## MA30055: Introduction to topology

[Page last updated: 05 August 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20218
Description: Aims:
To provide an introduction to topology and topological spaces, preparing students for later studies in algebraic topology, as well as the ideas underlying modern analysis and geometry.

Learning Outcomes:

* Familiarity with topological spaces and their role in topology, analysis and geometry.
* Understanding of compactness and connectedness in this general setting.
* Ability to apply these ideas and methods to examples. Skills:Numeracy T/F A Problem Solving T/F A Written Communication F (on problem sheets)

Content:
Topologies and topological spaces, continuous maps and homeomorphisms, subspaces, product spaces, quotient spaces, compactness and connectedness. Further topics will be discussed such as: function spaces and compact-open topologies; Hausdorff spaces and separation axioms; Tychonoff's theorem; Compact surfaces, their representation as quotient spaces, and a sketch of their classification.

Programme availability:

#### MA30055 is Optional on the following programmes:

Department of Computer Science
• USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
• USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
• USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.