BSc Mathematics

Program Overview

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Mathematics provides the logical foundations on which all of science, engineering and technology are built. Our BSc Mathematics course gives you the chance to study both fundamental topics and their modern applications, including:

• Pure mathematics, including geometry, algebra, analysis and number theory
• Applied topics such as mathematical physics, cryptography, mathematical modelling, differential equations and dynamical systems
• Statistical, financial and analytical methods such as optimisation and the study of risk

As well as these mathematical topics, your degree will develop your programming skills in languages such as Python and SQL, and you will learn to solve sophisticated problems using computational toolkits such as Matlab, Maple and R. Our department recognises the stand-alone and interdisciplinary aspects of mathematics, and your degree provides an exceptional range of in-demand transferrable skills for mathematically oriented careers, from business, to finance and commerce, industry, research, government, education and beyond. All our mathematical sciences degrees feature an employability component in every year, explicitly training sought-after skills and incorporating careers day events and seminars from speakers in industry.

Professional accreditation

This programme will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees. Why we're great.

• 85% of our Department of Mathematical Sciences graduates are in employment or further study (Graduate Outcomes 2023).
• We are 26th in the UK for Mathematics in The Guardian University Guide 2023.
• We are continually broadening the array of expertise in our department, giving you a wide range of options and letting you tailor your degree to your interests.

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Study abroad

Your education extends beyond the university campus. We support you in expanding your education through offering the opportunity to spend a year or a term studying abroad at one of our partner universities. The four-year version of our degree allows you to spend the third year abroad or employed on a placement abroad, while otherwise remaining identical to the three-year course. Studying abroad allows you to experience other cultures and languages, to broaden your degree socially and academically, and to demonstrate to employers that you are mature, adaptable, and organised. If you spend a full year abroad you'll only pay 15% of your usual tuition fee to Essex for that year. You won't pay any tuition fees to your host university

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Placement year

Alternatively, you can spend your third year with an external organisation, learning about a particular sector, company or job role, applying your academic knowledge in a practical working environment, and receiving inspiration for future career pathways. You will be responsible for finding your placement, but with support and guidance provided by both your department and the placements team. If you complete a placement year you'll only pay 20% of your usual tuition fee to Essex for that year.

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Our expert staff

As well as being world-class academics, our staff are award-winning teachers. Many of our academics have won national or regional awards for lecturing, and many of them are qualified and accredited teachers – something which is very rare at a university. Our department is committed to providing you with the academic support you need to succeed. Our flexible policy means some staff are always available, whilst others maintain regular drop-in times. Staff are always happy to arrange appointments for longer discussions, and no issue is too big or too small. Our innovative research groups are working on a broad range of collaborative areas tackling real-world issues. Here are a few examples:

• Our data scientists carefully consider how not to lie, and how not to get lied to with data. Interpreting data correctly is especially important because much of our data science research is applied directly or indirectly to social policies, including health, care and education.
• We do practical research with financial data (for example, assessing the risk of collapse of the UK’s banking system) as well as theoretical research in financial instruments such as insurance policies or asset portfolios.
• We also research how physical processes develop in time and space. Applications of this range from modelling epilepsy to modelling electronic cables.
• Our optimisation experts work out how to do the same job with less resource, or how to do more with the same resource.
• Our pure maths group are currently working on two new funded projects entitled ‘Machine learning for recognising tangled 3D objects’ and ‘Searching for gems in the landscape of cyclically presented groups’.
• We also do research into mathematical education and use exciting technologies such as electroencephalography or eye tracking to measure exactly what a learner is feeling. Our research aims to encourage the implementation of ‘the four Cs’ of modern education, which are critical thinking, communication, collaboration, and creativity.

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Specialist facilities

• We have a Maths Support Centre , which offers help to students on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
• We have a dedicated social and study space for maths students in the department, which is situated in the STEM Centre
• We host regular events and seminars throughout the year
• Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

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Your future

Clear thinkers are required in every profession, so the successful mathematician has an extensive choice of potential careers. Mathematics students are in demand from a wide range of employers in a host of occupations, including financial analysis, management, public administration and accountancy. The Council for Mathematical Sciences offers further information on careers in mathematics. Our recent graduates have gone on to work for a wide range of high-profile companies including:

• KPMG
• British Arab Commercial Bank
• Johal and Company

We also work with our University's Student Development Team to help you find out about further work experience, internships, placements, and voluntary opportunities. “I’m happy to say that I am working in a field that I genuinely enjoy. As a software developer for HM Land Registry my responsibilities change depending on the team I am working with. So far I’ve had experience in software development, software testing, data analysis and project architecture. Problem solving is the number one skill from my degree that I need to use every day. In fact, most maths graduates have really good problem-solving and critical-thinking skills which helps us become proficient in the software development field.” Vilius Gudziunas, BSc Mathematics, 2018

Program Outline

Course structure

Our research-led teaching is continually evolving to address the latest challenges and breakthroughs in the field. The following modules are based on the current course structure and may change in response to new curriculum developments and innovation. We understand that deciding where and what to study is a very important decision for you. We’ll make all reasonable efforts to provide you with the courses, services and facilities as described on our website. However, if we need to make material changes, for example due to significant disruption, or in response to COVID-19, we’ll let our applicants and students know as soon as possible.

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Components

Components are the blocks of study that make up your course. A component may have a set module which you must study, or a number of modules from which you can choose. Each component has a status and carries a certain number of credits towards your qualification.

Status	What this means
Core	You must take the set module for this component and you must pass. No failure can be permitted.
Core with Options	You can choose which module to study from the available options for this component but you must pass. No failure can be permitted.
Compulsory	You must take the set module for this component. There may be limited opportunities to continue on the course/be eligible for the qualification if you fail.
Compulsory with Options	You can choose which module to study from the available options for this component. There may be limited opportunities to continue on the course/be eligible for the qualification if you fail.
Optional	You can choose which module to study from the available options for this component. There may be limited opportunities to continue on the course/be eligible for the qualification if you fail.

The modules that are available for you to choose for each component will depend on several factors, including which modules you have chosen for other components, which modules you have completed in previous years of your course, and which term the module is taught in.

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Modules

Modules are the individual units of study for your course. Each module has its own set of learning outcomes and assessment criteria and also carries a certain number of credits. In most cases you will study one module per component, but in some cases you may need to study more than one module. For example, a 30-credit component may comprise of either one 30-credit module, or two 15-credit modules, depending on the options available. Modules may be taught at different times of the year and by a different department or school to the one your course is primarily based in. You can find this information from the module code . For example, the module code HR100-4-FY means:

HR	100	4	FY
The department or school the module will be taught by. In this example, the module would be taught by the Department of History.	The module number.	The UK academic level of the module. A standard undergraduate course will comprise of level 4, 5 and 6 modules - increasing as you progress through the course. A standard postgraduate taught course will comprise of level 7 modules. A postgraduate research degree is a level 8 qualification.	The term the module will be taught in. AU : Autumn term SP : Spring term SU : Summer term FY : Full year AP : Autumn and Spring terms PS: Spring and Summer terms AS: Autumn and Summer terms

Year 1 Year 2 Final Year This module will allow you to build your knowledge of differentiation and integration, how you can solve first and second order differential equations, Taylor Series and more. View Calculus on our Module Directory You'll be introduced to a range of important concepts which are used in all areas of mathematics and statistics. This module is structured in such a way that during learning sessions you'll develop good practical understanding of these concepts via discussion and exercises, and have an opportunity to ask questions. Theory is introduced via recorded videos and the corresponding notes published on Moodle, and also via recommendations of textbooks. The contact hours are dedicated to interactive activities such as lab exercises and flipped lecture quizzes; also you will have some additional formative tests in Moodle. View Matrices and Complex Numbers on our Module Directory How do you apply the addition rule of probability? Or construct appropriate diagrams to illustrate data sets? Learn the basics of probability (combinatorial analysis and axioms of probability), conditional probability and independence, and probability distributions. Understand how to handle data using descriptive statistics and gain experience of R software. View Statistics I on our Module Directory Want to understand Newtonian Dynamics? Interested in developing applications of mathematical ideas to study it? Enhance your skills and knowledge in the context of fundamental physical ideas that have been central to the development of mathematics. Analyse aspects of technology and gain experience in the use of computer packages. View Mechanics and Relativity on our Module Directory This module introduces you to programming skills in the context of a range of mathematical modelling topics. Mathematical modelling skills will be an important focus alongside learning how to structure and implement codes in both Matlab and R. A key part of the module will be investigative open-ended computational modelling studies at both the group and individual level. View Mathematical and Computational Modelling on our Module Directory Want to develop your mathematical skills by solving problems that are varied in nature and difficulty? Keen to write mathematical arguments that explain why your calculations are answer a question? Examine problem-solving techniques for situations across mathematics, including calculus, algebra, combinatorics, geometry and mechanics. View Introduction to Geometry, Algebra, and Number theory on our Module Directory This module will provide you with a foundation of knowledge on the mathematics of sets and relations. You will develop an appreciation of mathematical proof techniques, including proof by induction. View Discrete Mathematics on our Module Directory What skills do you need to succeed during your studies? And what about after university? How will you realise your career goals? Develop your transferable skills and experiences to create your personal profile. Reflect on and plan your ongoing personal development, with guidance from your personal advisor within the department. View Mathematics Careers and Employability on our Module Directory In this module you'll be introduced to the basics of probability and random variables. Topics you will discuss include distribution theory, estimation and Maximum Likelihood estimators, hypothesis testing, basic linear regression and multiple linear regression implemented in R. View Statistics II on our Module Directory How can we rigorously discuss notions of infinity and the infinitely small? When do limits and derivatives of functions make sense? This module introduces the mathematics which enables calculus to work, with the epsilon-and-delta definition of limits as its cornerstone. Fundamental theorems are proved about sequences and series of real numbers, and about continuous and differentiable functions of a single real variable. View Real Analysis on our Module Directory How do you define gradient, divergence and curl? Study the classical theory of vector calculus. Develop the two central theorems by outlining the proofs, then examining various applications and examples. Understand how to apply the ideas you have studied. View Vector Calculus on our Module Directory How do you prove simple properties of linear space from axioms? Can you check whether a set of vectors is a basis? How do you change a basis and recalculate the coordinates of vectors and the matrices of mapping? Study abstract linear algebra, learning to understand advanced abstract mathematical definitions. View Linear Algebra on our Module Directory The module introduces you to the key abstract algebraic objects of groups, rings and fields and develops their fundamental theory. The theory will be illustrated and made concrete through numerous examples in settings that you will already have encountered. View Abstract Algebra on our Module Directory The subject of ordinary differential equations is a very important branch of Applied Mathematics. Many phenomena from Physics, Biology, Engineering, Chemistry, Finance, among others, may be described using ordinary differential equations. To understand the underlying processes, we have to find and interpret the solutions to these equations. The last part of the module is devoted to the study of nonlinear differential equations and stability. This module provides an overview of standard methods for solving single ordinary differential equations and systems of ordinary differential equations, with an introduction to the underlying theory. View Ordinary Differential Equations on our Module Directory COMPONENT 07: OPTIOL Option(s) from list (30 CREDITS) What skills do you need to succeed during your studies? And what about after university? How will you realise your career goals? Develop your transferable skills and experiences to create your personal profile. Reflect on and plan your ongoing personal development, with guidance from your personal advisor within the department. View Mathematics Careers and Employability on our Module Directory Can you identify curves and regions in the complex plane defined by simple formulae? How do you evaluate residues at pole singularities? Study complex analysis, learning to apply the Residue Theorem to the calculation of real integrals. View Complex Variables on our Module Directory COMPONENT 02: COMPULSORY WITH OPTIONS MA829-6-AU or MA830-6-SP (15 CREDITS) COMPONENT 03: OPTIOL Mathematics option(s) from list (60 CREDITS) COMPONENT 04: OPTIOL Mathematics option(s) from list (30 CREDITS) What skills do you need to succeed during your studies? And what about after university? How will you realise your career goals? Develop your transferable skills and experiences to create your personal profile. Reflect on and plan your ongoing personal development, with guidance from your personal advisor within the department. View Mathematics Careers and Employability on our Module Directory

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Placement

On a placement year you gain relevant work experience within an external business or organisation, giving you a competitive edge in the graduate job market and providing you with key contacts within the industry. The rest of your course remains identical to the three-year degree.

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Year abroad

On your year abroad, you have the opportunity to experience other cultures and languages, to broaden your degree socially and academically, and to demonstrate to employers that you are mature, adaptable, and organised. The rest of your course remains identical to the three-year degree.

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Teaching

• Teaching mainly takes the form of lectures – you study roughly two 50-minute lectures and one 50-minute class per week, per module
• Take a mathematics careers and employability module, where you compile a portfolio of skills and experience

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Assessment

• Your final mark is a weighted combination of marks gained on coursework (eg homework problem sheets or tests) and your summer examinations
• Your first year of study does not count towards your final degree class
• Third-year students have the opportunity to complete a full-year or one-term project