It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.

    In "Musimathics," Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music -- a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.In Volume 1, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The examples given are all practical problems in music and audio.Additional material can be found at http: //www.musimathics.com.

    When the boy's eyes were healed they removed the bandages and, waving a hand in front of the child's physically perfect eyes, asked him what he saw. "I don't know," was his only reply. What he saw was only a varying brightness in front of him. However, when allowed to touch the hand as it began to move, he cried out in a voice of triumph, "It's moving!" He could feel it move, but he still needed laboriously to learn to see it move. Light and eyes were not enough to grant him sight. How, then, do we see? What's the difference between seeing and perception? What is light?From ancient times to the present, from philosophers to quantum physicists, nothing has so perplexed, so fascinated, so captivated the mind as the elusive definition of light. In Catching the Light, Arthur Zajonc takes us on an epic journey into history, tracing how humans have endeavored to understand the phenomenon of light. Blending mythology, religion, science, literature, and painting, Zajonc reveals in poetic detail the human struggle to identify the vital connection between the outer light of nature and the inner light of the human spirit. He explains the curiousness of the Greeks' blue and green "color blindness": Odysseus gazing longingly at the "wine-dark sea"; the use of chloros (green) as the color of honey in Homer's Odessey; and Euripides' use of the color green to describe the hue of tears and blood. He demonstrates the complexity of perception through the work of Paul Cézanne--the artist standing on the bank of a river, painting the same scene over and over again, the motifs multiplying before his eyes. And Zajonc goes on to show how our quest for an understanding of light, as well as the conclusions we draw, reveals as much about the nature of our own psyche as it does about the nature of light itself. For the ancient Egyptians the nature of light was clear--it simply was the gaze of God. In the hands of the ancient Greeks, light had become the luminous inner fire whose ethereal effluence brought sight. In our contemporary world of modern quantum physics, science plays the greatest part in our theories of light's origin--from scientific perspectives such as Sir Isaac Newton's "corpuscular theory of light" and Michael Faraday's "lines of force" to such revolutionary ideas as Max Planck's "discrete motion of a pendulum" (the basis of quantum mechanics), Albert Einstein's "particles of light" and "theory of relativity," and Niels Bohr's "quantum jumps." Yet the metaphysical aspects of the scientific search, Zajonc shows, still loom large. For the physicist Richard Feynman, a quantum particle travels all paths, eventually distilling to one path whose action is least--the most beautiful path of all. Whatever light is, here is where we will find it.With rare clarity and unmatched lyricism, Zajonc illuminates the profound implications of the relationships between the multifaceted strands of human experience and scientific endeavor. A fascinating search into our deepest scientific mystery, Catching the Light is a brilliant synthesis

    The book begins with an introduction to the language of statistics and then covers descriptive statistics and inferential statistics. Throughout, the author offers readers:- Difficulty Rating Index for each chapter′s material- Tips for doing and thinking about a statistical technique- Top tens for everything from the best ways to create a graph to the most effective techniques for data collection- Steps that break techniques down into a clear sequence of procedures- SPSS tips for executing each major statistical technique- Practice exercises at the end of each chapter, followed by worked out solutions.The book concludes with a statistical software sampler and a description of the best Internet sites for statistical information and data resources. Readers also have access to a website for downloading data that they can use to practice additional exercises from the book. Students and researchers will appreciate the book′s unhurried pace and thorough, friendly presentation.

    This humanized view of science opens up the mind-stretching visions of how quantum mechanics, God, human thought, and will are related, and provides profound implications for our understanding of the nature of reality and our relationship to the cosmos.

    Even the simplest numbers can become powerful forces when manipulated by politicians or the media, but in the case of the law, your liberty -- and your life -- can depend on the right calculation. In Math on Trial, mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used -- and disastrously misused -- as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt's will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge's misunderstanding of probability led him to discount critical evidence -- which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison. A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn't't always enough to prove a person innocent.

    Data is nuanced, and "a really excellent skeptic puts the term 'science' into 'data science.'" The big data revolution shouldn't be dismissed as hype, but current data science tools and models shouldn't be hailed as the end-all-be-all, either."

    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    Along the way we’ll learn how selection bias can explain why your boss doesn’t know he sucks (even when everyone else does); how to use Bayes’ Theorem to decide if your partner is cheating on you; and why Mark Zuckerberg should never be used as an example for anything. See the world in a whole new light, and make better decisions and judgements without ever going near a t-test. Think. Think Statistically.

    Written not from a post-crisis perspective – but from a preventative point of view – this book traces the development of financial derivatives from bonds to credit default swaps, and shows how mathematical formulas went beyond pricing to expand their use to the point where they dwarfed the real economy. You'll learn how the deadly allure of their ice-cold beauty has misled generations of economists and investors, and how continued reliance on these formulas can either assist future economic development, or send the global economy into the financial equivalent of a cardiac arrest. Rather than rehash tales of post-crisis fallout, this book focuses on preventing the next one. By exploring the heart of the shadow economy, you'll be better prepared to ride the rough waves of finance into the turbulent future. Delve into one of the world's least-understood but highest-impact industries Understand the key principles of quantitative finance and the evolution of the field Learn what quantitative finance has become, and how it affects us all Discover how the industry's next steps dictate the economy's future How do you create a quadrillion dollars out of nothing, blow it away and leave a hole so large that even years of "quantitative easing" can't fill it – and then go back to doing the same thing? Even amidst global recovery, the financial system still has the potential to seize up at any moment. The Money Formula explores the how and why of financial disaster, what must happen to prevent the next one.

    At less than half the price of a standard textbook, it offers an affordable alternative.  A built-in Study Guide, written by the author, offers a practical suite of learning aids that foster review and self-assessment without the expense of a separate guide.

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    Based on the experience of the authors in teaching Mathematics Courses for almost four decades at the Institute of Technology, New Delhi, this text book rather than a guide/problem book, lays emphasis on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner.

    Short-Cut Math is a concise, remarkably clear compendium of about 150 math short-cuts — timesaving tricks that provide faster, easier ways to add, subtract, multiply, and divide.By using the simple foolproof methods in this volume, you can double or triple your calculation speed — even if you always hated math in school. Here's a sampling of the amazingly effective techniques you will learn in minutes: Adding by 10 Groups; No-Carry Addition; Subtraction Without Borrowing; Multiplying by Aliquot Parts; Test for Divisibility by Odd and Even Numbers; Simplifying Dividends and Divisors; Fastest Way to Add or Subtract Any Pair of Fractions; Multiplying and Dividing with Mixed Numbers, and more.The short-cuts in this book require no special math ability. If you can do ordinary arithmetic, you will have no trouble with these methods. There are no complicated formulas or unfamiliar jargon — no long drills or exercises. For each problem, the author provides an explanation of the method and a step-by-step solution. Then the short-cut is applied, with a proof and an explanation of why it works.Students, teachers, businesspeople, accountants, bank tellers, check-out clerks — anyone who uses numbers and wishes to increase his or her speed and arithmetical agility, can benefit from the clear, easy-to-follow techniques given here.