Classical Geometry – Lecture Notes.pdf
Classical Geometry, is a lecture notes in pdf file that has been prepared by Danny Calegari. Taken from Appendix – What Is Geometry?: Geometry is a beast that can be approached from many angles. Four of the most important concepts that arise from our different primitive intuitions of geometry are symmetry, measurement, analysis, and continuity. We briefly discuss these four faces of geometry, and mention some fundamental concepts in each. Don’t worry if these concepts seem very technical or abstract-think of this section as an abstraction of the concrete notions found in the main body of the text.
- A CRASH COURSE IN GROUP THEORY
A group is an algebraic object which formalizes the mathematical notion which expresses the intuitive idea of symmetry.
- MODEL GEOMETRIES IN DIMENSION TWO [The Euclidean plane ~ The 2–sphere ~ The hyperbolic plane ]
- TESSELLATIONS [ The topology of surfaces ~ Finite subgroups of SO(3) and S3 ~ Discrete subgroups of PSL(2;R) ~ Dehn twists and Lickorish’s theorem ]
- APPENDIX – WHAT IS GEOMETRY?
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