Bachelor of Science (BSc)

BSc Actuarial Science and Mathematics

  • Duration: 3 years
  • Year of entry: 2025
  • UCAS course code: NG31 / Institution code: M20
  • Key features:
  • Scholarships available
  • Accredited course

Full entry requirementsHow to apply

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).

Scholarships/sponsorships

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .

Course unit details:
Topology and Analysis

Course unit fact file
Unit code MATH31010
Credit rating 20
Unit level Level 3
Teaching period(s) Full year
Available as a free choice unit? No

Overview

Topology provides the tools to study properties of shapes that are not affected by manipulations such as bending, stretching, or twisting. Such properties include compactness of the shape, whether the shape is connected, and how many holes the shape has. Topology is important in fields like algebraic geometry, functional analysis, theoretical physics, and has found successful applications in data analysis and computing.

Topological spaces also provide a foundation for analysis in settings where metrics are either not available or not immediately apparent, such as that of linear functionals on Banach spaces and bounded linear operators. The theory of linear operators is fundamental in areas such as partial differential equations, quantum physics, and representation theory. 

This unit will introduce the concept of a topological space; describe how shapes such as Klein bottles, Möbius bands, and tori can be thought of as topological spaces; cover various ways in which topological spaces can be distinguished; and cover some more advanced concepts in topology. It will then use some key topological ideas to develop the theory of Banach spaces and the operators between them; to equip spaces of operators with topologies; and to understand the spectra of such operators, concluding with applications to other parts of mathematics. 

Pre/co-requisites

Unit title Unit code Requirement type Description
Metric Spaces MATH21111 Pre-Requisite Compulsory
Mathematical Foundations & Analysis MATH11121 Pre-Requisite Compulsory
MATH31010 PRE-REQS

Aims

To introduce the theory of topological spaces and continuous functions. To develop ability working with Banach spaces and their operators. To study applications of and connections between these topics. 

Learning outcomes

  • Define and identify topologies on sets, continuous functions on topological spaces, and homeomorphisms between topological spaces.
  • Construct topological spaces using subspace, quotient and product topologies.
  • Distinguish topological spaces by their connectedness, compactness, convergence, and separation properties.
  • Use homotopy and covering spaces to classify topological spaces.
  • Recognise Banach spaces and Hilbert spaces, and deduce and apply properties of Banach spaces and Hilbert spaces.
  • Analyse spaces, functionals, and operators using strong and weak topologies.
  • Use spectra to classify and compare linear operators.
  • Apply the theory of linear operators to other areas of mathematics.

 

Teaching and learning methods

In addition to delivery of content in the two lectures per week, tutorials will provide an opportunity for students' work to be discussed and for feedback on their understanding to be given. Feedback on assessments will be provided. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

 

Assessment methods

Method Weight
Other 20%
Written exam 80%

Feedback methods

Coursework: On returned scripts within a week of submission

Study hours

Scheduled activity hours
Lectures 44
Tutorials 22
Independent study hours
Independent study 134

Teaching staff

Staff member Role
Donald Robertson Unit coordinator
Yotam Smilansky Unit coordinator
Yuri Bazlov Unit coordinator

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