As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

    While these are essential, many young ecologists need to figure out how to actually do research themselves. How to Do Ecology provides nuts-and-bolts advice on how to develop a successful thesis and research program. This book presents different approaches to posing testable ecological questions. In particular, it covers the uses, strengths, and limitations of manipulative experiments in ecology. It will help young ecologists consider meaningful treatments, controls, replication, independence, and randomization in experiments, as well as where to do experiments and how to organize a season of work. This book also presents strategies for analyzing natural patterns, the value of alternative hypotheses, and what to do with negative results.Science is only part of being a successful ecologist. This engagingly written book offers students advice on working with other people and navigating their way through the land mines of research. Findings that don't get communicated are of little value. How to Do Ecology suggests effective ways to communicate information in the form of journal articles, oral presentations, and posters. Finally, it outlines strategies for developing successful grant and research proposals. Numerous checklists, figures, and boxes throughout the book summarize and reinforce the main points. In short, this book makes explicit many of the unspoken assumptions behind doing good research in ecology, and provides an invaluable resource for meaningful conversations among ecologists.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.

    The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all, this is an excellent work, of equally high value for both student and teacher." Zentralblatt f�r Mathematik

    Fast Tract Digestion Heartburn is the first book to define and address the real cause of acid reflux. Acid reflux occurs as a result of digestive malabsorption of five difficult-to-digest carbohydrates. It leads to the overgrowth of gas-producing bacteria in the small intestine and the gas pressure drives acid reflux. Dropping a Mentos into a bottle of Coke is the perfect illustration of this phenomenon. Unfortunately, PPI drugs do not address the real cause, but also cause serious side effects including vitamin and mineral malabsorption, bone fractures, pneumonia, low blood magnesium levels, bacterial overgrowth, C diff infection and pneumonia as explained in the book.Fast Tract Digestion Heartburn offers science-based food choices and recipes (Fast Tract Diet) to limit the five difficult-to-digest carbohydrates, so that you can feel relief within a few days Also, it enables you to self-manage all of the symptoms of acid reflux going forward. The Fast Tract Diet is based on a scientific formula called Fermentation Potential (FP). FP is the key measure regardless of the carbohydrate count. Limiting foods with high FP will help control the overgrowth of bacteria in the small intestine and, as a result, acid reflux. The Fast Tract Diet was clinically tested on reflux sufferers in the Boston area. The results were overwhelming and proved the effectiveness of the diet as an alternative to proton pump inhibitor drugs.

    In 2007, Janet Belsky's "Experiencing the Lifespan" was published to widespread instructor and student acclaim, ultimately winning the 2008 Textbook Excellence Award from the Text and Academic Authors Association. Now that breakthrough text returns in a rigorously updated edition that explores the lifespan by combining the latest research with a practicing psychologist's understanding of people, and a teacher's understanding of students and classroom dynamics. And again, all of this in the right number of pages to fit comfortably in a single term course.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the twentieth century, and explores the wide range of applications in science, and in aspects of economics.About the Series: Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Chock full of easy to understand instructions and full color pictures for the 24 recipes included, you are sure to succeed with this book, regardless of your skill level. With a few simple ingredients, and a little bit of time, you’ll be making bath bombs in an afternoon. You’re in good hands with this quick and easy guide to showing you not only the basics, but also more fun and challenging recipes like the Fizzy Pops, designed to look like tasty cake pop treats. Taking it a step further she has also included cupcake bath bombs with a sugar scrub topping. Who wouldn't love to make these? This book can be a project for yourself, a gift for a friend, or an enhancement to your knowledge in the world of bath and body crafts. Whatever the purpose, the reader will enjoy!

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.