Ebook: Symmetry: A Mathematical Exploration

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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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.

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.

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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.

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.

Content:
Front Matter....Pages i-xiv
Introduction to Symmetry....Pages 1-16
The Algebra of Symmetry....Pages 17-33
Isomorphism....Pages 35-50
The Classification Theorems....Pages 51-62
Subgroups and Product Groups....Pages 63-74
Permutations....Pages 75-86
Symmetries of Solid Objects....Pages 87-114
The Five Platonic Solids....Pages 115-137
Symmetry and Optimization....Pages 139-148
What Is a Number?....Pages 149-165
Cantor’s Infinity....Pages 167-178
Euclidean Space....Pages 179-197
Symmetry and Matrices....Pages 199-211
Back Matter....Pages 213-215

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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.

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.

Content:
Front Matter....Pages i-xiv
Introduction to Symmetry....Pages 1-16
The Algebra of Symmetry....Pages 17-33
Isomorphism....Pages 35-50
The Classification Theorems....Pages 51-62
Subgroups and Product Groups....Pages 63-74
Permutations....Pages 75-86
Symmetries of Solid Objects....Pages 87-114
The Five Platonic Solids....Pages 115-137
Symmetry and Optimization....Pages 139-148
What Is a Number?....Pages 149-165
Cantor’s Infinity....Pages 167-178
Euclidean Space....Pages 179-197
Symmetry and Matrices....Pages 199-211
Back Matter....Pages 213-215
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