This module aims to provide an introduction to vector spaces and linear maps. The foundations are laid by studying basic manipulations of complex numbers, vectors and matrices. The underlying geometric meanings of these manipulations are emphasised and concrete examples are explored both by hand and with the help of computer software. Once the foundations have been developed, more advanced and abstract notions are studied for a deeper understanding.
This module builds on the topics covered in MSO2110 Groups and Rings. The module begins with a review of the material on rings encountered in the prerequisite and proceeds to build towards a study of fields, culminating in the development of Galois Theory. Students will develop their appreciation of the effect additional axioms have on the structure of rings by learning about commutative rings, Euclidean rings, integral domains, fields and other algebraic objects. In the second half of the module students will extend the work on fields and field extensions to develop Galois Theory.
This module builds on the discrete mathematics introduced in the second year to provide students with a range of methods for analysing and solving combinatorial problems, with applications across mathematics and to computer science, physics and beyond. It explores ideas of graph theory and design theory, and a range of techniques for solving counting problems both by hand and using computing. It also aims to develop students’ analytical and reasoning skills, and their ability to apply familiar techniques in unfamiliar settings.
This module introduces students to the main principles and ideas of functional analysis – a modern branch of mathematical analysis, largely influenced by progress in physics during the 20th century, such as quantum mechanics. The main object of study is a vector space, the elements of which are functions, so that the space is usually infinite-dimensional. Starting from simple geometric objects in vector spaces, the module will gradually introduce ideas from other areas of mathematics, such as topology, differentiation, integration, measure, optimisation, differential and integral equations. Functional analysis will help students to build a unified and beautiful picture about these topics, and achieve deeper understanding of various branches of mathematics and their applications.
There are a range of additional optional modules that you will be able to take during your fourth year that will continue building your knowledge and skills from previous modules to a more advanced level of study.
You can find more information about this course in the programme specification. Optional modules are usually available at levels 5 and 6, although optional modules are not offered on every course. Where optional modules are available, you will be asked to make your choice during the previous academic year. If we have insufficient numbers of students interested in an optional module, or there are staffing changes which affect the teaching, it may not be offered. If an optional module will not run, we will advise you after the module selection period when numbers are confirmed, or at the earliest time that the programme team make the decision not to run the module, and help you choose an alternative module.
Sabiha Akhtar Uddin
Mathematics BSc/MMath student
Dr. Jones studied undergraduate mathematics at Lancaster University and University of Maryland, College Park, USA, before completing his PhD at University College London. He works in complex analysis on Riemann surfaces, functional analysis and operator theory.
Professor Albrecht joined Middlesex in 2012, bringing extensive experience in the field of simulation and modelling. His interests are in applied mathematics in molecular biology. At Middlesex, he has been applying mathematical modelling techniques to study DNA strings, with a particular focus on the impact of microRNAs (short RNA sequences) on cell regulation as mutations have been linked to diseases, including cancer.
Dr. Megeney studied undergraduate mathematics, a masters in stochastic processes, achieving a distinction, and a PhD at University College London. She worked on packing and covering theorems in higher dimensions for her PhD; she has since worked in mathematics education and is interested in the interaction of mathematics and art.
Dr Bending studied mathematics at Cambridge University, achieving an MA and a distinction in Part III before studying for a PhD at Queen Mary and Westfield College, London. Thomas works in combinatorics, graph theory, and finite geometries.
Dr Matthew Jones
Mathematics BSc/MMath Course Leader
Professor Andreas Albrecht
Mathematics BSc/MMath academic
Start: Autumn 2018
Duration: BSc: 3 years full-time, 4 years with placement, 6 years part-time, MSci: 4 years part-time, 5 years with placement, 8 years part-time
Code: BSc: G111, MSci: G11A