Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    Authors Ruth Parker and Cathy Humphreys introduce  Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 3-10 , taking the readers into classrooms where their Number Talks routines are taught.Parker and Humphreys apply their 15 minute lessons to inspire and initiate math talks. Through vignettes in the book, you'll meet other teachers learning how to listen closely to students and how to prompt them into figuring out solutions to problems. You will learn how to make on-the-spot decisions, continually advancing and deepening the conversation.  Making Number Talks Matter  includes:Sample Problems: Making Number Talks Matter is filled with a range of Number Talks problems, 10-15 minute warm-up routines that lend themselves to mental math and comparison of strategiesNavigating Rough Spots: Learn how to create a safe environment for tricky, problematic, or challenging student discussions that can arise when talking through problems and sharing ideasResponding to Mistakes: Ways to handle misconceptions and mathematical errors that come up during the course of Number Talk conversations Making Number Talks Matter  is filled with teaching tips for honoring student contributions while still correcting errors, and teaching concepts while nudging independent thinking. Through daily practice and open conversation, you can build a solid foundation for the study of mathematics and make Number Talks Matter.

    As teen math prodigy Agnijo Banerjee and his teacher David Darling reveal, complex math surrounds us. If we think long enough about the universe, we're left not with material stuff, but a ghostly and beautiful set of equations. Packed with puzzles and paradoxes, mind-bending concepts, and surprising solutions, Weird Math leads us from a lyrical exploration of mathematics in our universe to profound questions about God, chance, and infinity. A magical introduction to the mysteries of math, it will entrance beginners and seasoned mathematicians alike.

    In The Universe and the Teacup, K. C. Cole demystifies mathematics and shows us-with humor and wonderfully accessible stories-why math need not be frightening. Using the O. J. Simpson trial, the bell curve, and Emmy Noether, the nineteenth-century woman scientist whose work was essential for Einstein's theory of relativity, Cole helps us see that more than just being a tool, math is a key to understanding the beauty of everything from rainbows to relativity.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    In this lively book of essays, Stephen Wolfram takes the reader along on some of his most surprising and engaging intellectual adventures in science, technology, artificial intelligence and language design.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    In A Brief History of Mathematical Thought, Luke Heaton explores how the language of mathematics has evolved over time, enabling new technologies and shaping the way people think. From stone-age rituals to algebra, calculus, and the concept of computation, Heaton shows the enormous influence of mathematics on science, philosophy and the broader human story. The book traces the fascinating history of mathematical practice, focusing on the impact of key conceptual innovations. Its structure of thirteen chapters split between four sections is dictated by a combination of historical and thematic considerations. In the first section, Heaton illuminates the fundamental concept of number. He begins with a speculative and rhetorical account of prehistoric rituals, before describing the practice of mathematics in Ancient Egypt, Babylon and Greece. He then examines the relationship between counting and the continuum of measurement, and explains how the rise of algebra has dramatically transformed our world. In the second section, he explores the origins of calculus and the conceptual shift that accompanied the birth of non-Euclidean geometries. In the third section, he examines the concept of the infinite and the fundamentals of formal logic. Finally, in section four, he considers the limits of formal proof, and the critical role of mathematics in our ongoing attempts to comprehend the world around us. The story of mathematics is fascinating in its own right, but Heaton does more than simply outline a history of mathematical ideas. More importantly, he shows clearly how the history and philosophy of maths provides an invaluable perspective on human nature.

    Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman, the course also featured, as occasional guest speakers, some of the most brilliant men in science at that time, including Marvin Minsky, Charles Bennett, and John Hopfield. Although the lectures are now thirteen years old, most of the material is timeless and presents a “Feynmanesque” overview of many standard and some not-so-standard topics in computer science such as reversible logic gates and quantum computers.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    Inside these pages some of the biggest (and smallest) mysteries of the natural world are explained in essays by real working scientists, which are then illustrated by artists given free rein to be as literal or as imaginative as they like. The result is a celebration of the wonder that inspires every new discovery. Featuring work by such contemporary luminaries as Lisa Congdon, Jen Corace, Neil Farber, Susie Ghahremani, Jeremyville, and many more, this is a work of scientific and artistic exploration to pique the interest of both the intellectually and imaginatively curious.

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.