They can begin to create their own pictures of sea life, placing them in an ocean that they imagine. The book can be used for school projects to get ideas that are related to science and Earth. Children can also use the information to come up with ideas about new animals that might live in the ocean.

    . . like a pendulum? These may not look like math questions, but they are-because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo's life-by turning the "dry" subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the "branches" of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive-from the sine waves we hear as "music" to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians-and It's a Numberful World.

    An extremely clever account.--The New Yorker.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

    This book surveys the most important computer algorithms currently in use and provides a full treatment of data structures and algorithms for sorting, searching, graph processing, and string processing -- including fifty algorithms every programmer should know. In this edition, new Java implementations are written in an accessible modular programming style, where all of the code is exposed to the reader and ready to use.The algorithms in this book represent a body of knowledge developed over the last 50 years that has become indispensable, not just for professional programmers and computer science students but for any student with interests in science, mathematics, and engineering, not to mention students who use computation in the liberal arts.The companion web site, algs4.cs.princeton.edu contains An online synopsis Full Java implementations Test data Exercises and answers Dynamic visualizations Lecture slides Programming assignments with checklists Links to related material The MOOC related to this book is accessible via the "Online Course" link at algs4.cs.princeton.edu. The course offers more than 100 video lecture segments that are integrated with the text, extensive online assessments, and the large-scale discussion forums that have proven so valuable. Offered each fall and spring, this course regularly attracts tens of thousands of registrants.Robert Sedgewick and Kevin Wayne are developing a modern approach to disseminating knowledge that fully embraces technology, enabling people all around the world to discover new ways of learning and teaching. By integrating their textbook, online content, and MOOC, all at the state of the art, they have built a unique resource that greatly expands the breadth and depth of the educational experience.

    We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is “probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant’s theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.Offering a powerful and elegant model that encompasses life’s complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

    By tracking a pendulum's path as it swung repeatedly across the interior of the large ceremonial hall, Foucault offered the first definitive proof -- before an audience that comprised the cream of Parisian society, including the future emperor, Napoleon III -- that the earth revolves on its axis.Through careful, primary research, world-renowned author Amir Aczel has revealed the life of a gifted physicist who had almost no formal education in science, and yet managed to succeed despite the adversity he suffered at the hands of his peers. The range and breadth of Foucault's discoveries is astonishing: He gave us the modern electric compass, devised an electric microscope, invented photographic technology, and made remarkable deductions about color theory, heat waves, and the speed of light. Yet until now so little has been known about his life.Richly detailed and evocative, Pendulum tells of the illustrious period in France during the Second Empire; of Foucault's relationship with Napoleon III, a colorful character in his own right; and -- most notably -- of the crucial triumph of science over religion.Dr. Aczel has crafted a fascinating narrative based on the life of this most astonishing and largely unrecognized scientist, whose findings answered many age-old scientific questions and posed new ones that are still relevant today.

    

    He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincare conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.Poincare's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award.In telling the vibrant story of The Poincare Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.

    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.

    Virtually every choice we make hinges on how someone generates data . . . and how someone else interprets it--whether we realize it or not.Where do you send your child for the best education? Big Data. Which airline should you choose to ensure a timely arrival? Big Data. Who will you vote for in the next election? Big Data.The problem is, the more data we have, the more difficult it is to interpret it. From world leaders to average citizens, everyone is prone to making critical decisions based on poor data interpretations.In Numbersense, expert statistician Kaiser Fung explains when you should accept the conclusions of the Big Data experts--and when you should say, Wait . . . what? He delves deeply into a wide range of topics, offering the answers to important questions, such as:How does the college ranking system really work?Can an obesity measure solve America's biggest healthcare crisis?Should you trust current unemployment data issued by the government?How do you improve your fantasy sports team?Should you worry about businesses that track your data?Don't take for granted statements made in the media, by our leaders, or even by your best friend. We're on information overload today, and there's a lot of bad information out there.Numbersense gives you the insight into how Big Data interpretation works--and how it too often doesn't work. You won't come away with the skills of a professional statistician. But you will have a keen understanding of the data traps even the best statisticians can fall into, and you'll trust the mental alarm that goes off in your head when something just doesn't seem to add up.Praise for NumbersenseNumbersense correctly puts the emphasis not on the size of big data, but on the analysis of it. Lots of fun stories, plenty of lessons learned--in short, a great way to acquire your own sense of numbers!Thomas H. Davenport, coauthor of Competing on Analytics and President's Distinguished Professor of IT and Management, Babson CollegeKaiser's accessible business book will blow your mind like no other. You'll be smarter, and you won't even realize it. Buy. It. Now.Avinash Kaushik, Digital Marketing Evangelist, Google, and author, Web Analytics 2.0Each story in Numbersense goes deep into what you have to think about before you trust the numbers. Kaiser Fung ably demonstrates that it takes skill and resourcefulness to make the numbers confess their meaning.John Sall, Executive Vice President, SAS InstituteKaiser Fung breaks the bad news--a ton more data is no panacea--but then has got your back, revealing the pitfalls of analysis with stimulating stories from the front lines of business, politics, health care, government, and education. The remedy isn't an advanced degree, nor is it common sense. You need Numbersense.Eric Siegel, founder, Predictive Analytics World, and author, Predictive AnalyticsI laughed my way through this superb-useful-fun book and learned and relearned a lot. Highly recommended! Tom Peters, author of In Search of Excellence

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    The text converts all programming code into the C++ language.

    But the dot, though perfect in every way, only had eyes for a wild and unkempt squiggle. All of the line's romantic dreams were in vain, until he discovered...angles! Now, with newfound self-expression, he can be anything he wants to be--a square, a triangle, a parallelogram....And that's just the beginning!First published in 1963 and made into an Academy Award-winning animated short film, here is a supremely witty love story with a twist that reveals profound truths about relationships--both human and mathematical--sure to tickle lovers of all ages.