Numbers And Symmetry

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Number, Shape, & Symmetry

Author : Diane L. Herrmann
Publisher : CRC Press
ISBN 13 : 1466554649
Total Pages : 446 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Number, Shape, & Symmetry by : Diane L. Herrmann

Download or read book Number, Shape, & Symmetry written by Diane L. Herrmann and published by CRC Press. This book was released on 2012-10-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Fearless Symmetry

Author : Avner Ash
Publisher : Princeton University Press
ISBN 13 : 0691138710
Total Pages : 308 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Fearless Symmetry by : Avner Ash

Download or read book Fearless Symmetry written by Avner Ash and published by Princeton University Press. This book was released on 2008-08-24 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.

Beautiful Symmetry

Author : Alex Berke
Publisher : MIT Press
ISBN 13 : 026253892X
Total Pages : 165 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Beautiful Symmetry by : Alex Berke

Download or read book Beautiful Symmetry written by Alex Berke and published by MIT Press. This book was released on 2020-02-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

Symmetry

Author : Kristopher Tapp
Publisher : Springer Nature
ISBN 13 : 3030516695
Total Pages : 263 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Symmetry by : Kristopher Tapp

Download or read book Symmetry written by Kristopher Tapp and published by Springer Nature. This book was released on 2021-08-28 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Why Beauty Is Truth

Author : Ian Stewart
Publisher :
ISBN 13 : 0465082378
Total Pages : 306 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis Why Beauty Is Truth by : Ian Stewart

Download or read book Why Beauty Is Truth written by Ian Stewart and published by . This book was released on 2008-04-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics.

Numbers and Symmetry

Author : Bernard L. Johnston
Publisher : CRC Press
ISBN 13 : 1000153371
Total Pages : 276 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Numbers and Symmetry by : Bernard L. Johnston

Download or read book Numbers and Symmetry written by Bernard L. Johnston and published by CRC Press. This book was released on 2020-07-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism. Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures. In terms of classical algebraic structures, the text divides roughly into three parts:

Mathematical Logic

Author : Roman Kossak
Publisher : Springer
ISBN 13 : 3319972987
Total Pages : 186 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Mathematical Logic by : Roman Kossak

Download or read book Mathematical Logic written by Roman Kossak and published by Springer. This book was released on 2018-10-03 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Symmetry

Author : Lynn Peppas
Publisher : Crabtree Publishing Company
ISBN 13 : 9780778743514
Total Pages : 28 pages
Book Rating : 4.7/5 (435 download)

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Book Synopsis Symmetry by : Lynn Peppas

Download or read book Symmetry written by Lynn Peppas and published by Crabtree Publishing Company. This book was released on 2010 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full-color illustrations and easy-to-read text introduce the basic concepts of symmetry, including angles, matches, and horizontal and vertical lines.

Groups and Symmetry: A Guide to Discovering Mathematics

Author : David W. Farmer
Publisher : American Mathematical Soc.
ISBN 13 : 0821804502
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Groups and Symmetry: A Guide to Discovering Mathematics by : David W. Farmer

Download or read book Groups and Symmetry: A Guide to Discovering Mathematics written by David W. Farmer and published by American Mathematical Soc.. This book was released on 1996 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This nicely produced volume focuses on the informal analysis of geometrical patterns. By means of a series of carefully selected tasks, the book leads readers to discover some real mathematics. There are no formulas to memorize and no procedures to follow. It is a guide to start you in the right direction and bring you back if you stray too far. Discovery is left to you.

The Equation That Couldn't Be Solved

Author : Mario Livio
Publisher : Simon and Schuster
ISBN 13 : 0743274628
Total Pages : 367 pages
Book Rating : 4.7/5 (432 download)

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Book Synopsis The Equation That Couldn't Be Solved by : Mario Livio

Download or read book The Equation That Couldn't Be Solved written by Mario Livio and published by Simon and Schuster. This book was released on 2005-09-19 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Number Theory and Symmetry

Author : Michel Planat
Publisher : MDPI
ISBN 13 : 3039366866
Total Pages : 206 pages
Book Rating : 4.0/5 (393 download)

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Book Synopsis Number Theory and Symmetry by : Michel Planat

Download or read book Number Theory and Symmetry written by Michel Planat and published by MDPI. This book was released on 2021-01-20 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.

Symmetry: A Very Short Introduction

Author : Ian Stewart
Publisher : OUP Oxford
ISBN 13 : 0191652741
Total Pages : 152 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Symmetry: A Very Short Introduction by : Ian Stewart

Download or read book Symmetry: A Very Short Introduction written by Ian Stewart and published by OUP Oxford. This book was released on 2013-05-30 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Groups and Symmetry

Author : Mark A. Armstrong
Publisher : Springer Science & Business Media
ISBN 13 : 1475740344
Total Pages : 197 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Groups and Symmetry by : Mark A. Armstrong

Download or read book Groups and Symmetry written by Mark A. Armstrong and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

Creating Symmetry

Author : Frank A. Farris
Publisher : Princeton University Press
ISBN 13 : 1400865670
Total Pages : 247 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Creating Symmetry by : Frank A. Farris

Download or read book Creating Symmetry written by Frank A. Farris and published by Princeton University Press. This book was released on 2015-06-02 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Geometry and Symmetry

Author : Paul B. Yale
Publisher : Courier Corporation
ISBN 13 : 0486169324
Total Pages : 288 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Geometry and Symmetry by : Paul B. Yale

Download or read book Geometry and Symmetry written by Paul B. Yale and published by Courier Corporation. This book was released on 2014-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVIntroduction to the geometry of euclidean, affine and projective spaces with special emphasis on the important groups of symmetries of these spaces. Many exercises, extensive bibliography. Advanced undergraduate level. /div

Symmetry and the Standard Model

Author : Matthew Robinson
Publisher : Springer Science & Business Media
ISBN 13 : 1441982671
Total Pages : 343 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Symmetry and the Standard Model by : Matthew Robinson

Download or read book Symmetry and the Standard Model written by Matthew Robinson and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students. This book represents the first in a series designed to assist students in the process of transitioning from coursework to research in particle physics. Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way. This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series.

Good Math

Author : Mark C. Chu-Carroll
Publisher : Pragmatic Bookshelf
ISBN 13 : 168050360X
Total Pages : 269 pages
Book Rating : 4.6/5 (85 download)

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Book Synopsis Good Math by : Mark C. Chu-Carroll

Download or read book Good Math written by Mark C. Chu-Carroll and published by Pragmatic Bookshelf. This book was released on 2013-07-18 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.