Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.
Author: Leon Harkleroad
Publisher: Cambridge University Press
Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations--just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself. A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.
The Math Behind the World's Most Popular Pencil Puzzle
Author: Jason Rosenhouse,Laura Taalman
Publisher: Oxford University Press
Based on interviews with the writers of The Simpsons and accompanied by images from the show, facsimiles of scripts, paintings and drawings and other imagery, this fascinating book reveals the meaningful mathematical concepts behind the most successful show in TV history.
Author: Simon Singh
Publisher: Bloomsbury Publishing USA
This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research.
The Mathematics Behind the Computer Graphics
Author: Robert L. Devaney,Linda Keen,Kathleen T. Alligood
Publisher: American Mathematical Soc.
Uses math as a tool for explaining the complicated patterns of love, tackling such common questions as the chance of finding love that will last, how online dating works, and when to compromise.
Patterns, Proofs, and the Search for the Ultimate Equation
Author: Hannah Fry
Publisher: Simon and Schuster
Category: Family & Relationships
The Theory Behind the Formulas, + Website
Author: Donald J. Smith
Publisher: John Wiley & Sons
Category: Business & Economics
"A compilation of everyday events analyzed for their probability of occurring. The odds are determined using mathematical equations and science. An entertaining illustrated reference to the role of mathematics in everyday life. Topics examined are: the human condition, sports and games, traveling from A to B, digital technology, chance and coincidence, and more."--
Discover the Mathematics of Everyday Events
Author: Colin Beveridge
Publisher: Firefly Books
Washington State is about to enter a new phase of the "math wars." Since the late 1980s, the debate over how best to teach mathematics to schoolchildren has raged worldwide among educators, politicians, and parents. The stakes are high. To operate effectively in a global, twenty-first-century economy and polity, the United states must provide an education in mathematics that is both excellent and equitable. In this volume, four scholars at the Washington School Research Center (WSRC) at Seattle Pacific University present original research drawn from statistical studies of state educational data and from thousands of classroom observations carried out by The BERC Group. They assess the current state of math education and review its history and development. The authors also provide a dispassionate review of the extensive international, national, and state literature. The in-depth observational research in Winning the Math Wars confirms that the real issue is neither the approach to teaching--traditional or reform--nor the type of curriculum. If America's goal of educational equity and excellence is to be achieved, then math teachers everywhere must be fully supported in developing the specific skills that are ideal for educating all students. The authors discussion focus on four principles for improving math teaching and learning: fidelity to reform efforts by all involved; an emphasis on instruction and instructional tools; the critical nature of mathematical knowledge; and the need for transformational change. Winning the Math Wars is an important book for policy makers, school leaders, practitioners of mathematics education, parents, and anyone who wants to make sense of the "math wars."
No Teacher Left Behind
Author: Martin L. Abbott,Brian Ferriso,Karen Smith
Publisher: University of Washington Press
In How Math Explains the World, mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number p , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time. Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.
A Guide to the Power of Numbers, from Car Repair to Modern Physics
Author: James D. Stein, Jr.
Publisher: Harper Collins
This comprehensive guide covers the history and development of mathematics, from the Ancient Egyptians and Pythagoreans to key figures such as Galileo, Dodgson, Babbage and Lovelace through to contemporary work of the 21st century. It tells of the remarkable stories that have shaped mathematics and also features sections on how maths can be used to solve the mysteries of the universe, what the Prisoner's Dilemma is as well as Fermat's Last Theorem amongst many more. Accessible, well-informed and fully-illustrated, this is a book that shows perfectly just how varied and fascinating mathematics is as a subject.
You, this book and 4,000 years of theories
Author: Colin Beveridge
The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages. A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.
Cryptography from Caesar Ciphers to Digital Encryption
Author: Joshua Holden
Publisher: Princeton University Press
"The theory of black holes is the most simple consequence of Einstein's relativity theory. Dealing with relativity theory, this book details one of the most beautiful areas of mathematical physics; the theory of black holes. It represents a personal testament to the work of the author, who spent several years working-out the subject matter." --WorldCat.
Author: Subrahmanyan Chandrasekhar
Publisher: Oxford University Press
"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--
The Power of Mathematical Thinking
Author: Jordan Ellenberg
Category: Business & Economics
Using plots and scenarios used in the television show "Numb3rs," shows how mathematics can be and is used to solve crimes, describing the techniques used and providing real-life examples of this crime-solving tool.
Solving Crime with Mathematics
Author: Keith J. Devlin,Gary Lorden
This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.
Author: Mark A. Lewis,Sergei V. Petrovskii,Jonathan R. Potts
"Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks."--Front flap.
Author: Hiroshi Yuki
Publisher: Bento Books Inc
The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples—from ice cream scoops and poker hands to measuring mountains and making magic squares—this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius! A mathematician who is known throughout the world as the “mathemagician,” Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In The Magic of Math, Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate math the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of math. If you are already someone who likes math, this book will dazzle and amuse you. If you never particularly liked or understood math, Benjamin will enlighten you and—with a wave of his magic wand—turn you into a math lover.
Solving for x and Figuring Out Why
Author: Arthur Benjamin
Publisher: Basic Books
Why do so many gamblers risk it all when they know the odds of winning are against them? Why do they believe dice are "hot" in a winning streak? Why do we expect heads on a coin toss after several flips have turned up tails? What's Luck Got to Do with It? takes a lively and eye-opening look at the mathematics, history, and psychology of gambling to reveal the most widely held misconceptions about luck. It exposes the hazards of feeling lucky, and uses the mathematics of predictable outcomes to show when our chances of winning are actually good. Mathematician Joseph Mazur traces the history of gambling from the earliest known archaeological evidence of dice playing among Neolithic peoples to the first systematic mathematical studies of games of chance during the Renaissance, from government-administered lotteries to the glittering seductions of grand casinos, and on to the global economic crisis brought on by financiers' trillion-dollar bets. Using plenty of engaging anecdotes, Mazur explains the mathematics behind gambling--including the laws of probability, statistics, betting against expectations, and the law of large numbers--and describes the psychological and emotional factors that entice people to put their faith in winning that ever-elusive jackpot despite its mathematical improbability. As entertaining as it is informative, What's Luck Got to Do with It? demonstrates the pervasive nature of our belief in luck and the deceptive psychology of winning and losing. Some images inside the book are unavailable due to digital copyright restrictions.
The History, Mathematics, and Psychology of the Gambler's Illusion
Author: Joseph Mazur
Publisher: Princeton University Press