Course Details in 2025/26 Session

Module Title	LM Algebraic and Differential Topology
School	Mathematics
Department	Mathematics
Module Code	06 34176
Module Lead	Prof Marta Mazzocco
Level	Masters Level
Credits	20
Semester	Semester 2
Pre-requisites	LH Metric Spaces and Topology - (06 27722) LI Real & Complex Analysis - (06 25666) Real & Complex Analysis - (06 27146)
Co-requisites
Restrictions	None
Contact Hours	Lecture-44 hours Practical Classes and workshops-10 hours Guided independent study-146 hours Total: 200 hours
Exclusions
Description	Topology is the study of properties of spaces invariant under continuous deformation. This course will cover: Topological spaces and basic examples; compactness; connectedness and path-connectedness; homotopy and the fundamental group; winding numbers and applications. Differentiable manifolds, Differential topology, i.e. the study of those properties of differentiable manifolds which are invariant under diffeomorphism (differentiable homeomorphism). It will address the problem of identifying (or not) differentiable manifold as boundaries of some other differentiable manifold. As an application Stokes’ theorem will also be studied. Students will be expected to demonstrate and apply their knowledge of the topics at a proportionately higher level in the LM module compared to the LH version
Learning Outcomes	By the end of the module students should be able to: Demonstrate a full and rigorous understanding of all definitions associated with topological spaces. Demonstrate a sound understanding of the fundamental concepts of algebraic and differential topology and their role and application in a modern mathematical and research-informed context. Demonstrate an accurate and efficient use of algebraic and differential topological techniques and apply these successfully within modern mathematical and research-informed contexts. Demonstrate capacity for advanced mathematical reasoning through analysing, proving and explaining concepts from algebraic and differential topology. Engage in problem solving, using advanced algebraic and differential topological techniques, in diverse situations drawn from physics, engineering and other mathematical contexts.
Assessment	34176-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	3 hour Written Unseen Examination (80%); In-course Assessment (20%).
Other
Reading List