Applied Algebraic Topology - MAST9640

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Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2021 to 2022
Canterbury
Spring Term 7 15 (7.5) Constanze Roitzheim checkmark-circle

Overview

There is growing interest in applying the methods of algebraic topology to data analysis, sensor networks, robotics, etc. The module will develop the necessary elements of algebra and topology, and investigate how these techniques are used in various applications. The syllabus will include: an introduction to manifolds, CW complexes and simplicial complexes; an investigation of the elements of homotopy theory; an exploration of homological and computational methods; applications such as homological sensor networks and topological data analysis.

Details

Contact hours

Total contact hours: 32
Private study hours: 118
Total study hours: 150

Method of assessment

70% Examination, 15% Coursework, 15% Project

Indicative reading

Introduction to Metric & Topological Spaces, W A Sutherland, 2nd edition, Oxford UP, 2009.
Basic Topology, M A Armstrong, Springer, 1983.
A Basic Course in Algebraic Topology, W S Massey, Springer, 1991.
Computational Homology, Kaczynski, Mischaikow & Mrozek, Springer, 2004.
Introduction to Topology: Pure and Applied, C Adams & R Franzosa, Pearson/Prentice Hall, 2008.
Algebaric Topology, A Hatcher, Cambridge UP, 2012.

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes. On successfully completing the module students will be able to:

1 understand the basic concepts of topology with particular emphasis on CW complexes, manifolds and simplicial complexes;
2 apply topological methods to real-world problems;
3 use homological and computational methods to solve topological problems;
4 demonstrate geometric and algebraic intuition;
5 demonstrate the ability to formulate and prove abstract mathematical statements, and appreciate their connection with concrete calculation;
6 demonstrate enhanced computational skills.

The intended generic learning outcomes. On successfully completing the module students will be able to:

1 communicate their own ideas clearly and coherently;
2 read and comprehend sophisticated mathematical ideas;
3 apply problem solving skills;
4 demonstrate an understanding of abstract concepts;
5 demonstrate their grasp of a wide variety of mathematical techniques and methods.

Notes

  1. Credit level 7. Undergraduate or postgraduate masters level module.
  2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
  3. The named convenor is the convenor for the current academic session.
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