(Really looking forward to the finished product in a few years,though. Prerequisites are kept to an absolute minimum nothing beyond first courses in linear algebra and multivariable calculus and the most direct and straightforward approach is used. Lastly, there are lots of free online resources for students now - the aforementioned lecture notes by Shifrin are outstanding, and we should enjoy them as long he makes them freely available before converting them to a real book. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Spivak and Frankel, although both wonderful texts, are really graduate level. ![]() For that reason, I can't really recommend it as a class text, but it definitely should be kept on reserve when teaching such a course. But the incomprehensibly inserted program code is really distracting and breaks the flow and organization of the text - it should be relegated to software or online. Andrew Pressley Elementary Differential Geometry a: ‘Diggioa 3 : i 8 Springer Andrew Pressley Department of Mathematics, King’s College, The Strand, London WC2R 2LS, UK Cover ilustration elements reproduced by kind permission of Aptech Systems Inc, Publisher of the GAUSS Mathematical and Statistical System, 23804 SE. Gray's mammoth tome is probably the single most complete source on classical DG: everything is very clearly done with lots of fascinating computer drawn images and historical asides. That being said, he does emphasize linear algebra aspects and covers quite a few topics not found in the other texts. Thorpe is OK, but doesn't excite me his notation gets unnecessarily dense. I'd love to see Dover put out a nice cheap paperback of it. I love Millman and Parker as well, although it's not as complete as one would like. Prerequisites are kept to an absolute minimum - nothing beyond first courses in linear algebra and. curves and surfaces in R3, emphazing vector space properties) before going anywhere near forms or manifolds - linear algebra should be automatic for any student learning differential geometry at any level. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. ![]() I do think it's important to study a modern version of classical DG first (i.e. That being said, there's probably no gentler place to learn about them. ![]() O'Neill is a bit more complete, but be warned - the use of differential forms can be a little unnerving to undergraduates. When I learned undergraduate differential geometry with John Terrilla, we used O'Neill and Do Carmo and both are very good indeed. I've reviewed a few books online for the MAA.
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