Symmetry

This 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, 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.

Stretches the imagination of math and non-math majors alike by exploring symmetry across the built and natural world Supports instructors with a complete set of animated lecture slides prepared by the author Offers an appealing spatial approach to meeting quantitative requirements for non-STEM majors Brings countless illustrations to life using the Springer Nature More Media app

Autorentext

Kristopher Tapp is Professor of Mathematics at Saint Joseph's University in Philadelphia. The recipient of numerous teaching awards, he is particularly interested in communicating ideas from mathematics to students in other fields. His research extends from differential geometry to the mathematical study of gerrymandering. Previous books include Differential Geometry of Curves and Surfaces, which appears in Undergraduate Texts in Mathematics.

Zusammenfassung
"This book has much to recommend it. The material is presented clearly and enthusiastically ... . there are a lot of well-chosen exercises, ranging from very easy to more challenging. ... this is a well-written book, covering interesting material, that can serve a number of possible audiences. ... many math majors will never have seen many of the topics discussed in this book ... technical details by the instructor, serve as a useful text for a capstone course for majors." (Mark Hunacek MAA Reviews, November 14, 2021)

Inhalt
Preface.- 1. Introduction to Symmetry.- 2. The Algebra of Symmetry.- 3. The Classification Theorems.- 4. Isomorphic Groups.- 5. Subgroups & Product Groups.- 6. Permutation Groups.- 7. Symmetries of 3D Objects.- 8. The Five Platonic Solids.- 9. Symmetry and Optimization.- 10. What is a Number?.- 11. Excursions in Numbers.- 12. Rigid Motions as Functions.- 13. Rigid Motions as Matrices.- Image Credits.- Index.