02642nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245008600160250001700246260004800263300006500311505037400376653002500750653004000775653001300815653001300828653001600841653005400857710003400911041001900945989003600964856007201000082000801072520124801080EB000363579EBX0100000000000000021663100000000000000.0cr|||||||||||||||||||||130626 ||| eng a97814614029921 aTapp, Kristopher00aSymmetryhElektronische RessourcebA Mathematical Explorationcby Kristopher Tapp a1st ed. 2012 aNew York, NYbSpringer New Yorkc2012, 2012 aXIV, 215 p. 159 illus., 152 illus. in colorbonline resource0 aPreface -- 1 Introduction to Symmetry -- 2 The Algebra of Symmetry -- 3 Isomorphism -- 4 The Classification Theorems -- 5 Subgroups and Product Groups -- 6 Permutations -- 7 Symmetries of Solid Objects -- 8 The Five Platonic Solids -- 9 Symmetry and Optimization -- 10 What is a Number? -- 11 Cantor's Infinity -- 12 Euclidean Space -- 13 Symmetry and Matrices -- Index aMathematics, general aMathematics in Art and Architecture aGeometry aGeometry aMathematics aMathematics in the Humanities and Social Sciences2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005- uhttps://doi.org/10.1007/978-1-4614-0299-2?nosfx=yxVerlag3Volltext0 a510 aThis textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Eulerâ€™s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric. Kristopher Tapp is currently a mathematics professor at Saint Joseph's University. He is the author of 17 research papers and one well-reviewed undergraduate textbook, Matrix Groups for Undergraduates. He has been awarded two National Science Foundation research grants and several teaching awards