In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    It now has 600,000 to a million page hits daily. Every now and then, Munroe would get emails asking him to arbitrate a science debate. 'My friend and I were arguing about what would happen if a bullet got struck by lightning, and we agreed that you should resolve it . . . ' He liked these questions so much that he started up What If. If your cells suddenly lost the power to divide, how long would you survive? How dangerous is it, really, to be in a swimming pool in a thunderstorm? If we hooked turbines to people exercising in gyms, how much power could we produce? What if everyone only had one soulmate?When (if ever) did the sun go down on the British empire? How fast can you hit a speed bump while driving and live?What would happen if the moon went away?In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations, and consults with nuclear reactor operators. His responses are masterpieces of clarity and hilarity, studded with memorable cartoons and infographics. They often predict the complete annihilation of humankind, or at least a really big explosion. Far more than a book for geeks, WHAT IF: Serious Scientific Answers to Absurd Hypothetical Questions explains the laws of science in operation in a way that every intelligent reader will enjoy and feel much the smarter for having read.

    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.

    Mathematics, Applied & Natural Sciences

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    . . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun. In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.

    This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms. First Edition HB (2000): 0-521-62304-9

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    In adollars-and-cents, bottom-line world, where numbers influenceeverything, none of us can afford to let our math skills atrophy.This step-by-step personal math trainer:Refreshes practical math skills for your personal andprofessional needs, with examples based on everyday situations. Offers straightforward techniques for working with decimals and fractions. Demonstrates simple ways to figure discounts, calculatemortgage interest rates, and work out time, rate, and distance problems. Contains no complex formulas and no unnecessary technical terms.

    For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.

    This book reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

    Dozens of examples in innumeracy show us how it affects not only personal economics and travel plans, but explains mis-chosen mates, inappropriate drug-testing, and the allure of pseudo-science.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.

     In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone.Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.