Mathematics

Mathematics
Maths isn’t just numbers and theory. It’s a key to unlocking your future.

The skills and ideas you’ll learn on this course are in demand in many exciting careers – from finance to computing, engineering, science and media.

At Kent, we focus on application as well as theory. We’ll give you a firm grounding in core principles such as algebra, probability and statistics. But you’ll also learn how you can solve real-world challenges with machine learning, data analysis, cryptography, numerical methods and optimisation techniques.

Through experiential learning and industry-led projects, we’ll challenge you to apply what you learn - and help you develop in-demand skills such as programming, technical writing, communication, and problem-solving.

Mathematicians today are playing pivotal roles in tackling huge global challenges, from addressing inequality and climate change, to advancing AI and quantum technologies. You’ll be taught by research experts, who will help you discover the many opportunities you have to make a real impact.

Foundation year

If your qualifications are not sufficient, for whatever reason, for direct entry onto a degree course, you can apply for this course. It covers the mathematical skills you need to enter Stage 1 of the degree.

Year in Industry

Your year in industry takes place between your second and final year, giving you invaluable work experience. You earn a salary and there may be the possibility of a job with the same company after graduation.

Your Future
A maths degree from Kent will set you up for a wide range of careers in areas including medical statistics, pharmaceuticals, aerospace, accounting and software development.

Year 1

The following modules are what students typically study, but this may change year to year in response to new developments and innovations.

Year 1 compulsory modules currently include the following:

• Principles of Probability and Statistics - Many professions require skills in extracting useful information from data and managing and presenting data accurately. You’ll learn the core methods and principles of probability theory and statistics, and gain skills in applying these methods to analyse sample data and draw inferences or generalisations.

• Applications and Practice with R and Python - As you progress through the module, you'll delve into the intricacies of R, Python, and Excel, mastering their functionalities through real-world applications. From data analysis to visualisation and interpretation, you'll gain a holistic understanding of how these tools can be harnessed to extract insights from complex datasets and analyse complex problems.

• Linear Algebra - This module in linear algebra prepares you for advanced topics in the fields of algebra, multivariable calculus, differential equations, data analysis, and financial mathematics.

• Calculus - This module delves deep into the fundamental concepts of differentiation and integration. You’ll explore the properties of core functions including polynomials, exponentials and logarithms, trigonometric functions and their inverses, as well as hyperbolic functions. You’ll become proficient in the fundamental techniques of differentiation and integration of single-variable functions.

• Mathematical Structures and Proofs - You'll learn about the logical structures underpinning proofs and common types of proofs. You’ll acquire strategies for devising your own proofs and learn to identify key ideas and steps by analysing numerous classic proofs in different areas of mathematics. You'll also enhance your skills in working and reasoning with abstract mathematical structures and strengthen your ability to formulate and communicate rigorous solutions to mathematical problems concisely. Mathematics is an exact science with special conventions for notation and communication that allow you to present solutions and ideas in a straightforward way.

• Analysis and Mathematical Modelling - The module examines difference equations, exploring their functions and thereby helping you gain clear insight into their applications. From deciphering dynamical systems to predicting future trends, you'll become adept at using the tools of mathematical analysis. This is where the potent mathematical techniques underpinned by fixed point theorems come into their own, amplifying your problem-solving abilities and allowing you to conquer challenges you once found insurmountable.

For more detailed information about these modules, please visit our website.

Year 2

The following modules are what students typically study, but this may change year to year in response to new developments and innovations.

Year 2 compulsory modules currently include the following:

• Optimisation for Data Analysis - You'll gain expertise in the theory and applications of optimisation techniques and algorithms, focusing on the methods most relevant to data science. You'll master how to optimise solutions, analyse and improve the performance of algorithms, and acquire decision-making techniques. The module will equip you with an understanding of the way many standard problems in data science can be formulated as optimisation problems. In addition, you’ll gain skills in applying basic optimisation algorithms and techniques, including Newton's and gradient based methods, to solve problems. Throughout the module computing tools will be used to illustrate how optimisation techniques and algorithms are used to compute solutions to relevant problems in data science.

• Numerical Methods and Differential Equations - You’ll learn to use analytical and numerical tools for resolving differential equations, which is essential explicit solutions of differential equations are often not known. You’ll explore numerical approximation methods, such as Euler's method and Runge-Kutta's method, and learn about stability analysis and error estimation to gauge the reliability of these techniques.

• Mathematical Statistics - You’ll learn advanced techniques in probability and statistics, including maximum likelihood estimation, advanced hypothesis testing, moments and moment-generating functions. You’ll also discover bivariate and multivariate discrete and continuous distributions.

• Multivariable and Vector Calculus - In the module, you'll learn how to differentiate and integrate functions of several variables and how to work with curves, surfaces and volumes. You’ll also examine core concepts including partial derivatives, gradients, multiple integrals, line and surface integrals, vector algebra, and vector fields.

• Cryptography and Number Theory - Numbers are one of the most fundamental concepts in mathematics and indeed in everyday life. Their study dates back thousands of years to Chinese, Babylonian, Greek, Indian, and Persian thinkers. In the second half of the twentieth century, amazing and far-reaching applications to the emerging information technology industry were found. Nowadays their theory provides the basis for all security on the internet and other communication channels, keeping your messages and bank details safe, for example. Surprising new applications continue to be discovered! In the first half of the module you’ll learn the core results of number theory such as the Chinese Remainder Theorem and Fermat’s Little Theorem and gain technical skills in working with prime numbers, modular arithmetic, and Diophantine equations. In the second half of the module you’ll see how these core results and techniques are applied in cryptography, the science of protecting information. More specifically, you’ll learn about: classical cryptosystems and their weak point, the “key distribution problem”, the public key ciphers and computational security, and the challenge coming from quantum computing.

• Preparing for Professional Practice - Gaining work experience is vital to improving your chances of finding employment once you graduate. This module is designed to simulate real-world work experiences, where you will work in groups on open-ended projects requiring a combination of diverse skills and knowledge.

For more detailed information about these modules, please visit our website.

Year in Industry

Year in Industry

You have the option to add a year in industry to this course. We already know you have the confidence and commitment to thrive in the workplace and kick-start your career. This is your chance to prove it, to yourself and to employers.

Any questions? We have the answers.

When should I start looking? Companies will recruit at different times of the year based on their size. It's good to be application ready by the summer of your first year.

Where can I get help finding a placement? Book an appointment with a placement adviser via the careers service.

Will I get paid? Most of our placements are paid.

Do I have to pay tuition fees? Yes, you’ll pay a substantially reduced fee. Fees for the current year (subject to changes) can be found on our tuition fees website.

Where can I get visa advice if I’m an international student? Kent Students' Union can help with any visa queries.

Does the University keep in touch? You receive four-weekly check-in emails, a visit from the team every three months and you can reach out to us any time by email or phone.

Do I work for a full year? The minimum requirement for an industrial placement is 44 weeks.

Year 3

The following modules are what students typically study, but this may change year to year in response to new developments and innovations.

Year 3 compulsory modules currently include the following:

• Experience and Research in Mathematics - You’ll delve into the fascinating realm of mathematics through immersive experiences tailored to your interests and aspirations. Under the guidance of expert academics, embark on a journey of intellectual discovery, culminating in a dissertation that delves deep into the core of your chosen mathematical domain. You can forge connections and expand your horizons by doing a research internship, where you'll tackle a mathematical research challenge in a team led by one of our scholars.

• Groups, Fields and Applications - You’ll develop a versatile toolkit in studying groups and fields, extending your ability to think abstractly and reason logically. You’ll cultivate a deep understanding of the abstract theory that allows you to see inside the algorithms and processes that underpin a variety of applications.

• Complex Analysis - You'll explore in detail the intricate relationships between the functions of a complex variable and the geometry and algebra of the complex plane. This provides many striking results including Cauchy's integral formula, Laurent's theorem, and the residue theorem.

• Partial Differential Equations with Applications - Get ready to sharpen your expertise in specific techniques as you examine both linear and nonlinear PDEs, gaining qualitative understanding using graphical and phase space methods.

Optional modules may include the following:

• Machine Learning and Deep Learning - A strong grasp of statistical modelling and optimisation principles forms the bedrock of machine learning. This module covers essential and advanced topics of machine learning and deep learning, blending theory with practical computing tools, such as R and Python.

• Financial Economics and Derivatives - You’ll gain a strong foundation in financial economics modelling techniques and be able to apply them in quantitative risk management situations, including portfolio selection and the pricing and valuation of financial derivatives.

For more detailed information about these modules, please visit our website.

Foundation Year

The following modules are what students typically study, but this may change year to year in response to new developments and innovations.

Foundation Year compulsory modules currently include the following:

• Foundation Skills for Engineering, Mathematics and Physics - Your preparation for an engineering, mathematics or physics degree starts here. You will develop critical thinking and problem solving skills required to underpin your studies as well as beginning to gain knowledge to enable you to start using measurement instruments, understand forces, and fundamental electric circuits. Your ability to work with results including measurement errors as well as report writing skills will also be developed to support you throughout the degree and your professional life.

• Foundation Algebra and Geometry - A solid grasp of algebra and geometry is a fundamental requirement for advanced study in any STEM subject. In this module, you will study foundational algebra and coordinate geometry required for Stage 1 entry into your chosen degree. You will see why they are so vital to your subject area. In addition you will learn how to reason with logarithms, exponentials and gain skills in solving equations.

• Foundation Statistics and Programming to Explore Your Subject - You’ll learn the basics of probability, statistics, and hypothesis testing necessary for advanced study. In particular, you’ll gain skills in using measures of central tendency such as the mean, median, and mode, and measures of dispersion such as the range, variance, and standard deviation. You’ll learn how to use quartiles and percentiles, and to interpret and create histograms, box plots, and other graphical representations of data. In probability theory you’ll gain an understanding of the core probability rules, see how to use conditional probability, and become familiar with the binomial and normal distributions, expectation, and variance. You’ll also learn how to use basic programming techniques to help solve problems in statistics.

• Foundation Mechanics and Materials - Learn about the interplay of the core concepts physicists and engineers use to describe the behaviour of objects in the world around us. Establish the relevant quantities, units and dimensions giving you the tools to understand mechanics and materials. Learn about characterising the motion of objects through distance, velocity and acceleration with time graphs. You will examine the behaviours of forces through Newtons' Laws and the relationship between those forces and work, power and energy. You will learn about gravity as a force field, as well as circular and rotational motion. Physical bodies are usually solids, but liquids and gases also obey the laws of mechanics. The property of temperature provides an explanation for the different phases of matter.

• Foundation Functions and Calculus - In this module, you will develop your knowledge of mathematical functions to give you a solid foundation with which to grasp calculus and other advanced topics. You will then move on to study differential calculus and its applications – allowing you to quantify and model rates of change mathematically and consistently and find the gradient of any curve – followed by integral calculus and differential equations – allowing you to find anti-derivatives and model real-life situations.

• Foundation Waves, Vibrations and Electromagnetics - To prepare you for future study in your chosen degree, you will learn to analyse physical waves, vibrations, alternating current and electromagnetic waves. You will also gain awareness of the principles of electrostatics and magnetism, as well as being introduced to atomic physics.

For more detailed information about these modules, please visit our website.