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Geometry

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Author(s): A. G. Kovalev, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; euclidean; spherical

Introduction
Euclidean geometry
Isometries of the Euclidean plane
Curves in Rn
Spherical geometry
Triangles on a sphere
Mobius geometry
Triangulations and the Euler number
Hyperbolic geometry
Review of derivatives and chain rule
Riemannian metrics
Two models for the hyperbolic plane
Geometry of the hyperbolic disk
Hyperbolic triangles
Hyperboloid model
Smooth embedded surfaces (in R3)
Smooth embedded surfaces
Geodesics
Surfaces of revolution
Gaussian curvature
Abstract smooth surfaces