Modules
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Choose your adventure
On our two main degrees, core modules will give you a grounding in mathematics, and in your second and third years, you can choose to explore the topics that interest you the most. Whatever you choose, you are taught by staff that lead the field in their chosen disciplines.
Maths modules
Our core modules in the first and second year, outlined below, will provide you with a strong foundation in mathematics. You will begin exploring option modules in your first year, and then in your second and further years, you can choose from a wide array of optional modules to suit your academic, creative, social, and career interests.
Your tutors are keen to discuss the topics that motivate and excite you, and will carefully guide you to take the direction that’s best for you.
First-year core Maths modules
Foundations, Analysis I and II, Algebra I and II, Maths by Computer, Methods of Mathematical Modelling I and II, Introduction to Probability.
It is in its proofs that the strength and richness of mathematics are to be found. University mathematics introduces progressively more abstract ideas and structures and demands more in the way of proof until most of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on the calculation, and gradually moving towards abstraction and proof.
This module also looks at algorithms and operational complexity, including cryptographic keys and RSA.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Analysis is the rigorous study of calculus. In this module, there will be a considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers, and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. The module will allow you to deal carefully with limits and infinite summations, approximations to pi and e, and the Taylor series. The module ends with the construction of the integral and the Fundamental Theorem of Calculus.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
This first half of this module will introduce you to abstract algebra, covering group theory and ring theory, making you familiar with symmetry groups and groups of permutations and matrices, subgroups and Lagrange’s theorem. You will understand the abstract definition of a group, and become familiar with the basic types of examples, including number systems, polynomials, and matrices. You will be able to calculate the unit groups of the integers modulo n.
The second half concerns linear algebra, and addresses simultaneous linear equations. You will learn about the properties of vector spaces, linear mappings and their representation by matrices. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
This module contains a Python mini-course and an introduction to the Latex scientific document preparation package. It will involve a group project, involving computation, and students will develop their research skills, including planning and use of library and internet resources, and their presentation skills including a video presentation.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Methods of Mathematical Modelling 1 introduces you to the fundamentals of mathematical modelling and scaling analysis, before discussing and analysing difference and differential equation models in the context of physics, chemistry, engineering as well as the life and social sciences. This will require the basic theory of ordinary differential equations (ODEs), the cornerstone of all applied mathematics. ODE theory later proves invaluable in branches of pure mathematics, such as geometry and topology. You will be introduced to simple differential and difference equations, methods for obtaining their solutions and numerical approximation.
In the second term for Methods of Mathematical Modelling 2, you will study the differential geometry of curves, calculus of functions of several variables, multi-dimensional integrals, calculus of vector functions of several variables (divergence and circulation), and their uses in line and surface integrals.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
This module takes you further in your exploration of probability and random outcomes. Starting with examples of discrete and continuous probability spaces, you will learn methods of counting (inclusion-exclusion formula and multinomial coefficients), and examine theoretical topics including independence of events and conditional probabilities. You will study random variables and their probability distribution functions. Finally, you will study variance and co-variance, including Chebyshev’s and Cauchy-Schwarz inequalities. The module ends with a discussion of the celebrated Central Limit Theorem.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
First-year optional Maths modules
Choose from an extensive list of optional modules offered from a wide range of other departments.
Programming for Scientists, Statistical Laboratory.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Classical Mechanics and Special Relativity, Electricity and Magnetism, Astronomy, Quantum Phenomena.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Discrete Mathematics and its Applications 2.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Mind and Reality, Reason, Argument and Analysis, Logic I:Introduction to Symbolic Logic.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Introduction to Quantitative Economics.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Mathematical Programming I.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
The Language Centre offers academic modules in Arabic, Chinese, French, German, Italian, Japanese, Korean, Portuguese, Russian and Spanish at a wide range of levels.
For more in-depth information on this module, visit the undergraduate handbook.Link opens in a new window
Second-year Maths modules
During your second year of study, you will have the opportunity to deepen your knowledge of key mathematical areas. The core modules include Analysis III, Algebra III, Methods of Mathematical Modelling III, Norms, Metrics and Topologies and Scientific Communication. Additionally you will develop communication skills by writing an essay on a topic of special interest to you, decided in consultation with your tutor.
You will also have an opportunity to pursue optional modules in another subject of your choice.
Further module information can be found in the Year 2 section of the Undergraduate Handbook.Link opens in a new window
Third-year Maths modules
There are no core modules in the third year. You have the freedom to choose from an extensive list of approximately 30 mathematics modules in areas of algebra, analysis, number theory, geometry, as well as a whole host of topical applications of mathematics.
You will also have an opportunity to pursue optional modules in another subject of your choice.
Further module information can be found in the Year 3 section of the Undergraduate Handbook.Link opens in a new window
Fourth-year Maths module
You have the freedom to choose from an extensive list of advanced modules in both pure and applied mathematics.
The distinguishing feature of the fourth year is a substantial core project, either working toward open mathematical research or else exploring the deep underpinnings of mathematics in society, science, technology, or industry.
Further module information can be found in the Year 4 section of the Undergraduate Handbook.Link opens in a new window
Please note: We update our modules every year based on availability and demand, and we update our course content too. The content on this page gives you a really strong indication of what your course will offer, but given the interval between the publication of courses and enrolment, some of the information may change. Read our terms and conditions to find out more.