# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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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
 Academic year 2017/18, Available to all students (SV1) Quota:  None Course Start Full Year Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 44, Seminar/Tutorial Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 139 ) Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 % Additional Information (Assessment) Coursework 5%, Examination 95% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) MATH10075 General and Algebraic Topology 3:00
 1. 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. 2. Construct homotopies and prove homotopy equivalence for simple examples. 3. Calculate fundamental groups of simple topological spaces, using generators and relations or covering spaces as necessary. 4. Calculate simple topological invariants, such as numbers of path components, degrees and winding numbers. 5. 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. 6. 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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