Kristopher Tapp – författare

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups.Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

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.

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.

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.

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.

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging.Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships.Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book,applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging.Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships.Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens'' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book,applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.