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

    Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every kind. This revolution goes far beyond the limitless content that fills our lives, because information also underlies our understanding of ourselves, the natural world, and the universe. It is the key that unites fields as different as linguistics, cryptography, neuroscience, genetics, economics, and quantum mechanics. And the fact that information bears no necessary connection to meaning makes it a profound puzzle that people with a passion for philosophy have pondered for centuries.Table of ContentsLECTURE 1The Transformability of Information 4LECTURE 2Computation and Logic Gates 17LECTURE 3Measuring Information 26LECTURE 4Entropy and the Average Surprise 34LECTURE 5Data Compression and Prefix-Free Codes 44LECTURE 6Encoding Images and Sounds 57LECTURE 7Noise and Channel Capacity 69LECTURE 8Error-Correcting Codes 82LECTURE 9Signals and Bandwidth 94LECTURE 10Cryptography and Key Entropy 110LECTURE 11Cryptanalysis and Unraveling the Enigma 119LECTURE 12Unbreakable Codes and Public Keys 130LECTURE 13What Genetic Information Can Do 140LECTURE 14Life’s Origins and DNA Computing 152LECTURE 15Neural Codes in the Brain 169LECTURE 16Entropy and Microstate Information 185LECTURE 17Erasure Cost and Reversible Computing 198LECTURE 18Horse Races and Stock Markets 213LECTURE 19Turing Machines and Algorithmic Information 226LECTURE 20Uncomputable Functions and Incompleteness 239LECTURE 21Qubits and Quantum Information 253LECTURE 22Quantum Cryptography via Entanglement 266LECTURE 23It from Bit: Physics from Information 281LECTURE 24The Meaning of Information 293

    Aczel turns his sights on probability theory -- the branch of mathematics that measures the likelihood of a random event. He explains probability in clear, layman's terms, and shows its practical applications. What is commonly called luck has mathematical roots and in Chance, you'll learn to increase your odds of success in everything from true love to the stock market. For thousands of years, the twin forces of chance and mischance have beguiled humanity like none other. Why does fortune smile on some people, and smirk on others? What is luck, and why does it so often visit the undeserving? How can we predict the random events happening around us? Even better, how can we manipulate them? In this delightful and lucid voyage through the realm of the random, Dr. Aczel once again makes higher mathematics intelligible to us.

    The Age of Reason represents the results of years of study and reflection by Thomas Paine on the place of religion in society.Paine wrote: "Of all the tyrannies that affect mankind, tyranny in religion is the worst; every other species of tyranny is limited to the world we live in; but this attempts to stride beyond the grave, and seeks to pursue us into eternity."The cool rationale of Paine's The Age of Reason influenced religious thinking throughout the world; and its pervasieve influence continues to the present day.

    Gould's brilliant, funny, engaging prose dissects the motivations behind those who would judge intelligence, and hence worth, by cranial size, convolutions, or score on extremely narrow tests. How did scientists decide that intelligence was unipolar and quantifiable? Why did the standard keep changing over time? Gould's answer is clear and simple: power maintains itself. European men of the 19th century, even before Darwin, saw themselves as the pinnacle of creation and sought to prove this assertion through hard measurement. When one measure was found to place members of some "inferior" group such as women or Southeast Asians over the supposedly rightful champions, it would be discarded and replaced with a new, more comfortable measure. The 20th-century obsession with numbers led to the institutionalization of IQ testing and subsequent assignment to work (and rewards) commensurate with the score, shown by Gould to be not simply misguided--for surely intelligence is multifactorial--but also regressive, creating a feedback loop rewarding the rich and powerful. The revised edition includes a scathing critique of Herrnstein and Murray's The Bell Curve, taking them to task for rehashing old arguments to exploit a new political wave of uncaring belt tightening. It might not make you any smarter, but The Mismeasure of Man will certainly make you think.--Rob LightnerThis edition is revised and expanded, with a new introduction

    The text covers reason and religious belief, human knowledge, mind and its place in nature, determinism, free will and responsibility, and morality and its critics in five parts with careful attention to opposing points of view.

    Individual chapters discuss the representativeness and availability heuristics, problems in judging covariation and control, overconfidence, multistage inference, social perception, medical diagnosis, risk perception, and methods for correcting and improving judgments under uncertainty. About half of the chapters are edited versions of classic articles; the remaining chapters are newly written for this book. Most review multiple studies or entire subareas of research and application rather than describing single experimental studies. This book will be useful to a wide range of students and researchers, as well as to decision makers seeking to gain insight into their judgments and to improve them.

    Topics are structured in three parts in the book. Part I, Reference and Referring Expressions, includes topics such as Russell's Theory of Desciptions, Donnellan's distinction, problems of anaphora, the description theory of proper names, Searle's cluster theory, and the causal-historical theory. Part II, Theories of Meaning, surveys the competing theories of linguistic meaning and compares their various advantages and liabilities. Part III, Pragmatics and Speech Acts, introduces the basic concepts of linguistic pragmatics, includes a detailed discussion of the problem of indirect force and surveys approaches to metaphor.Unique features of the text: * chapter overviews and summaries* clear supportive examples* study questions* annotated further reading* glossary.

    Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines:Children's innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK-12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points