UNIVERSITY OF KENT
Confirmation that this version of the module specification has been approved by the School
Learning and Teaching Committee:
…18th December 2014………………………………….(date)
MODULE SPECIFICATION
1.
Title of the module: Applied Algebraic Topology (MA964)
2.
School or partner institution which will be responsible for management of the module: School
of Mathematics, Statistics and Actuarial Science
3.
Start date of the module: September 2011 (revised version start date September 2015)
4.
The number of students expected to take the module: 15
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with
other relevant Schools and Faculties regarding the withdrawal: This is an existing module.
6.
The level of the module: M-level
7.
The number of credits and the ECTS value which the module represents 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Autumn/Spring
9.
Prerequisite and co-requisite modules:
Prerequisite module: MA567 (Topology) or the equivalent
There are no co-requisite modules.
10. The programmes of study to which the module contributes: This is an optional module for the
MSc in Mathematics and its Applications, MMath Mathematics, MMathStat Mathematics and
Statistics
11. The intended subject specific learning outcomes:
On successful completion of this module, students will:
a) understand the basic concepts of topology with particular emphasis on CW complexes,
manifolds and simplicial complexes;
b) be able to apply topological methods to real-world problems;
c) be able to use homological and computational methods to solve topological problems;
d) have an improved geometric and algebraic intuition;
e) have an enhanced ability to formulate and prove abstract mathematical statements, and
appreciate their connection with concrete calculation;
f) have enhanced their computational skills.
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12. The intended generic learning outcomes
On successful completion of this module, students will have:
a) an enhanced ability to communicate their own ideas clearly and coherently;
b) an enhanced ability to read and comprehend mathematical ideas;
c) matured in their problem solving skills;
d) a greater appreciation of abstract concepts;
e) consolidated their grasp of a wide variety of mathematical techniques and methods.
13. A synopsis of the curriculum
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:
a) an introduction to manifolds, CW complexes and simplicial complexes;
b) an investigation of the elements of homotopy theory;
c) an exploration of homological and computational methods;
d) applications such as homological sensor networks and topological data analysis.
14. Indicative Reading List
Recommended books for background 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.
Review articles (will be made available online):
Homological Sensor Networks, de Silva & Ghrist, Notices of the AMS, vol 54, no 1 (2007) 10-17.
Bar codes: The persistent topology of data, Ghrist, Bulletin of the AMS, vol 45, no 1 (2008) 61-75.
15. Learning and Teaching Methods, including the nature and number of contact hours and the
total study hours which will be expected of students, and how these relate to achievement of
the intended module learning outcomes
Number of contact hours: 24-36 if lectured. Module may be offered as a directed reading course.
Number of independent learning hours: 114-126 if lectured.
Total study hours: 150
In the event of a small number of students and/or a group of students with disparate background
knowledge such that a traditional lecture course is not viable, this course may in part or whole be
taught as a directed reading course. In such a case the directed reading will be supported by a mix
of lectures, tutorials and enhanced office hours. The assessment methods described below will not
change.
Contact hours comprise a mix of lecture, example class, and computer laboratory activity.
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Student study hours would be distributed between consolidation of lecture material, the working of
exercises on exercise sheets, assessed exercises, using a computer to obtain results and check
their work, completion of a short project and exam preparation.
16. Assessment methods and how these relate to testing achievement of the intended module
learning outcomes
The module is assessed on the basis of examination (70%), coursework (15%), project work (15%).
Examination: A 3-hour written examination in Term 3 that consists of multi-part questions requiring a
mix of long and short answers to test at varying levels of proficiency the learning outcomes (LO:
11(a,c,e), 12(b,c,d,e)).
Coursework: This would normally consist of open-book assignments of unseen problems, either to
be worked by hand or with the use of appropriate software (LO: 11(a,c,d,e,f), 12(b,c,d,e)).
Project work: a project designed to develop analytical and computational skills on a larger scale than
an exercise. The output will consist of a report of the investigation (LO: 11(b,c,d,e,f), 12(a,b,c,d)).
17. Implications for learning resources, including staff, library, IT and space
Convener and moderator
Library: school library budget will be used to purchase a copy of Computational Homology
IT and Space: suitable rooms for lectures and/or computer classes (max of 3 per week)
18. The School recognises and has embedded the expectations of current disability equality
legislation, and supports students with a declared disability or special educational need in its
teaching. Within this module we will make reasonable adjustments wherever necessary,
including additional or substitute materials, teaching modes or assessment methods for
students who have declared and discussed their learning support needs. Arrangements for
students with declared disabilities will be made on an individual basis, in consultation with
the University’s disability/dyslexia support service, and specialist support will be provided
where needed.
19. Campus(es) or Centre(s) where module will be delivered: Canterbury
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