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Classical Differential Geometry - UCLA Mathematics

Classical Differential GeometryPeterPetersenPrefaceThis is an evolving set of lecture notes on the Classical theory of curves andsurfaces. Pictures will be added eventually. I recommend people download3DX-plorMathto check out the constructions of curves and surfaces with this app. Itcan also be used to create new curves and surfaces in parametric form. Other usefuland free apps are Geogebra, Grapher (on Mac), and a minimum a one quarter course should cover sections , , , , , and chapters 4, 5. In a semester course it d be possible to cover more fromchapter 2 and also delve into chapter 6. Chapters 6 and 7 can be covered in asecond quarter class. Note that section is a necessary prerequisite for provingthe general Gauss-Bonnet in section excellent reference for the Classical treatment of Differential Geometry is thebook by Struik [2].

also highly recommended. This book covers both geometry and differential geome-try essentially without the use of calculus. It contains many interesting results and gives excellent descriptions of many of the constructions and results in differential geometry. This text is fairly classical and is not intended as an introduction to abstract

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