Symmetry: The Ordering Principle


David G. Wade - 2006
    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.

Calculus


Ron Larson - 1999
    It has been widely praised by a generation of users for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

The Essential Writings of Machiavelli


Niccolò Machiavelli - 2007
    Refreshingly accessible, these superb new translations are faithful to Machiavelli’s original, beautifully crafted writings.The volume features essays that appear in English for the first time, such as “A Caution to the Medici” and “The Persecution of Africa.” Also included are complete versions of the political treatise, The Prince, the comic satire The Mandrake, The Life of Castruccio Castracani, and the classic story “Belfagor”, along with selections from The Discourses, The Art of War, and Florentine Histories. Augmented with useful features–vital and concise annotations and cross-references–this unique compendium is certain to become the standard one-volume reference to this influential, versatile, and ever timely writer.“Machiavelli's stress on political necessity rather than moral perfection helped inspire the Renaissance by renewing links with Thucydides and other classical thinkers. This new collection provides deeper insight into Machiavelli’s personality as a writer, thus broadening our understanding of him.”–Robert D. Kaplan, author of Warrior Politics: Why Leadership Demands a Pagan Ethos “Constantine’s selection is not only intelligent; his translations are astonishingly good. Thoughtfully introduced by Albert Russell Ascoli, this edition belongs in everyone’s library.”–John Jeffries Martin, professor and chair, department of history, Trinity University“If one were to assign a single edition of Machiavelli's works, this most certainly would be it.”–John P. McCormick, professor, department of political science, University of Chicago

A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics


David Stipp - 2017
    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

How to Think About Analysis


Lara Alcock - 2014
    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

Calculus


Dale E. Varberg - 1999
    Covering various the materials needed by students in engineering, science, and mathematics, this calculus text makes effective use of computing technology, graphics, and applications. It presents at least two technology projects in each chapter.

How to Lie with Statistics


Darrell Huff - 1954
    Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way the results are derived from the figures, and points up the countless number of dodges which are used to fool rather than to inform.

Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications


Nassim Nicholas Taleb - 2020
    Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "na�ve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts


Stanislas Dehaene - 2014
    We can now pin down the neurons that fire when a person reports becoming aware of a piece of information and understand the crucial role unconscious computations play in how we make decisions. The emerging theory enables a test of consciousness in animals, babies, and those with severe brain injuries.A joyous exploration of the mind and its thrilling complexities, Consciousness and the Brain will excite anyone interestedin cutting-edge science and technology and the vast philosophical, personal, and ethical implications of finally quantifyingconsciousness.