Symmetry : a mathematical exploration / Kristopher Tapp.
2021
QA174.7.S96
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Details
Title
Symmetry : a mathematical exploration / Kristopher Tapp.
Edition
Second edition.
ISBN
9783030516697 (electronic bk.)
3030516695 (electronic bk.)
9783030516680 (print)
3030516695 (electronic bk.)
9783030516680 (print)
Published
Cham, Switzerland : Springer, 2021.
Language
English
Description
1 online resource (xii, 259 pages) : illustrations (some color)
Item Number
10.1007/978-3-030-51669-7 doi
Call Number
QA174.7.S96
Dewey Decimal Classification
516/.1
Summary
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
Note
Includes index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed September 2, 2021).
Series
Texts for quantitative critical thinking, 2523-8655
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Online Access
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Online Resources > Ebooks
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Table of Contents
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.
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.