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

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

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

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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3.6 (25 Ratings)

This is the Introductory lecture to a beginners course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010.
This first lecture introduces some of the topics of the course and three problems.

44%

16%

8%

16%

16%

*5 Really enjoying this course so far.

- 1.AlgTop0 Introduction to Algebraic Topology
- 2.AlgTop1 One-dimensional objects
- 3.AlgTop2 Homeomorphism and the group structure on a circle
- 4.AlgTop3 Two-dimensional surfaces the sphere
- 5.AlgTop4 More on the sphere
- 6.AlgTop5 Two-dimensional objects- the torus and genus
- 7.AlgTop6 Non-orientable surfaces---the Mobius band
- 8.AlgTop7 The Klein bottle and projective plane
- 9.AlgTop8 Polyhedra and Eulers formula
- 10.AlgTop9 Applications of Eulers formula and graphs
- 11.AlgTop10 More on graphs and Eulers formula
- 12.AlgTop11 Rational curvature, winding and turning
- 13.AlgTop12 Duality for polygons and the Fundamental Theorem of Algebra
- 14.AlgTop13 More applications of winding numbers
- 15.AlgTop15 Rational curvature of a polytope
- 16.AlgTop16 Rational curvature of polytopes and the Euler number
- 17.AlgTop20 The geometry of surfaces
- 18.AlgTop21 The two-holed torus and 3-crosscaps surface
- 19.AlgTop22 Knots and surfaces I

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