The aim of the **[course_title]** is to show how basic geometric structures may be studied by transforming them into algebraic questions that are then subject to computations, thus measuring geometric and topological complexity. These methods are often used in other parts of mathematics, and also in biology, physics and other areas of application. The course is meant to give a basis for studies in topology, geometry, algebra, and applications.

**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**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

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Course Credit: Open Culture

### Course Curriculum

Module: 01 | |||

AlgTop0: Introduction to Algebraic Topology | 00:30:00 | ||

AlgTop1: One-dimensional objects | 00:32:00 | ||

AlgTop2: Homeomorphism and the group structure on a circle | 00:52:00 | ||

AlgTop3: Two-dimensional surfaces: the sphere | 00:42:00 | ||

AlgTop4: More on the sphere | 00:41:00 | ||

AlgTop5: Two-dimensional objects- the torus and genus | 00:49:00 | ||

AlgTop6: Non-orientable surfaces—the Mobius band | 00:42:00 | ||

AlgTop7: The Klein bottle and projective plane | 00:40:00 | ||

AlgTop8: Polyhedra and Euler’s formula | 00:45:00 | ||

AlgTop9: Applications of Euler’s formula and graphs | 00:42:00 | ||

Module: 02 | |||

AlgTop10: More on graphs and Euler’s formula | 00:48:00 | ||

AlgTop11: Rational curvature, winding and turning | 00:48:00 | ||

AlgTop12: Duality for polygons and the Fundamental Theorem of Algebra | 00:45:00 | ||

AlgTop13: More applications of winding numbers | 00:27:00 | ||

AlgTop14: The Ham Sandwich theorem and the continuum | 00:36:00 | ||

AlgTop15: Rational curvature of a polytope | 00:50:00 | ||

AlgTop16: Rational curvature of polytopes and the Euler number | 00:35:00 | ||

AlgTop17: Classification of combinatorial surfaces I | 00:50:00 | ||

AlgTop18: Classification of combinatorial surfaces II | 00:59:00 | ||

AlgTop19: An algebraic ZIP proof | 00:42:00 | ||

Module: 03 | |||

AlgTop20: The geometry of surfaces | 00:44:00 | ||

AlgTop21: The two-holed torus and 3-crosscaps surface | 00:39:00 | ||

AlgTop22: Knots and surfaces I | 00:52:00 | ||

AlgTop23: Knots and surfaces II | 00:38:00 | ||

AlgTop24: The fundamental group | 00:43:00 | ||

AlgTop25: More on the fundamental group | 00:35:00 | ||

AlgTop26: Covering spaces | 00:54:00 | ||

AlgTop27: Covering spaces and 2-oriented graphs | 00:31:00 | ||

AlgTop28: Covering spaces and fundamental groups | 00:47:00 | ||

AlgTop29: Universal covering spaces | 00:48:00 | ||

Module: 04 | |||

AlgTop30: An introduction to homology | 00:47:00 | ||

AlgTop31: An introduction to homology (cont.) | 00:41:00 | ||

AlgTop32: Simplices and simplicial complexes | 00:49:00 | ||

AlgTop33: Computing homology groups | 00:41:00 | ||

AlgTop34: More homology computations | 00:43:00 | ||

AlgTop35: Delta complexes, Betti numbers and torsion | 00:48:00 | ||

Module: 05 | |||

AlgTopReview: An informal introduction to abstract algebra | 00:49:00 | ||

AlgTopReview2: Introduction to group theory | 00:47:00 | ||

AlgTopReview3: More on commutative groups—isomorphisms, homomorphisms, cosets and quotient groups | 00:32:00 | ||

AlgTopReview4: Free abelian groups and non-commutative groups | 00:51:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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