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MA3F1-15 Introduction to Topology

Department
Warwick Mathematics Institute
Level
Undergraduate Level 3
Module leader
Martin Lotz
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry
Introductory description

Topology is the study of properties of spaces invariant under continuous deformation. For this reason it is often called ``rubber-sheet geometry''. The module covers: topological spaces and basic examples; compactness; connectedness and path-connectedness; identification topology; Cartesian products; homotopy and the fundamental group; winding numbers and applications; an outline of the classification of surfaces.

Module web page

Module aims

To introduce and illustrate the main ideas and problems of topology.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

N/A

Learning outcomes

By the end of the module, students should be able to:

  • To explain how to distinguish spaces by means of simple topological invariants (compactness, connectedness and the fundamental group)
  • To explain how to construct spaces by gluing and to prove that in certain cases that the result is homeomorphic to a standard space
  • To construct simple examples of spaces with given properties (eg compact but not connected or connected but not path connected).
Indicative reading list

Books:
Chapter 1 of Allen Hatcher's book Algebraic Topology
MA Armstrong Basic Topology Springer (recommended but not essential).

Subject specific skills

See learning outcomes.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.

Study time

Type Required
Lectures 30 sessions of 1 hour (20%)
Tutorials 9 sessions of 1 hour (6%)
Private study 111 hours (74%)
Total 150 hours
Private study description

Review lectured material and work on set exercises.

Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

Assessment group D1
Weighting Study time
Assignment 15%
In-person Examination 85%
  • Answerbook Gold (24 page)
Assessment group R
Weighting Study time
In-person Examination - Resit 100%
  • Answerbook Gold (24 page)
Feedback on assessment

Marked assignments and exam feedback.

Past exam papers for MA3F1

Courses

This module is Optional for:

  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • UCSA-G4G1 Undergraduate Discrete Mathematics
    • Year 3 of G4G1 Discrete Mathematics
    • Year 3 of G4G1 Discrete Mathematics
  • Year 3 of UCSA-G4G3 Undergraduate Discrete Mathematics
  • Year 4 of UCSA-G4G2 Undergraduate Discrete Mathematics with Intercalated Year
  • USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
    • Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
    • Year 4 of G300 Mathematics, Operational Research, Statistics and Economics
  • Year 3 of UMAA-GL11 Undergraduate Mathematics and Economics
  • Year 4 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)

This module is Core option list B for:

  • UMAA-GV17 Undergraduate Mathematics and Philosophy
    • Year 3 of GV17 Mathematics and Philosophy
    • Year 3 of GV17 Mathematics and Philosophy
    • Year 3 of GV17 Mathematics and Philosophy
  • Year 3 of UMAA-GV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations

This module is Core option list D for:

  • Year 4 of UMAA-GV19 Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations

This module is Option list A for:

  • Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
  • Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
  • Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
  • UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
    • Year 3 of G105 Mathematics (MMath) with Intercalated Year
    • Year 5 of G105 Mathematics (MMath) with Intercalated Year
  • UMAA-G100 Undergraduate Mathematics (BSc)
    • Year 3 of G100 Mathematics
    • Year 3 of G100 Mathematics
    • Year 3 of G100 Mathematics
  • UMAA-G103 Undergraduate Mathematics (MMath)
    • Year 3 of G100 Mathematics
    • Year 3 of G103 Mathematics (MMath)
    • Year 3 of G103 Mathematics (MMath)
    • Year 4 of G103 Mathematics (MMath)
    • Year 4 of G103 Mathematics (MMath)
  • UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
    • Year 3 of G106 Mathematics (MMath) with Study in Europe
    • Year 4 of G106 Mathematics (MMath) with Study in Europe
  • Year 3 of UPXA-FG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
  • UPXA-GF13 Undergraduate Mathematics and Physics (BSc)
    • Year 3 of GF13 Mathematics and Physics
    • Year 3 of GF13 Mathematics and Physics
  • UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
    • Year 3 of FG31 Mathematics and Physics (MMathPhys)
    • Year 3 of FG31 Mathematics and Physics (MMathPhys)
  • Year 4 of UPXA-GF14 Undergraduate Mathematics and Physics (with Intercalated Year)
  • Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
  • Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year
  • USTA-Y602 Undergraduate Mathematics,Operational Research,Statistics and Economics
    • Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
    • Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
  • Year 4 of USTA-Y603 Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year)

This module is Option list B for:

  • Year 1 of TMAA-G1PE Master of Advanced Study in Mathematical Sciences
  • Year 3 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
  • Year 4 of USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
  • USTA-GG14 Undergraduate Mathematics and Statistics (BSc)
    • Year 3 of GG14 Mathematics and Statistics
    • Year 3 of GG14 Mathematics and Statistics
  • Year 4 of USTA-GG17 Undergraduate Mathematics and Statistics (with Intercalated Year)

This module is Option list E for:

  • USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
    • Year 3 of G30D Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
    • Year 4 of G30D Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
  • USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
    • Year 3 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
    • Year 4 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
    • Year 5 of G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)