Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

    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.

    In The Irrationals , the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them. That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random". Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

     Building Thinking Classrooms in Mathematics, Grades K-12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guideProvides the what, why, and how of each practice Includes firsthand accounts of how these practices foster thinking Offers a plethora of macro moves, micro moves, and rich tasks to get started

    These 30 short chapters each deal with a particular programming problem drawn from sources as diverse as games and puzzles, intriguing combinatorial tasks, and more familiar areas such as data compression and string matching. Each pearl starts with the statement of the problem expressed using the functional programming language Haskell, a powerful yet succinct language for capturing algorithmic ideas clearly and simply. The novel aspect of the book is that each solution is calculated from an initial formulation of the problem in Haskell by appealing to the laws of functional programming. Pearls of Functional Algorithm Design will appeal to the aspiring functional programmer, students and teachers interested in the principles of algorithm design, and anyone seeking to master the techniques of reasoning about programs in an equational style.

    The other books in the series are The Black Swan, Antifragile,and The Bed of Procrustes.

    The book assumes no prior knowledge, taking the student through every stage of their research project in manageable steps. Advice on planning and conducting studies, analyzing data, and writing up practical reports is given, and examples are provided, as well as advice on how to report results in conventional (APA) style. Unlike other introductory texts, there is practical guidance on qualitative research, as well as discussion of issues of bias, interpretation, and variance. Content on qualitative methods has been expanded for the fifth edition and now includes additional material on widely used methods, such as grounded theory, thematic analysis, interpretive phenomenological analysis (IPA), and discourse analysis. The book provides clear coverage of statistical procedures, and includes everything needed at an undergraduate level from nominal level tests, to multi-factorial ANOVA designs, multiple regression, and log linear analysis. In addition, the book provides detailed and illustrated SPSS textbook. Each chapter contains a self-test glossary, key terms, and exercises, ensuring that key concepts have been understood. Students are further supported. Students are further supported by an accompanying website that provides additional exercises, revision flash cards, links to further reading, and data for use with SPSS. The website will also include updated coverage of SPSS should a new version be launched. The bestselling research methods text for over a decade, Research Methods and Statistics in Psychology remains an invaluable resource for students of psychology throughout their studies.

    As well as looking at logic in theoretical terms the book considers its everyday uses and demonstrates how it has genuine practical applications. It will take you step by step through the most difficult concepts and is packed with exercises to help you consolidate your learning at every stage. Covering everything from syllogistic logic to logical paradoxes and even looking at logic in Alice in Wonderland, this is the only guide you will ever need.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    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

    For the most part the book is a discussion of good writing style and effective research strategies. Some of the material is accepted wisdom, some is controversial, and some is my opinions. Although the book is brief, it is designed to be comprehensive: some readers may be interested in exploring topics further, but for most readers this book should be suf?cient. The ?rst edition of this book was almost entirely about writing. This e- tion, partly in response to reader feedback and partly in response to issues that arose in my ownexperiences as an advisor, researcher, and referee, is also about research methods. Indeed, the two topics writing about and doing research are not clearly separated. It is a small step from asking how do I write? to askingwhatisitthatIwriteabout? As previously, the guidance on writing focuses on research, but much of the material is applicable to general technical and professional communication. Likewise, the guidance on the practice of research has broader lessons. A pr- titioner trying a new algorithm or explaining to colleagues why one solution is preferable to another should be con?dent that the arguments are built on robust foundations. And, while this edition has a stronger emphasis on research than did the ?rst, nothing has been deleted; there is additional material on research, but the guidance on writing has not been taken away."

    Contributors include Steven Weinberg, Peter Galison, John Maynard Smith, and Frank Wilczek.