This textbook is perfect for a math course for non-math majors, with the goalof encouraging effective analytical thinking and exposing students to elegantmathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’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 expositionis 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. Symmetry is an ideal topic for a one semester math course for non-math majors. Includes many topics commonly found in sampler courses, but weaves these topics into a single compelling story about symmetry. Encourages effective analytical thinking and exposes non-math majors to elegant mathematical ideas. Contains excellent exercises for the intended audience; these exercises should help students attain good understanding of the main points. Hints of humor and easily accessible language coupled with a plethora of exercises provides the necessary motivation for a non-math major in a math-oriented class. Contains hundreds of beautiful illustrations. INDICE: Preface. 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
- ISBN: 978-1-4614-0298-5
- Editorial: Springer New York
- Encuadernacion: Cartoné
- Páginas: 199
- Fecha Publicación: 28/12/2011
- Nº Volúmenes: 1
- Idioma: Inglés