Undergraduate Course: General and Algebraic Topology (MATH10075)
Course Outline
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, pathconnectedness.
Identification spaces.
Compact surfaces.
Homotopy.
Fundamental groups and their calculation.
Covering spaces.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
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.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  GATop 
Contacts
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 

