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This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.

Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes.

Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable
Guesstimation is a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet. Guesstimation enables anyone with basic math and science skills to estimate virtually anything--quickly--using plausible assumptions and elementary arithmetic.

Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same. The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones--and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches, Guesstimation will delight popular-math enthusiasts and is ideal for the classroom.

Data meets literature in this “enlightening” (The Wall Street Journal), “brilliant” (The Boston Globe), “Nate Silver-esque” (O, The Oprah Magazine) look at what the numbers have to say about our favorite authors and their masterpieces.

There’s a famous piece of writing advice—offered by Ernest Hemingway, Stephen King, and myriad writers in between—not to use -ly adverbs like “quickly” or “angrily.” It sounds like solid advice, but can we actually test it? If we were to count all the -ly adverbs these authors used in their careers, do they follow their own advice? What’s more, do great books in general—the classics and the bestsellers—share this trait?

In the age of big data we can answer questions like these in the blink of an eye. In Nabokov’s Favorite Word Is Mauve, a “literary detective story: fast-paced, thought-provoking, and intriguing” (Brian Christian, coauthor of Algorithms to Live By), statistician and journalist Ben Blatt explores the wealth of fun findings that can be discovered by using text and data analysis. He assembles a database of thousands of books and hundreds of millions of words, and then he asks the questions that have intrigued book lovers for generations: What are our favorite authors’ favorite words? Do men and women write differently? Which bestselling writer uses the most clichés? What makes a great opening sentence? And which writerly advice is worth following or ignoring?

All of Blatt’s investigations and experiments are original, conducted himself, and no math knowledge is needed to enjoy the book. On every page, there are new and eye-opening findings. By the end, you will have a newfound appreciation of your favorite authors and also come away with a fresh perspective on your own writing. “Blatt’s new book reveals surprising literary secrets” (Entertainment Weekly) and casts an x-ray through literature, allowing us to see both the patterns that hold it together and the brilliant flourishes that allow it to spring to life.
"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." — Mathematical Gazette
This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others — but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book.
The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal.
Some of the most celebrated and intriguing items are: Archimedes' "Problema Bovinum," Euler's problem of polygon division, Omar Khayyam's binomial expansion, the Euler number, Newton's exponential series, the sine and cosine series, Mercator's logarithmic series, the Fermat-Euler prime number theorem, the Feuerbach circle, the tangency problem of Apollonius, Archimedes' determination of pi, Pascal's hexagon theorem, Desargues' involution theorem, the five regular solids, the Mercator projection, the Kepler equation, determination of the position of a ship at sea, Lambert's comet problem, and Steiner's ellipse, circle, and sphere problems.
This translation, prepared especially for Dover by David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language audience for the first time.
Ernst Heinrich Haeckel (1834–1919) was renowned as one of the foremost early exponents of Darwinism. His work was credited with having caused the acceptance of Darwinism in Europe, and his popular studies ― preaching the continuity of all life, organic and inorganic, from prehistoric time to the present ― converted tens of thousands of readers all over the world. Today, although no one is greatly interested in Haeckel the biologist-philosopher, his work is increasingly prized for something he himself would probably have considered secondary. These are the remarkable plates with which his work was illustrated, particularly his famous Kunstformen. The Kunstformen contains 100 beautiful lithographic plates which show a multitude of unusual life forms: Radiolaria, Foraminifera, and other forms of microscopic life; jellyfishes, starfishes, calcareous sponges, star corals, barnacles, and other sea life; mosses, lichens, red algae, ferns, fungi, orchids, and other plants; and turtles, moths, spiders, bats, frogs, lizards, hummingbirds, and antelope. With many drawings on each plate, each carefully drawn from nature, the subtle details of nature's art forms are easily compared and appreciated.
In addition to being marvelous renderings, these plates have long been noted for the peculiar emotional appeal that they have for most viewers, a premonition of surrealism with exotic organic life forms stretching back to their roots in the inorganic, and individual details drawn with awareness of subtle evolutionary changes and millennia-long developments. Artists, illustrators, and others will find them still powerful as one of the landmarks of applied art.
Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is "yes," then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book—all you need is a sense of curiosity and adventure!

Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same—or different—on all the cards. SET’s strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions—playing this game has generated new mathematics, and the math has led to new questions about the game itself.

The first book devoted to the mathematics of one of today’s most popular card games, The Joy of SET will entertain and enlighten the game enthusiast in all of us.

Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens?

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.


Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.

Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.


The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.



Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can’t be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated—they technically didn’t exist in the land of the pharaohs. You’ll be counting like an Egyptian in no time, and along the way you’ll learn firsthand how mathematics is an expression of the culture that uses it, and why there’s more to math than rote memorization and bewildering abstraction.

Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you’ll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.

Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation—the precursor to our modern system—and compares ancient Egyptian mathematics to today’s math, letting you decide for yourself which is better.

What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds.

If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions.


Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

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