Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

    These intriguing problems, collected from Gardner's Scientific American columns, involve knots, interlocking rings, rotations and reflections, logical paradox, two-dimensional universes, chess strategies, and gambling odds."Gardner conjures problems that are both profound and silly; exquisite truths and outrageous absurdities; paradoxes, anagrams, palindromes and party tricks. . . . He knows, better than most, how many amazing true things there are in the world."—Newsweek

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    Beginning with the above questions, she began informally researching every affliction that she encountered in humans to learn whether it happened with animals, too. And usually, it did: dinosaurs suffered from brain cancer, koalas can catch chlamydia, reindeer seek narcotic escape in hallucinogenic mushrooms, stallions self-mutilate, and gorillas experience clinical depression. Natterson-Horowitz and science writer Kathryn Bowers have dubbed this pan-species approach to medicine zoobiquity. Here, they present a revelatory understanding of what animals can teach us about the human body and mind, exploring how animal and human commonality can be used to diagnose, treat, and heal patients of all species.

    The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    And the beauty of it is that it's all approximate!Using Enrico Fermi's theory of approximation, Santos brings the world of numbers into perspective. For puzzle junkies and trivia fanatics, these 70 word puzzles will show the reader how to take a bit of information, add what they already know, and extrapolate an answer.Santos has done the impossible: make math and the multiple possibilities of numbers fun and informative. Can you really cry a river? Is it possible to dig your way out of jail with just a teaspoon and before your life sentence is up?Taking an academic subject and using it as the prism to view everyday off-the-wall questions as math problems to be solved is a natural step for the lovers of sudoku, cryptograms, word puzzles, and other thought-provoking games.