Durham University
Programme and Module Handbook

Undergraduate Programme and Module Handbook 2020-2021 (archived)

Module MATH2627: GEOMETRIC TOPOLOGY II

Department: Mathematical Sciences

MATH2627: GEOMETRIC TOPOLOGY II

Type Open Level 2 Credits 10 Availability Available in 2020/21 Module Cap Location Durham

Prerequisites

  • Calculus 1 (MATH1061) and Linear Algebra 1 (MATH1071)

Corequisites

  • None

Excluded Combination of Modules

  • None

Aims

  • To provide basic notions of topology in an intuitive visual way by studying knots, links and surfaces.

Content

  • topology: knots, surfaces, knot invariants.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will:
  • be able to solve a range of predictable and unpredictable problems in the given topics,
  • have an awareness of the abstract concepts of theoretical mathematics in the field of the given topics,
  • have a knowledge and understanding of the major theories of these subjects demonstrated through one or more of the following topic areas: knots, surfaces, knot invariants.
Subject-specific Skills:
  • In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling.
Key Skills:

    Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

    • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
    • Weekly/Fortnightly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
    • Tutorials provide active engagement and feedback to the learning process.
    • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

    Teaching Methods and Learning Hours

    Activity Number Frequency Duration Total/Hours
    Lectures 22 2 per week in Epiphany and in first week of Easter 1 Hour 22
    Tutorials 5 Fortnightly in Epiphany and one in Easter 1 Hour 5 ■
    Problems Classes 5 Fortnightly in Epiphany 1 Hour 5
    Preparation and Reading 68
    Total 100

    Summative Assessment

    Component: Examination Component Weighting: 90%
    Element Length / duration Element Weighting Resit Opportunity
    End of year written examination 2 hours 100% Yes
    Component: Continuous Assessment Component Weighting: 10%
    Element Length / duration Element Weighting Resit Opportunity
    Fortnightly or Weekly written assignments. 100%

    Formative Assessment:

    ■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University