Programme And Module Handbook
Course Details in 2024/25 Session

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Module Title LH Algebraic and Differential Topology
Department Mathematics
Module Code 06 34175
Module Lead Prof Marta Mazzocco
Level Honours Level
Credits 20
Semester Semester 2
Pre-requisites LI Real & Complex Analysis - (06 25666) Real & Complex Analysis - (06 27146)
Co-requisites LH Metric Spaces and Topology - (06 27722)
Restrictions None
Contact Hours Lecture-44 hours
Practical Classes and workshops-10 hours
Guided independent study-146 hours
Total: 200 hours
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.
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 context.
  • Demonstrate an accurate and efficient use of algebraic and differential topological techniques and understand how these may be applied successfully within modern mathematical and research-informed contexts.
  • Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts from algebraic and differential topology.
  • Engage in problem solving, using algebraic and differential topological techniques, in situations drawn from physics, engineering and other mathematical contexts.
Assessment 34175-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions 2 hour Written Unseen January Examination (80%); In-course Assessment (20%).
Reading List