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  6. MX4546: ALGEBRAIC TOPOLOGY

MX4546: ALGEBRAIC TOPOLOGY (2015-2016)

Last modified: 25 Mar 2016 11:35


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 Undergraduate Level 4
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Diarmuid Crowley

Qualification Prerequisites

None.

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

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 naturality properties.
  • Fundamental groups and covering spaces.
  • Free groups and subgroups of free groups.
  • The Seifert-VanKampen theorem.
  • Presentations of groups.
  • The concept of a surface.
  • Triangulations.
  • The classification of compact surfaces without boundary.
  • If time allows, 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

1st attempt: 1 two-hour written examination (80%) and in-course assessment (20%).

Resit: If required and permitted by Regulations, there will be 1 two-hour written examination. The CAS mark will be based on the maximum of examination (100%) and examination (80%) together with in-course-assessment (20%).

Only the marks obtained at the first attempt can count towards Honours classification.

Formative Assessment

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination. Students do practice questions in tutorials allowing formative assessment and feedback from tutors.

Feedback

In-course assessment will be marked and feedback provided to the students.

Course Learning Outcomes

None.
 

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