Integrated Master in Science: Mathematics and Data Science

Program Overview

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Data is the lifeblood of our society and mathematics is the language that underpins the science of understanding that data. From medicine to government offices, and market research to the environment, the collection and analysis of data is crucial to understanding how to improve, create and guide products and services across the globe. The techniques we use to model and manipulate data guide the political, financial and social decisions that shape our modern society and are the basis of growth of the economy and success of businesses. Technology is growing and evolving at an incredible speed, and both the rate of growth of data we generate and the devices we use to process it can only increase. Our MSci Mathematics and Data Science is an Integrated Masters course that will cover key skills in mathematics and data science giving you the opportunity to apply theory and methods to real-world problems. You will foster your understanding of mathematics, develop skills to use smart devices efficiently and use statistical techniques and methods to interpret and exploit big data. Skill with programming is crucial in managing processes and databases, analysing data sets and developing data processing pipelines. This course will introduce you to Python and R for statistical analysis and data visualisation. In the latter years of your degree, you will undertake a Capstone project, allowing you to apply the techniques you’ve learned to a data science topic of your own. Topics include:

• Mathematical skills including, applied mathematics, pure mathematics and optimisation
• Computer science and programming
• Statistics and operations research
• Artificial intelligence, databases and information retrieval
• Ethical issues around the use and processing of data
• Specialist skills in the areas of big data, data analytics and data science

Our Integrated Masters gives you the opportunity to fast track your degree and complete your final year in nine months compared to a regular MSc which usually takes twelve months. Combining your undergraduate and postgraduate study in one degree will give you a strong theoretical background as well as specialist expertise through independent research. This combination makes graduates from our course attractive candidates for many employers. Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines. You therefore can gain an exceptional range of knowledge and skills that are currently in demand in mathematically oriented employment; in business, commerce, industry, government service, education and in the wider economy. Why we're great.

• You have access to our ultramodern facilities at our STEM Centre.
• We are 26th in the UK for Mathematics in The Guardian University Guide 2023.
• 85% of our Department of Mathematical Sciences graduates are in employment or further study (Graduate Outcomes 2023).

Our expert staff

We are also home to many of the world’s top scientists, and our staff are driven by creativity and imagination as well as technical excellence. We conduct world-leading research in areas such as explorative data analysis, classification and clustering, evolutionary computation, data visualisation and financial forecasting. 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.

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Specialist facilities

• In addition to teaching, 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 have six laboratories that are exclusively for computer science students. Three are open 24/7, and you have free access to the labs except when there is a scheduled practical class in progress
• We also have specialist facilities for research into areas including non-invasive brain-computer interfaces, intelligent environments, robotics, optoelectronics, video, RF and MW, printed circuit milling, and semiconductors

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Your future

Demand for skilled graduates in the areas of mathematics, big data and data science is growing rapidly in both the public and private sector, and there is a predicted shortage of data scientists with the skills to understand and make commercial decisions based on the analysis of big data. A successful career in data science requires you to possess truly interdisciplinary knowledge, so we’ll ensure you graduate with a wide-ranging yet specialised set of skills in this area. You are taught mainly within our Department of Mathematical Sciences and our School of Computer Science and Electronic Engineering, but also benefit from input from our Essex Business School, and our Essex Pathways Department. Mathematicians and data scientists are required in every sector, carrying out statistical analysis or mining data on social media, so our course can open the door to almost any industry, from health, to government, to publishing. Essex is bridging the gap between academia and business, and we are at the forefront of helping the UK grasp the big data opportunities to get ahead in the global race. Our graduates in data science have been very successful in finding employment in the public sector, consulting, technology, retail, and utilities, while a number have gone on to postgraduate study or research. We have a large pool of external contacts, ranging from companies providing robots for the media industry, through vehicle diagnostics, to the transforming of unstructured data to cloud-based multidimensional data cubes, who work with us and our students to provide advice, placements and eventually graduate opportunities. We also work with our University's Student Development Team to help you find out about further work experience, internships, placements, and voluntary opportunities.

Program Outline

Course structure

We offer a flexible course structure with a mixture of core/compulsory modules, and optional modules chosen from lists. Our research-led teaching is continually evolving to address the latest challenges and breakthroughs in the field. The course content is therefore reviewed on an annual basis to ensure our courses remain up-to-date so modules listed are subject to change. 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 Year 3 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 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 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 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 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 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 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 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 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 COMPONENT 07: OPTIOL Options 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 This module will allow you to step out of the classroom and gain real experience in your selected branch of Mathematics that you could not gain from a lecture. You will be able to develop your ability to work independently on research and produce a project report on your topic of interest. View Capstone Project: Mathematics on our Module Directory COMPONENT 03: OPTIOL Options from list (60 CREDITS) COMPONENT 04: OPTIOL Options 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 Our Advanced Capstone Projects are opportunities for students to study independently a topic in mathematics, statistics and related areas (such as mathematical physics, data science, modelling and so on) and develop skills such as writing reports and giving presentations. You will be monitored by a supervisor, who will periodically set tasks and discuss the progress of the work. The key purpose of Advanced Capstone Projects is that you should be given the opportunity to show your strengths and be allowed a certain amount of freedom and leeway in how you complete the project. It will also provide opportunities for you to develop transferable communication, time- and task-management skills, through researching the topic and organising and producing the written and oral reports. View Advanced Capstone Project: Actuarial Science, Data Science or Mathematics on our Module Directory Humans can often perform a task extremely well (e.g., telling cats from dogs) but are unable to understand and describe the decision process followed. Without this explicit knowledge, we cannot write computer programs that can be used by machines to perform the same task. “Machine learning” is the study and application of methods to learn such algorithms automatically from sets of examples, just like babies can learn to tell cats from dogs simply by being shown examples of dogs and cats by their parents. Machine learning has proven particularly suited to cases such as optical character recognition, dictation software, language translators, fraud detection in financial transactions, and many others. View Machine Learning on our Module Directory View Applied Regression and Experimental Data Analysis on our Module Directory COMPONENT 04: OPTIOL Options from list (60 CREDITS)

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Teaching

• Courses are taught by a combination of lectures, laboratory work, assignments, and individual and group project activities
• Group work
• A significant amount of practical lab work will need to be undertaken for written assignments and as part of your learning

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Assessment

• You are assessed through a combination of written examinations and coursework
• All our modules include a significant coursework element
• You receive regular feedback on your progress through in-term tests
• Courses are assessed on the results of your written examinations, together with continual assessments of your practical work and coursework