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MX4546: ALGEBRAIC TOPOLOGY (2023-2024)

Last modified: 31 Jul 2023 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
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Professor Jaroslaw J. Kedra

Qualification Prerequisites

  • Programme Level 4

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 amalgamated products

The Seifert-Van Kampen theorem

Presentations of groups.

 

Syllabus:

 

Revision of topological spaces

Topological equivalence, homotopy and homotopy equivalence, deformation retraction.

The fundamental group, homomorphisms induced by continuous maps, and homotopy invariance.

The fundamental group of a circle and introduction to covering spaces

Applications: The fundamental theorem of algebra, Brauer fixed point, and Borsuk-Ulam.

Covering spaces: Concept, existence and classification.

Desk transformation and group actions.

The Seifert Van-Kampen theorem.

Computation of the fundamental group


Contact Teaching Time

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

Teaching Breakdown

  • 1 Lecture during University weeks 26 - 35, 39
  • 1 Tutorial during University weeks 27 - 35, 39

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Exam

Assessment Type Summative Weighting 50
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback
Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

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Feedback

Best of (resit exam mark) or (resit exam mark with carried forward CA marks).

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualUnderstandNot Available

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