Kristopher Tapp

Symmetry (eBook, PDF)

A Mathematical Exploration

• Format: PDF

Produktbeschreibung

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.

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 215
• Erscheinungstermin: 2. Dezember 2011
• Englisch
• ISBN-13: 9781461402992
• Artikelnr.: 37351119

Autorenporträt

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. He lives in the Philadelphia area with his wife and daughter, whose pictures appear in this book.

Inhaltsangabe

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.

Rezensionen

"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)