The University of New South Wales, , Prof. N J Wildberger
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Updated On 02 Feb, 19
Introduction to Algebraic Topology - One-dimensional objects - Homeomorphism and the group structure on a circle - Two-dimensional surfaces: the sphere - More on the sphere - Two-dimensional objects - the torus and genus - Non-orientable surfaces - the Mobius band - The Klein bottle and projective plane - Polyhedra and Euler's formula
Applications of Euler's formula and graphs - More on graphs and Euler's formula - Rational curvature, winding and turning - Duality for polygons and the Fundamental Theorem of Algebra - More applications of winding numbers - rational curvature of a polytope - Rational curvature of polytopes and the Euler number - The geometry of surfaces - The two-holed torus and 3-crosscaps surface - Knots and surfaces I
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We discuss applications of Eulers formula to various planar situations, in particular to planar graphs, including complete and complete bipartite graphs, the Five neighbours theorem, the Six colouring theorem, and to Picks formula, which lets us compute the area of an integral polygonal figure by counting lattice points inside and on the boundary.
This is the tenth lecture of this beginners course in Algebraic Topology by N J Wildberger of UNSW.
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
March 29, 2019
Great course. Thank you very much.