Symmetry

A Mathematical Exploration
2012
ISBN: 978-1-4614-0298-5
Verlag: Springer-Verlag New York Inc.

Buch, Englisch, 215 Seiten, Book, Format (B × H): 159 mm x 239 mm, Gewicht: 519 g

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Tapp, Kristopher

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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

Über Autor(innen)

Tapp, Kristopher
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.

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.