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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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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
Course Delivery Information
Academic year 2015/16, 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 Topology3:00
Learning Outcomes
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.
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsGATop
Contacts
Course organiserDr Thomas Leinster
Tel: (0131 6)50 5057
Email:
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email:
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