BSc Computer Science and Mathematics

Groups are abstract algebraic structures which are central to almost every area of modern pure mathematics, and also to many application areas. In geometry, they manifest themselves as the natural way to describe and study symmetry.  The course will provide an introduction to the algebraic theory of groups, and to some of their applications in geometric settings. It will also develop skills in abstract reasoning and mathematical writing, which are essential for later study in pure mathematics and also applicable in other areas. 

The unit aims (i) to introduce students to fundamental notions of abstract algebra which are central to most of pure mathematics and many applications, (ii) to illustrate how these ideas can be applied in a geometric setting and (iii) to develop the skills students will need for later study in (especially pure) mathematics, such as reasoning about mathematical objects and accurate writing of mathematics proofs and arguments

• Reason accurately about abstractly defined mathematical objects, constructing formal arguments to prove or disprove mathematical statements about the objects introduced in this course and prerequisite courses, and distinguishing between correct and incorrect reasoning.
• Write mathematics (including proofs) accurately and clearly, making appropriate use of both the English language and mathematical notation.
• Recognise how abstract structures such as groups can manifest themselves in different settings, and apply knowledge about abstract groups to solve problems in concrete settings where they arise.
• State the group axioms, identify and calculate with common examples of groups, and determine whether or not a given structure is a group.
• Define, recognise and reason about basic concepts of group theory (such as groups, subgroups, cosets, conjugacy, homomorphisms, isomorphisms, factor groups, group actions, orbits, stabilisers, fundamental sets/domains and quotient spaces). 
• State, apply and recall the proofs of some elementary theorems of group theory (such as Lagrange’s Theorem, the First Isomorphism Theorem and the Class Equation) and apply this knowledge in familiar and unseen settings.
• Define basic geometric concepts of Euclidean space and of the Riemann sphere, and solve elementary problems involving these.
• Determine which elements are conjugate in a given group using classification theorems, e.g. for symmetric groups, isometries of Euclidean space, or Möbius transformations. Determine explicit conjugators/centralisers.

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Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £39,700 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

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