, have the chance to explore “Monte Carlo” simulation, and develop an understanding of Bayesian inference, and the basic concepts of a generalised linear model.