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Algebraic Topology

The University of New South Wales, , Prof. N J Wildberger

Updated On 02 Feb, 19

Overview

Contents:
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

Includes

Lecture 2: AlgTop1 One-dimensional objects

4.1 ( 11 )


Lecture Details

This is the first lecture of this beginners course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects the line and circle. The latter has quite a few different manifestations as a usual Euclidean circle, as the projective line of one-dimensional subspaces of a two-dimensional space, as a polygon, or as a space of orbits of a translation group on the line.

This course is given by Assoc Prof N J WIldberger of the School of Mathematics and Statistics at UNSW. See also his series on Rational Trigonometry (WildTrig) and Foundations of Mathematics (MathFoundations) as well as Linear Algebra (WildLinAlg) at YouTube user njwildberger.

Ratings

4.1


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Comments
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Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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