This module is suitable for students with A level Mathematic (grade B or higher). – Students with AS level Mathematics are required to take MATH1004 instead. The aim of the module is to provide students with the necessary skills and confidence to apply a range of mathematical methods to problems in the physical sciences. Both MATH1006 and MATH1008 cover essentially the same topics in calculus that are of relevance to applications in the physical sciences but MATH1008 is aimed at students taking degrees in chemistry, geology and oceanography. Physics students should take MATH1006. The aim of the module is to provide students with the necessary skills and confidence to apply a range of mathematical methods to problems in physics. The module begins by looking at vectors in 2 and 3 dimensions, introducing the dot and cross products, and discussing some simple applications. This is followed by a section on matrices, determinants, and eigenvalue problems. The course then reviews polynomial equations and introduces complex numbers. After this, some basic abstract concepts related to functions and their inverses are discussed. The main part of the unit covers the basics of calculus, starting with limits, and going on to look at derivatives and Taylor series. The concept of integration is then defined, followed by an exploration (by means of examples) of various methods of integration. One of the pre-requisites for MATH1007, MATH1049, MATH2015 and MATH3072
The module provides advanced mathematics training necessary for students planning to specialise in physical chemistry, computational chemistry, spectroscopy, data science and quantitative finance. It also aims to provide training of rational reasoning skills in a subject-independent way: studying mathematical proofs and derivations introduces a more rigorous logical system than practical or applied skills training alone. First year students should be aware that this module requires A-level mathematics. There are no pre-requisite modules for second and third year students.
This module provides training in advanced mathematics and numerical methods that will allow in-depth understanding and solving of problems in physical chemistry, computational chemistry, and spectroscopy. It will also provide transferable skills that can be applied to other areas such as data science and quantitative finance. It involves learning to solve problems both “on paper” and on a computer by developing code in Python.
- Linear programs: their basic properties; the simplex algorithm. - Duality: the relationship between a linear program and its dual, duality theorems, complementarity, and the alternative; sensitivity analysis. - The interior point method for convex optimization: optimality conditions; the central path; convergence analysis; applications to linear programming and general convex optimization. - Integer Programming: Branch and bound algorithms and/or cutting plane methods. - The use of a computer software to solve mathematical programming problems.
This course is designed to develop key mathematical and analytical chemistry skills. The course will introduce student who have not studied A-level maths to the key mathematical concepts required for successful completion of the chemistry degree. This will be taught alongside an introduction to analytical chemistry that can provide qualitative or quantitative information about the chemical composition of a sample. The analytical chemistry components of the module will provide an introduction into the fundamentals of chemical analysis, including an understanding of sample preparation, chromatographic separations, and some of the most important analytical techniques today, including IR, NMR, Raman and UV-visible spectroscopies, and mass spectrometry.
This course is designed to develop fundamental mathematical skills which engineers need in order to tackle a wide variety of engineering and design problems. There is a particular focus on developing an understanding of mathematics as a toolbox through practical examples based on case studies from academia and industry
This module offers an introduction to the algebra and trigonometry that underpin engineering mathematics
This module provides you with a foundation in mathematics and statistics which will allow you a smooth transition to an undergraduate module containing quantitative material.
This module offers an introduction to the differential and integral calculus that underpins engineering mathematics.
This module provides students with some fundamental mathematical concepts relevant to applications in AI and CE. The focus will be on applying mathematical proofs to solve computer science problems as well as introducing basic concepts and techniques in linear algebra and calculus. In addition to theoretical treatments, there will be laboratory applications using Python and Jupyter to visualize, manipulate and explore mathematics.
This module provides students with fundamental mathematical concepts relevant to applications in AI and CE. The focus will be on probability, statistical inference, combinatorics, optimization techniques, calculus – partial derivatives and ordinary differential equations, and symbolic maths. There will be laboratory applications using Python and Jupyter to visualise, manipulate and explore these topics.
This module provides a bridge between A-level mathematics and university mathematics. It provides a good grounding and an in depth understanding of the theory and application of differential calculus, and other techniques widely used in Economics and Finance. It is aimed at students who hold an A level in Mathematics at Grade B or above. Topics of study include functions, univariate optimisation, elasticity, financial mathematics, multivariate optimisation, constrained optimization, matrices, integration, difference and differential equations, and Taylor/Maclaurin series expansions. The module is designed to prepare students for more advanced quantitative modules in 2nd and 3rd year. It also complements the teaching of first year microeconomics and macroeconomics modules.
This course lays the mathematical foundation for all engineering degrees. Its structure allows students with different levels of previous knowledge to work at their own pace. Pre-requisite for MATH2048 One of the pre-requisites for MATH3081 and MATH3082
The module aims to teach mathematical methods relevant for engineering. The first part is about differential equations and how solve them, from ordinary differential equations to partial differential equations. The second part is about either vector calculus (for Mech, Ship, Aero and ISVR) or statistics (for Civil Engineering). There are 3 lectures and 1 problem class per week. Problems are assigned each week. They are discussed in the problem class and then the solutions are posted on blackboard. Feedback and student support during module study (formative assessment) - Entire cohort: 4 on-line coursework assignments, which are marked as soon as they are completed and the corrected answers are given. Fully worked out solutions are posted on blackboard after the deadline. For Mech, Ship, Aero and ISVR: 2 additional on-line coursework. For Civil Engineering: coursework in the form of Minitab exercises - 1 class test - Lecture notes, coursework assignments, solutions and past examination papers available on the blackboard site One of the pre-requisites for MATH3083 and MATH3084
This module is designed to provide students with the mathematics knowledge and skills required for a successful transition to degree-level study in disciplines related to the chemical and biological sciences. The material covered is at a level corresponding to pre-university qualifications such as AS level in the UK.
This module aims to: - Introduce the logical and mathematical foundations of computer science. - Illustrate the use of formal languages in computer science, including in algorithms and programming. - Extend students' mathematical sophistication and skills. - Present basic concepts and techniques of combinatorics, statistics and probability. - Give mathematical background necessary for other compulsory modules. - Develop the study skills necessary for students to learn new concepts of mathematics and programming (including those we do not cover in the degree). - Instill a range of useful problem solving skills.
This module aims to cover the continuous mathematics that's required for the computer science and software engineering programmes.
Machine Learning is about extracting useful information from large and complex datasets. Although driven by applications, the techniques used are based on a broad mathematical basis. This course provides the mathematical foundations of the subject from functional analysis through to optimisation, convexity and information theory.
This module is compulsory for every Year 3 student of any Mathematical Sciences degree programme. Its main goal is to provide the student with an opportunity to research an area of mathematics that interests them, while strengthening their transferrable skills and supporting them in growing their CV and achievements that will make them more attractive to employers. As to the latter, there will be specific sessions devoted to various topics related to employability, CV preparation, and other aspects of job hunting. The remainder of this module overview is however about the former, the main part of this module. This module provides an opportunity to develop skills and knowledge in an area of mathematical science that excites the student and matches their particular strengths. We will provide support to guide the student through their research and report preparation, while giving them the freedom to explore the subject on their own. Support is provided through plenary lectures and through individual (roughly bi-weekly) supervision meetings. The work may involve directed reading of books or original papers in journals and the provision of examples to illustrate particular aspects of a topic. Some topics may also present the opportunity for students to pursue their own investigations, undertake practical work using the computer or working on a project brief from an industry partner. In summary, the student will learn how to: (a) Write up a report on their topic: a preliminary report at the end of Semester 1 leading to feedback and advice followed by a completed final report at the end of Semester 2. (b) Carry out a literature survey appropriate to their topic and how to use a wide variety of sources in an imaginative way, how to give proper credit to the work of others, and in particular what constitutes and how to avoid plagiarism. (c) Present their work to a small audience. This is great training for communicating a technical subject succinctly, and a skill a student will definitely use after graduating. There is an opportunity to present their work both at the end of Semester 1 and at the end of Semester 2.
‘I have here in my hand a list of 205 names that were made known to the Secretary of State as being members of Communist Party and who nevertheless are still working and shaping policy in that State Department.' With these words, asserting both the existence of an internal communist menace and the government failure to act against it, Senator Joseph McCarthy thrust himself into the centre of US national politics. His inquisition into communist subversives and spies lasted from 1950 to 1954. But ‘McCarthyism' as a phenomenon was more deeply-rooted, more enduring and much broader in scope than the career and campaigns of a single politician. This module explores the causes, course and effects of McCarthyism writ large, from the end of the Second World War through to the late 1950s.
