Symmetry

1. Front Matter

   Pages i-xii

   PDF

2. Introduction to Symmetry

   • Kristopher Tapp

   Pages 1-27

3. The Algebra of Symmetry

   • Kristopher Tapp

   Pages 29-53

4. The Classification Theorems

   • Kristopher Tapp

   Pages 55-78

5. Isomorphic Groups

   • Kristopher Tapp

   Pages 79-93

6. Subgroups and Product Groups

   • Kristopher Tapp

   Pages 95-110

7. Permutation Groups

   • Kristopher Tapp

   Pages 111-133

8. Symmetries of 3D Objects

   • Kristopher Tapp

   Pages 135-170

9. The Five Platonic Solids

   • Kristopher Tapp

   Pages 171-189

10. Symmetry and Optimization

    • Kristopher Tapp

    Pages 191-199

11. What Is a Number?

    • Kristopher Tapp

    Pages 201-215

12. Excursions in Numbers

    • Kristopher Tapp

    Pages 217-229

13. Rigid Motions as Functions

    • Kristopher Tapp

    Pages 231-242

14. Rigid Motions as Matrices

    • Kristopher Tapp

    Pages 243-252

15. Back Matter

    Pages 253-259

    PDF

This textbook invites readers to explore the properties of objects that we effortlessly recognize as symmetrical. From the human body, to elaborate artworks and abstract networks, symmetry is ubiquitous in the world around us; it is essential to function and beauty across the built and natural world. By developing mathematical language to describe symmetry, this textbook equips readers to explore symmetries with precision, illuminating commonalities across art and science.

Beginning with an exploration of intuitive notions of symmetry, the author introduces the algebraic structure of groups by examining rotations and reflections. Topics that follow include the classification of two-dimensional patterns, the Platonic solids, and a study of real and prime numbers. This second edition features numerous new examples and exercises, “Elements of Mathematics” sections that more closely examine mathematical tools, and optional content that offers opportunities for extension. Figures are woven into the presentation throughout, with many illustrations now offered in motion as integrated video content.

Symmetry suits a wide audience, demanding no mathematical training past high school basics, yet stretching the imagination of math and non-math majors alike. Its engaging yet rigorous style offers a window into mathematicians’ ways of thinking. By developing mathematical reasoning skills in a spatial context, this text is ideal for a course that meets quantitative requirements for non-STEM majors. Instructors will appreciate the author’s comprehensive online resources, which include a full set of animated lecture slides; all readers will delight in watching the book’s content come alive using the multimedia app.

• Cayley table
• Euclidean space
• Euler characteristic
• Platonic solid
• Pythagorean Theorem for liberal arts
• alternating group
• chirality
• group theory for liberal arts
• prime numbers for liberal arts
• geometry for liberal arts
• symmetry for liberal arts
• symmetry group
• wallpaper group
• border pattern
• symmetry video
• math for liberal arts textbook
• mathematical symmetry

“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)

• Department of Mathematics, Saint Joseph’s University, Philadelphia, USA

  Kristopher Tapp

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.

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