- UCAS course code
- G101
- UCAS institution code
- M20
Bachelor of Science (BSc)
BSc Mathematics with Placement Year
Duration: 4 years
Year of entry: 2025
UCAS course code: G101 / Institution code: M20
- Key features:
Industrial experience
Accredited course
- Typical A-level offer: A*AA including specific subjects
- Typical contextual A-level offer: A*AB including specific subjects
- Refugee/care-experienced offer: A*BB including specific subjects
- Typical International Baccalaureate offer: 37 points overall with 7,6,6 at HL, including specific requirements
Fees and funding
Fees
Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £34,500 per annum. For general information please see the undergraduate finance pages.
Policy on additional costs
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).
Course unit details:
Analysis and Geometry in Affine Space
| Unit code | MATH31061 |
|---|---|
| Credit rating | 10 |
| Unit level | Level 3 |
| Teaching period(s) | Semester 1 |
| Available as a free choice unit? | No |
Overview
Differential and integral calculus, whose origins go back to Newton and Leibniz and their predecessors, has undergone spectacular development in the past centuries to become modern analysis deeply related with multidimensional geometry, topology and abstract algebra. In one aspect, however, it remains close to the founding fathers, namely, in being grounded in applications such as in physics. The course aims to emphasize both abstract and applied sides and to give skills and knowledge for later studies including other year 3 and year 4 courses.
Pre/co-requisites
| Unit title | Unit code | Requirement type | Description |
|---|---|---|---|
| Calculus of Several Variables | MATH20132 | Anti-requisite | Compulsory |
| Groups and Geometry | MATH21120 | Pre-Requisite | Compulsory |
Anti-requisites: MATH20132 Calculus of Several Variables (from 2022-23 or earlier)
Aims
The unit aims to:
- Introduce the students to main concepts of modern analysis in multidimensional space such as the idea of differential as the linear operator approximating a function at a given point, and the apparatus of differential forms;
- Develop geometric understanding behind the fundamental theorems such as the implicit function theorem and inverse function theorem (local diffeomorphisms, submanifolds specified by equations, curvilinear coordinates, tangent spaces).
Learning outcomes
On the successful completion of the course, students will be able to:
- State and use the definitions and main properties of open sets in affine space and of continuous maps.
- State and use the definition and main properties of the differential of a map, and to work with differentials practically.
- State and use the inverse function theorem and the implicit function theorem, and to apply them to related geometric concepts.
- Calculate with differential forms including their exterior multiplication and integration.
- Calculate exterior differentials applying them in particular to integrals by using variants of Ostrogradsky-Gauss-Stokes formula.
Teaching and learning methods
Traditional format (2 lectures and 1 tutorial per week).
The possibility is considered of switching to blended format (1 review class and 1 tutorial per week, together with lecture notes, example sheets and videos to watch).
Assessment methods
| Method | Weight |
|---|---|
| Written exam | 100% |
Formative assessment consisting of marked homework
Feedback methods
General feedback is available after the exam is marked.
Recommended reading
R.Abraham, J.Marsden, T.Ratiu. Manifolds, tensor analysis and applications. - Springer, 2nd corrected ed. 1988
B.A.Dubrovin, A.T.Fomenko, S.P.Novikov. Modern Geometry - Methods and Applications: Part I. - Springer, 2nd ed. 1992
H.Flanders. Differential forms with applications to physical sciences. - Dover, 2003
W.Rudin. Principles of mathematical analysis. - McGraw Hill, 1976
V.A.Zorich. Mathematical analysis II. - Springer, 2008
Study hours
| Scheduled activity hours | |
|---|---|
| Lectures | 22 |
| Tutorials | 11 |
| Independent study hours | |
|---|---|
| Independent study | 67 |
Teaching staff
| Staff member | Role |
|---|---|
| Theodore Voronov | Unit coordinator |