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MA40040: Algebraic topology

Follow this link for further information on academic years Academic Year: 2015/6
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment: MA40040 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA10209 AND take MA10210 AND take MA30055
Further information on descriptions Description: Aims & Learning Objectives:
The course will provide a solid introduction to one of the Big Machines of modern mathematics which is also a major topic of current research. In particular, this course provides the necessary prerequisites for post-graduate study of Algebraic Topology.
Objectives: At the end of the course, the students will be conversant with the basic ideas of homotopy theory and, in particular, will be able to compute the fundamental group of several topological spaces.

Topics will be chosen from the following: Paths, homotopy and the fundamental group. Homotopy of maps; homotopy equivalence and deformation retracts. Computation of the fundamental group and applications: Fundamental Theorem of Algebra; Brouwer Fixed Point Theorem. Covering spaces. Path-lifting and homotopy lifting properties. Deck translations and the fundamental group. Universal covers. Loop spaces and their topology. Inductive definition of higher homotopy groups. Long exact sequence in homotopy for fibrations.
Further information on programme availabilityProgramme availability:

MA40040 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences Department of Physics
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)

* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.