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  6. MX5506: Algebraic Topology

MX5506: ALGEBRAIC TOPOLOGY (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

Algebraic topology is a tool for solving topological or geometric problems with the use of algebra. Typically, a difficult geometric or topological problem is translated into a problem in commutative algebra or group theory. Solutions to the algebraic problem then provide us with a partial solution to the original topological one.

Course Details

Study Type Postgraduate Level 5
Term Second Term Credit Points 20 credits (10 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Diarmuid Crowley

What courses & programmes must have been taken before this course?

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Elementary concepts of homotopy theory. The fundamental group and its natural properties. Fundamental groups and covering spaces. Free groups and subgroups of free groups. The Seifert-van Kampen theorem. Presentations of groups. The concept of a surface. Triangulations. The classification of Compact surfaces without boundary. If time allow, an introduction to homology theory.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

One 3-hour written examination (80%); one in-course assessment (20%).

Formative Assessment

There are no assessments for this course.

Feedback

None.

Course Learning Outcomes

None.
 

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