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Unit information: Algebraic Topology in 2021/22

Unit name Algebraic Topology
Unit code MATHM1200
Credit points 20
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Mark Hagen
Open unit status Not open
Pre-requisites

MATH20006 Metric Spaces and MATH33300 Group Theory

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

Unit Aims

The aim of the unit is to give an introduction to algebraic topology with an emphasis on cell complexes, fundamental groups and homology.

Unit Description

Algebraic Topology concerns constructing and understanding topological spaces through algebraic, combinatorial and geometric techniques. In particular, groups are associated to spaces to reveal their essential structural features and to distinguish them. In cruder terms, it is about adjectives that capture and distinguish essential features of spaces.

The theory is powerful. We will give applications including proofs of The Fundamental Theory of Algebra and Brouwer's Fixed Point Theorem (which is important in economics).

Relation to Other Units

This is one of three Level M units which develop group theory in various directions. The others are Representation Theory and Galois Theory.

Intended Learning Outcomes

Learning Objectives

Students should absorb the idea of algebraic invariants to distinguish between complex objects, their geometric intuition should be sharpened, they should have a better appreciation of the interconnectivity of different fields of mathematics, and they should have a keener sense of the power and applicability of abstract theories.

Transferable Skills

  • The assimilation of abstract and novel ideas.
  • Geometric intuition.
  • How to place intuitive ideas on a rigorous footing.
  • Presentation skills.

Teaching Information

Lectures, problem sets and discussion of problems, student presentations.

Assessment Information

50% Exam, 50% Coursework - assessed problem sheets

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM1200).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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