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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2020/2021

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: General and Algebraic Topology (MATH10075)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryThis 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.
Entry Requirements (not applicable to Visiting Students)
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
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  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, and calculate simple topological invariants, such as numbers of path components, degrees and winding numbers.
  4. 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.
  5. Provide an elementary example illustrating specified behaviour in relation to a given combination of basic definitions and key theorems across the course.
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsGATop
Contacts
Course organiserDr Jonathan Pridham
Tel: (0131 6)50 3300
Email: J.Pridham@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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