OverviewThere 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.
This module appears in:
Method of assessment
70% Examination, 15% Coursework, 15% Project
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.
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.