# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: General and Algebraic Topology (MATH10075)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 10 (Year 4 Undergraduate) Availability Available to all students SCQF Credits 20 ECTS Credits 10 Summary This course will introduce students to essential notions in topology, such as topological spaces, continuous functions, and compactness, and move on to study of compact surfaces, homotopies, fundamental groups and covering spaces. Course description Topological spaces. Continuous functions. Compactness, connectedness, path-connectedness. Identification spaces. Compact surfaces. Homotopy. Fundamental groups and their calculation. Covering spaces.
 Pre-requisites Students MUST have passed: Fundamentals of Pure Mathematics (MATH08064) AND Honours Analysis (MATH10068) Co-requisites Prohibited Combinations Students MUST NOT also be taking General Topology (MATH10076) OR Algebraic Topology (MATH10077) Other requirements None
 Pre-requisites None High Demand Course? Yes
 Not being delivered
 On completion of this course, the student will be able to: State and prove standard results regarding topological spaces and continuous functions, and decide whether a simple unseen statement about them is true, providing a proof or counterexample as appropriate.Construct homotopies and prove homotopy equivalence for simple examples.Calculate fundamental groups of simple topological spaces, using generators and relations or covering spaces as necessary, and calculate simple topological invariants, such as numbers of path components, degrees and winding numbers.State and prove standard results about homotopy, and decide whether a simple unseen statement about them is true, providing a proof or counterexample as appropriate.Provide an elementary example illustrating specified behaviour in relation to a given combination of basic definitions and key theorems across the course.
 None
 Graduate Attributes and Skills Not entered Keywords GATop
 Course organiser Dr Jonathan Pridham Tel: (0131 6)50 3300 Email: J.Pridham@ed.ac.uk Course secretary Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk
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