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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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