Mathematics BSc (Hons)

About the course

If you are looking for a career that involves shaping technological or scientific progress then mathematics is an ideal degree programme for you. It is a vital practical skill with deep insight which holds the key to advances in virtually all areas of our daily lives - from financial to computing to design, logistics to medicine, travel to weather forecasting. The BSc Honours Mathematics offers a wide choice of modules to meet your unfolding interests. Approachable and enthusiastic staff use a variety of teaching methods - lectures, tutorials, practicals, teamwork and project work - to bring the topic to life. Assessment is also varied enabling you to demonstrate your strengths and knowledge.

In your first year you will build on material taught at A level, and progress to more abstract and advanced mathematical concepts. Using mathematical and statistical software, you'll develop skills needed later in the programme, while group work and computer-based applications reinforce what you learn in lectures.

In your second year you have a wide choice of mathematics and statistics options which allows you to study your developing interests in greater depth.

In your third year you may choose to spend a year working on professional placement.

In your final year you undertake a project in an area of your interest, in addition to taught study.

What our students say

Why choose this course?

• You will be part of a small and friendly department within the School of Physics, Astronomy and Mathematics. Visit our School web page.
• You can choose a general study of Mathematics or specialize in either Computing or Financial Mathematics.

Study routes

• Sandwich, 4 Years
• Part Time, 5 Years
• Full Time, 3 Years

Locations

• University of Hertfordshire, Hatfield

Careers

As a mathematics graduate your expertise in problem solving, processing information, rational thinking and working logically will be in high demand, and be a sound basis for many careers. Accountancy, business or financial services, economics and teaching are popular student choices, but many go on to secure well-paid jobs in areas such as computing, consultancy, engineering, the environment, medicine, research and telecommunications.

Teaching methods

Most of the teaching is delivered in the form of lectures, with class sizes typically between 20 and 30. Our lectures are supported by the University's e-learning system StudyNet and it is possible to download lecture notes, assessments and submit coursework through StudyNet. Lecture material is reinforced by tutorials and workshops, where you will receive one-on-one guidance. Finally, we place a strong emphasis on project work and you will spend part of your final year working on a substantial research project with the support of a member of staff.

Work Placement

You have the opportunity to spend a year working either in a professional research environment or within industry. The practical experience you gain will be of tremendous benefit both when you resume your studies and when you embark on a career. Students have previously undertaken placements in organisations such as:

• RFI Global Services Ltd
• National Audit Office

Professional Accreditations

Accredited by the Institute of Mathematics and its Applications (IGradIMA)

Accredited by the Institute of Analysts and Programmers (GradIAP), depending on modules studied.

Structure

Year 1

Core Modules

• Basic Statistics

  This is an introductory module in statistics. Basic ideas such as initial data analysis, the mean, standard deviation and variance, probability, statistical distributions, the use of a statistical package, the use of data for inference and decision making are covered. This involves confidence intervals for means and techniques for hypothesis testing for differences between means, differences between proportions and for the size of a correlation. Other topics covered include simple linear regression, and the analysis of category data and contingency tables. A wide variety of situations in which these techniques may be employed will be considered, with examples taken from business, engineering, science, social sciences, etc. The emphasis throughout is on conceptual understanding and the development of practical statistical skills, supported by the use of a statistical computer package.

• Mathematical Techniques 1 (L1)

  On entry students will have different mathematical knowledge and this module has been designed to standardise their mathematical knowledge. The module will initially review core areas of A-Level Mathematics which will be extended to improve students' knowledge. You will learn the standard mathematical techniques in calculus, matrices and vectors.

• Applications of Computing

  In this module, you will learn how to program in a high-level language. You will see how to develop scientific and mathematical models and how they can be implemented in a computational environment. At the end of the module you will be capable of writing a technical report in which you present the results of an investigation using computer packages.

• Applications of Mathematics

  Students will learn about the Kinematics and Dynamics of particles and rigid bodies. In particular they will learn about Newtons laws in 1 and 2-D including the application to vertical motion under gravity and resistive motion. The concepts of Impulse and momentum will be introduced and applied along with the principles of work and energy. More advanced areas of mechanics will be investigated including rotational kinematics and projectile motion. Frequency and oscillations will be introduced leading to investigating and applying simple harmonic oscillators. Refer to the teaching plan for a more detailed description.

• Linear Algebra and Analysis

  You will learn fundamental ideas and language on which the rest of mathematics is based. The module also investigates the idea of tending to a limit, on which calculus is based, and some of the ideas of linear algebra which occur throughout mathematics.

• Financial and Actuarial Mathematics

  You learn fundamental ideas about companies and the range of investment types traded in the markets. Information on the financial performance of companies is collected from various sources such as the financial press and financial websites. This information is used to plot graphs and to construct trendlines. A variety of techniques are used to evaluate companies and to predict their future share price movements. You will understand the risk involved and will be able to estimate it. Finally you will appreciate the need to spread investments across a portfolio. Throughout the module live data will be downloaded from the internet and used in spreadsheets to illustrate the methods and ideas discussed in the module. Refer to the teaching plan for a more detailed description.

• Small Group Tutorial

  The module will require students to attempt a range of problems, mostly of a mathematical nature, broadly in the students' subject area. Some problems will be associated with other specific taught modules on the programme, while others will have a synoptic role sitting across several modules. The work will challenge students to develop problem solving skills that enable them to approach unfamiliar as well as familiar problems.

Optional

Year 2

Core Modules

• Mathematical Techniques 2

  You will learn how to integrate functions of two and three variables along plane and space curves and how to evaluate multiple integrals of such functions. You will learn about gradient, divergence and curl. You will be able to obtain Fourier series expansions of simple functions and perform calculations involving functions of a complex variable.

• Differential Equations

  This module employs a variety of mathematical methods and techniques to explore, describe and predict the behaviour of scientific, industrial and engineering phenomena. The subject appeals to individuals interested in applying their mathematical interests and skills to real-word problems. In this module, we will focus on ordinary differential equations. The emphasis is on the development of methods important in applications. Topics include:- Theory and applications of first, second and higher order differential equations, The Laplace transform methods, Systems of linear differential equations.

• Real Analysis

  In this module we will formalize what we mean by a function of a real variable, and what it means for it to be continuous and differentiable. We will also formalize integration as a limit of a sum, and give many applications.

Optional

• Statistical Modelling

  This module has been developed to give students a detailed understanding of the commonly used statistical modelling techniques of analysis of variance and regression analysis. The following topics are considered on this module: - Regression Analysis including: simple linear regression; ANOVA applied to regression; multiple regression; polynomial regression; simple examination of residuals; choice of regressors; multicollinearity; use of dummy variables. - Analysis of Variance including: one and two factor designs, partitioning of sums of squares; fixed and random effects; interaction. The module is supported throughout by the use of a statistical computer package (eg MINITAB or SPSS) which facilitates the analysis of data sets, taken from a variety of application areas, using the methods taught in the lectures.

• Mathematical Techniques 2

  You will learn how to integrate functions of two and three variables along plane and space curves and how to evaluate multiple integrals of such functions. You will learn about gradient, divergence and curl. You will be able to obtain Fourier series expansions of simple functions and perform calculations involving functions of a complex variable.

• Portfolio Risk Management

  This module concerns itself with the mathematical analysis of portfolios of securities. A variety of techniques are introduced to analyse the risk and expected return of portfolios leading to the construction of efficient portfolios. Throughout the course live data will be downloaded from the internet and used in variety of software packages to illustrate the methods and ideas discussed in the course. Refer to the course plan for a more detailed description.

• Professional Skills

  The overall aim of this module is to develop the skills necessary to be able to contribute as a graduate in the world of work. The content includes opportunities to develop further the techniques of effective presentation, both in written reports and in oral presentation. Also, you will learn to develop further the ability to work in a team. You will learn to address circumstances requiring professional judgement. During the module you will also develop skills in the area of career management. This will be achieved through the following: researching information on post-graduation opportunities, the the introduction of MAPS PDP tool as a way of gathering information relating to your skills and experiences, and participation in activies to prepare you for applying for future opportunities. The aim of this part of the module is to raise awareness of employability issues and be confident in putting forward your skills and experiences for future opportunities.

• Professional Teaching Skills

  This is an excellent practical training for anyone who thinks they may wish to become a school teacher. After receiving initial training in writing a CV and job application you obtain a placement in a school for ten half days to work with the class teacher. You develop teaching skills and build a relationship with the class teacher. You also benefit from the help and advice of a University Mentor. At the end of that period you give a presentation to the class, which is assessed. You keep a diary throughout and write a final report. During the module you will also develop skills in the area of career management. This will be achieved through the following: researching information on post-graduation opportunities, the introduction of MAPS PDP tool as a way of gathering information relating to your skills and experiences, and participation in activities to prepare you for applying for future opportunities. The aim of this part of the module is to raise awareness of employability issues and be confident in putting forward your skills and experiences for future opportunities.

• Number Theory

  Number theory is one of the oldest branches of mathematics and is concerned with the properties of integers. Number theory has many practical applications including such topics as cryptography. This module will look at divisibility among integers, the Euclidean algorithm and factorization into prime numbers. The distribution of the primes will be investigated. Modular ("clock") arithmetic leads to the investigation of congruences, Fermat's little theorem, Chineses remainder theorem, and quadratic reciprocity. We also consider Euler's phi function, and other topics such as Diophantine equations and continued fractions.

• Differential Equations

  This module employs a variety of mathematical methods and techniques to explore, describe and predict the behaviour of scientific, industrial and engineering phenomena. The subject appeals to individuals interested in applying their mathematical interests and skills to real-word problems. In this module, we will focus on ordinary differential equations. The emphasis is on the development of methods important in applications. Topics include:- Theory and applications of first, second and higher order differential equations, The Laplace transform methods, Systems of linear differential equations.

• Real Analysis

  In this module we will formalize what we mean by a function of a real variable, and what it means for it to be continuous and differentiable. We will also formalize integration as a limit of a sum, and give many applications.

• Mechanics

  You will learn about motion and how to determine the way a particle moves. This has applications in almost every area of human endeavour from spaceships to sport.

• Numerical Methods

  You discover how to use numerical methods to solve mathematical problems, and to discuss relative performance of different methods in terms of accuracy and efficiency. You also learn about the theoretical background to the methods. Refer to the teaching plan for a more detailed description.

• Algebra

  In this module we introduce the two main foundations of algebra - linear algebra and group theory. The linear algebra is continuation of the Linear Algebra and Analysis module of the first year. We discuss linear transformations and applications of eigenvalues and eigenvectors to quadratic forms. Group theory is developed from the axioms of a group. We discuss the structure of groups, permutation groups, subgroups and quotient groups.

Year 3

Core Modules

Optional

• Professional Placement

  Supervised work experience provides students with the opportunity to set their academic studies in a broader context, to gain practical experience in specific technical areas and to strengthen their communication and time-management skills. It greatly assists them in developing as independent learners, so that they are able to gain the maximum benefit from the learning opportunities provided at level 3 of the programme.

• Year Abroad

  The Year Abroad will provide students with the opportunity to expand, develop and apply the knowledge and skills gained in the first two taught years of the degree within a different organisational and cultural environment in a partner academic institution. The host institution will appoint a Programme Co-ordinator who will oversee the student's programme during the Year Abroad and will liaise with the appointed UH Supervisor.

Year 4

Core Modules

• Complex Analysis

  Complex Numbers are two dimensional, and are an unordered set. This leads to many startling and bizarre ideas. We apply the ideas of continuity and differentiability to functions of a complex variable, and reach some surprising conclusions. However, it is when applying the ideas of integration that the most beautiful and impressive results emerge, with many practical applications. Finally we investigate iterations of a complex function, which will lead to the Mandelbrot set, fractals and chaos.

• Investigation in Mathematics

  Students will choose a topic from a list of typically 5-10 different mathematics topics offered by School staff (tutors), and will conduct an open-ended investigation into that topic. The students working on each topic will work independently on their investigations, under the guidance of a tutor. They will be required to produce an original, substantial and professionally presented printed report on their findings, and to prepare a poster to summarise your findings. Students will be interviewed about their report when their poster is displayed.

Optional

• Linear Modelling

  This is a module in statistics for students who wish to study techniques widely used by statisticians. Linear modelling brings together regression and analysis of variance into a single modelling approach based on matrix algebra and extends these methods to include category response variables. The main topics studied are likely to include: - the matrix algebra approach to linear regression; - methods of analysing non-orthogonal sums of squares; - the dummy variables approach to the analysis of experimental design models; - the analysis of contingency tables by use of log-linear models; - logistic regression; - the principles of the generalised linear model.

• Multivariate Statistics

  This is a module in statistics for students who wish to study techniques widely used by statisticians working in research, commerce and industry. Multivariate statistics introduces techniques for examining relationships among a group of variables, and a number of multivariate statistical methods are introduced. Throughout the module, computer packages are used wherever relevant to analyse case studies relating to the techniques taught. The main topics studied are likely to include: - methods of viewing multivariate data; - how to describe multivariate data in a statistical manner; - how to conduct hypothesis tests using multivariate data; - how to carry out various methods of multivariate data analysis; - how to interpret the results of various methods of multivariate data analysis.

• Quantum Computing A

  Quantum information processing continues to be an extremely active research area exploiting fundamental quantum phenomena in new applications from computation, secure data communication and information processing. A major paradigm shift, the area is of significant interest and potential benefit to computer scientists, mathematicians and physicists. This module will be theoretical in nature, exploring concepts and applications from the area of Quantum Information Processing with an emphasis on Quantum Computing. Content will vary according to current research directions.

• Quantum Computing B

  The content for this module builds upon that presented in Quantum Computing A tackling for example more advanced topics such as Shor's algorithm and Grover's algorithm. The content is theoretical in nature, exploring concepts and applications from the area of Quantum Information Processing with an emphasis on Quantum Computing. Content will vary according to current research directions.

• Mathematics of Derivatives and Option Pricing

  You will learn about the mathematical modelling of options, futures and derivatives. After some initial definitions, you will concentrate on the classical Black-Scholes analysis, using a risk neutral process. Arbitrage arguments will be used to derive the Black-Scholes partial differential equation for the fair value of an option. A variety of different kinds of option will then be considered and valued either by applying the Black-Scholes equation or the binomial model. Refer to the course plan for a more detailed description.

• Waves and Fluids

  This module develops the basic physics required to understand core topics in wave and fluid physics.

• Linear Optimisation

  You learn to tease out the relevant information from business problems and to develop linear models to represent them. A number of different solution methods are developed and used to solve these problems. You will develop the ability to interpret the results in management terms and how to handle changes in the data after the problem has been solved. You also learn about other practical difficulties involved in the process. Refer to the teaching plan for a more detailed description.

• Boundary Value Problems

  You will learn how to solve one and two-dimensional boundary-value problems both analytically and numerically. Through practical sessions you will use suitable numerical software to investigate the numerical processes. Refer to the teaching plan for a more detailed description.

• Financial Optimisation

  You will learn about the minimum-risk portfolio selection problem and how to solve it using a number of different optimisation techniques. You will then meet the more difficult problem of maximising return for a given risk which involves nonlinear equality constraints and must be tackled using iterative methods. You will study the convergence properties of these iterative methods and learn how to use software implementations of them. You will also study how to model and solve extensions of these basic portfolio problems which involve additional conditions and restrictions. Refer to the teaching plan for a more detailed description.

• Space Dynamics

  Spacecraft dynamics is studied using core physical ideas, case studies and modelling techniques.

• Further Algebra

  This course builds on the level 5 course Algebra. We aim at deepening results on known algebraic structures by focusing on some of the following topics: polynomial rings; field extensions and introduction to Galois theory; finite fields and applications in crytography; permutation groups. Also to introduce new structures such as ordered sets, lattices and universal algebra, and their applications.

• Nonlinear Systems

  You will learn how to investigate and evaluate the qualitative behaviour of the solutions of differential equations which relate to problems in a wide variety of application areas. You will recognise that the behaviour of the solution of a differential equation can be drastically altered by the small change of a coefficient. These observations may have important contributions in improving the applications of mathematics in industry, business and the physical sciences. The module provides the student with a deep understanding of differential equations.

Fees & funding

Fees 2013

UK/EU Students

Full time: £8,500 for the 2013 academic year

International Students

Full time: £9,500 for the 2013 academic year

Discounts are available for International students if payment is made in full at registration

View detailed information about tuition fees

Scholarships

• National Scholarship Programme

Find out more about scholarships for UK/EU and international students

Other financial support

Find out more about other financial support available to UK and EU students

Living costs / accommodation

The University of Hertfordshire offers a great choice of student accommodation, on campus or nearby in the local area, to suit every student budget.

View detailed information about our accommodation

How to apply