![]() (Really looking forward to the finished product in a few years,though. 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. Spivak and Frankel, although both wonderful texts, are really graduate level. Download it once and read it on your Kindle device, PC, phones or tablets. 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. Elementary Differential Geometry (Springer Undergraduate Mathematics Series) - Kindle edition by Pressley, A.N. 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. 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. Prerequisites are kept to an absolute minimum - nothing beyond first courses in linear algebra and. Each geodesic in the sense of classic differential geometry can be approximated by a sequence of normal geodesics under the defined flow. That being said, he does emphasize linear algebra aspects and covers quite a few topics not found in the other texts. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Elementary Differential Geometry - Andrew Pressley1 amna anwar. ![]() 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. 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. Pressley wont feel like improving this great book and that would be a shame. I do think it's important to study a modern version of classical DG first (i.e. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. 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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