Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    Luckily, algebra will help you solve each problem. By using simple addition, subtraction, mulitplication, and division, you'll discover that solving math mysteries isn't scary at all -- it's fun!

    In Decoding the Universe, Charles Seife draws on his gift for making cutting-edge science accessible to explain how this new tool is deciphering everything from the purpose of our DNA to the parallel universes of our Byzantine cosmos. The result is an exhilarating adventure that deftly combines cryptology, physics, biology, and mathematics to cast light on the new understanding of the laws that govern life and the universe.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    Twenty-two years later, he did. April 1945 – Berlin. The world had been at war for more than five-and-a-half years – approximately seventy million people were dead across the globe. The epicentre of the twelve-year-old Third Reich was now surrounded, enveloped by bitter Soviet forces hardened by Nazi barbarity in the east over the last four years. As the buildings were blasted into rubble, pounded by Russian guns and bombs, before their troops and tanks, Hitler was hunkered down in his last headquarters – the dark and damp bunker under the Reich Chancellery. As the Third Reich began to crumble as fast as the city’s buildings, what was the state of mind of the tyrant? Only his closest and fanatical allies saw the collapse, none more so than Hitler’s servants, Otto Gunsche and Heinz Linge – two individuals which witnessed the final act of their regime. An act tinged over the last ten days in late April with selfish betrayal, increasingly forlorn hope, pleas, desperation and eventually suicide. As the Soviets closed in with impending vigour, in the concrete tomb below ground and under the thunderous booms of the petrifying battle for Berlin, the mind of the dictator disintegrated into drugs, delusion and a determination to die. Not by the enemy bullet but one of his own. This is the story of the people who held a unique place in world history – the ones who were there when the nightmare of Nazism and the horrors which accompanied it was finally banished as a dark chapter in the story of the human race.

    

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    The nature of football continually changes, which means its analysis must also keep pace. This book is for students, thinkers, and theorists of the game.'Ted Hopkins - Carlton premiership player, author, and co-founder of Champion Data. Australian Rules football has been described as the most data-rich sport on Earth. Every time and everywhere an AFL side takes to the field, it is shadowed by an army of statisticians and number crunchers. The information they gather has become the sport's new language and currency. ABC journalist James Coventry, author of the acclaimed Time and Space, has joined forces with a group of razor-sharp analysts to decipher the data, and to use it to question some of football's long-held truisms. Do umpires really favour the home side? Has goal kicking accuracy deteriorated? Is Geelong the true master of the draft? Are blonds unfairly favoured in Brownlow medal voting? And are Victorians the most passionate fans? Through a blend of entertaining storytelling and expert analysis, this book will answer more questions about footy than you ever thought to ask. Praise for Time and Space:'Brilliant, masterful' - The Guardian'Arguably one of the most important books yet written on Australian Rules football.' - Inside History'Should find its way into the hands of every coach.' - AFL Record

    The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein. Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.Calculus For Dummies is intended for three groups of readers:Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:Real-world examples of calculus The two big ideas of calculus: differentiation and integration Why calculus works Pre-algebra and algebra review Common functions and their graphs Limits and continuity Integration and approximating area Sequences and series Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression.

    In an era of the military space race, Erich von Däniken boldly proclaimed that Earth had been visited by more advanced beings early in our history. But prescientific man had no concept of space ships, so he called their vehicles “chariots,” and those driving the chariots became “gods.” Over the next five decades, von Däniken’s more than 40 books built an ever-stronger case for Earth being visited by extraterrestrial visitors. And Chariots became an international best seller, with 30 million copies sold in more than two dozen languages. Also during that time, the case for ET visitations millennia ago was being reexamined by contemporary UFO researchers, who found evidence of modern visitations. And von Däniken expanded his perspective to encompass the present. Now, he presents his long-awaited sequel to Chariots of the Gods, proclaiming that the gods never left us with all-new material to show that ancient aliens are still with us. The Gods Never Left Us contends that recent advancements in biotechnology, astrophysics, engineering, and artificial intelligence not only give us a fresh perspective on his ancient astronaut theory but actually validates it. We are—as a race—embarking on the exact same trajectory of our own interplanetary colonization, just as von Däniken suggested Earth itself was colonized. ETs are definitely at work today. And that affects all of us. Why do they do what they do? What could an extraterrestrial species possibly gain from observing us in the same way we look at ants? What have these strangers wanted for the past thousands of years? Can’t they leave us alone? And what makes it so difficult for us to acknowledge the existence of these extraterrestrials? That is what this book deals with. "Erich's newest book is a fascination journey from the ancient past into the present with a plethora of scientific evidence and documented research. As always, he ads his own "to the point" take on it all. Readers may also like that his newest work moves in a slightly different direction from his past books. A thoroughly enlightening and enjoyable Read." —Bruce Cunningham, Director, Ancient Mysteries International LLC & Publisher of Advanced Archaeology Review magazine