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Algebraic Topology is used for finding Algebraic invariants classifying topological spaces up to homeomorphism or homotopy equivalence. By studying [course_title], you will be able to use algebra to study topological problems and vice versa. This [course_title] will also support you to study problems related to Brouwer Fixed Point Theorem, Knot Theory, Simplicial Complex, CW Complex, The Hurewicz Theorem, vector bundles etc.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

Module: 01
Category Theory 00:15:00
Compactly Generated Spaces 00:15:00
Pointed Spaces and Homotopy Groups 00:15:00
Simple Computations, the Action of the Fundamental Groupoid 00:15:00
Cofibrations, Well Pointedness, Weak Equivalences, Relative Homotopy 00:15:00
Pushouts and Pullbacks, the Homotopy Fiber 00:15:00
Cofibers 00:15:00
Module: 02
Puppe Sequences 00:15:00
Fibrations 00:15:00
Hopf Fibrations, Whitehead Theorem 00:15:00
Help! Whitehead Theorem and Cellular Approximation 00:15:00
Homotopy Excision 00:15:00
The Hurewicz Homomorphism 00:15:00
Proof of Hurewicz 00:15:00
Module: 03
Eilenberg-Maclane Spaces 00:15:00
Spectral Sequences 00:15:00
The Spectral Sequence of a Filtered Complex 00:15:00
Line Bundles 00:15:00
Induced Maps Between Classifying Spaces, H*(BU(n)) 00:15:00
Completion of a Deferred Proof, Whitney Sum, and Chern Classes 00:15:00
Properties of Chern Classes, the Splitting Principle 00:15:00
Chern Classes and Elementary Symmetric Polynomials 00:15:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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