Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives—from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.Many of the greatest names in intellectual history—Pythagoras, Plato, Archimedes, Euclid— were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions—his famed Coxeter groups and Coxeter diagrams—have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

    The first half of the book deals with classical physical optics; the second principally with the quantum nature of light. Chapters 1 and 2 treat the propagation of light waves, including the concepts of phase and group velocities, and the vectorial nature of light. Chapter 3 applies the concepts of partial coherence and coherence length to the study of interference, and Chapter 4 takes up multiple-beam interference and includes Fabry-Perot interferometry and multilayer-film theory. Diffraction and holography are the subjects of Chapter 5, and the propagation of light in material media (including crystal and nonlinear optics) are central to Chapter 6. Chapters 7 and 8 introduce the quantum theory of light and elementary optical spectra, and Chapter 9 explores the theory of light amplification and lasers. Chapter 10 briefly outlines ray optics in order to introduce students to the matrix method for treating optical systems and to apply the ray matrix to the study of laser resonators.Many applications of the laser to the study of optics are integrated throughout the text. The author assumes students have had an intermediate course in electricity and magnetism and some advanced mathematics beyond calculus. For classroom use, a list of problems is included at the end of each chapter, with selected answers at the end of the book.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    A historian and journalist who was one of the earliest and staunchest Afrikaner opponents of apartheid, Hermann Giliomee weaves together life stories and historical interpretation to create a narrative history of the Afrikaners from their beginnings with the colonization of the Cape of Good Hope by the Dutch East India Company to the dismantling of apartheid and beyond. The Afrikaners emphasizes the crucial role played by historical actors without underplaying the impact of social forces over which they had little control. Throughout their history, Giliomee's Afrikaners are both colonizers and colonized. Actual or virtual servants of the Dutch East India Company, the Dutch "burghers" nonetheless owned slaves and commanded servant labor. The British conquests of 1795 and 1806 extended the rights of British subjects to Afrikaners, even as they took away the Afrikaners' political autonomy and confirmed an economic and cultural subordination that was only partly alleviated by their dominance of South African politics in the latter part of the twentieth century.Demographically squeezed between far more numerous Africans (and other nonwhite groups) and their more affluent and culturally confident English compatriots, the Afrikaners forged a language-based national identity in which die-hard defense of privilege and opposition to various forms of British domination are inextricably intertwined with fears about cultural and even physical group survival. This nationalism underlay the Great Trek, in which Afrikaners opposed the abolition of slavery and legalized racial discrimination by the British; the irony of their becoming the twentieth century's first fighters against imperial domination in the Boer War; and the Afrikaners' rise to political dominance over their English rivals and nonwhite South Africans alike, even as they remained economically and culturally subordinate to the former. This same language-based nationalism spawned the blunders and horrors of apartheid, but it also led the Afrikaners to relinquish power peacefully when this seemed the safest route to their survival as a people.While documenting--and in important ways revising--the history of the Afrikaners' pursuit of racial domination (as well as British contributions to that enterprise), Giliomee supplies Afrikaners' own, often divided, perspectives on their history, perspectives not always or entirely skewed by their struggle for privilege at Africans' expense. The result is not only a magisterial history of the Afrikaners but a fuller understanding of their history, which, for good or ill, resonates far beyond the borders of South Africa.

    

    In 1979, Thatcher's Britain was a country crippled by strikes, joblessness, and economic gloom, divided by race and class—and skanking to a new beat: 2 Tone. The unruly offspring of white boy punk and rude boy ska, the Specials burst on to the scene. On stage they were electric, and at the heart of this energy was the vocal chemistry of the ethereal Terry Hall and Jamaican rude boy Neville Staple. In 1961, five-year-old Neville was sent to England to live with his father, a man for whom discipline bordered on child abuse. As he recounts here, growing up black in the Midlands of the 1960s and 1970s wasn't easy, and his youth was marked by scuffles with skins, compulsive womanizing, and a life of crime that led from shoplifting to burglary and eventually prison. But throughout there was music, and Nev reveals how he became part of the most important band of the 1980s. He remembers sound system battles; the legendary 2 Tone tour with the Selecter, Madness, and Dexy's, and their clashes with white nationalist thugs. He recalls the band's increasing tensions and eventual split; his subsequent foray into bubblegum pop with Fun Boy Three; and a newfound fame in America as godfather to Third Wave ska bands. Finally he reflects on the Specials' reunion and how even now, 30 years later, they can't help tearing themselves apart.

    A Key Strength Of This Text Is Zill'S Emphasis On Differential Equations As Mathematical Models, Discussing The Constructs And Pitfalls Of Each. The Third Edition Is Comprehensive, Yet Flexible, To Meet The Unique Needs Of Various Course Offerings Ranging From Ordinary Differential Equations To Vector Calculus. Numerous New Projects Contributed By Esteemed Mathematicians Have Been Added. Key Features O The Entire Text Has Been Modernized To Prepare Engineers And Scientists With The Mathematical Skills Required To Meet Current Technological Challenges. O The New Larger Trim Size And 2-Color Design Make The Text A Pleasure To Read And Learn From. O Numerous NEW Engineering And Science Projects Contributed By Top Mathematicians Have Been Added, And Are Tied To Key Mathematical Topics In The Text. O Divided Into Five Major Parts, The Text'S Flexibility Allows Instructors To Customize The Text To Fit Their Needs. The First Eight Chapters Are Ideal For A Complete Short Course In Ordinary Differential Equations. O The Gram-Schmidt Orthogonalization Process Has Been Added In Chapter 7 And Is Used In Subsequent Chapters. O All Figures Now Have Explanatory Captions. Supplements O Complete Instructor'S Solutions: Includes All Solutions To The Exercises Found In The Text. Powerpoint Lecture Slides And Additional Instructor'S Resources Are Available Online. O Student Solutions To Accompany Advanced Engineering Mathematics, Third Edition: This Student Supplement Contains The Answers To Every Third Problem In The Textbook, Allowing Students To Assess Their Progress And Review Key Ideas And Concepts Discussed Throughout The Text. ISBN: 0-7637-4095-0

    " Fox has inspired millions of people over the past forty years through his simple, practical guidelines. In Diagrams for Living he presents valuable keys to living a more fulfilled life drawn from the eloquent spiritual wisdom of the Bible.If we read the Bible literally, cautions Fox, we miss the eternal power and personal relevance found in its symbols, allegories, and parables. "Whether you realize it or not," he writes, "you are on every page from Genesis to Revelation." Fox shows how to read dramatic biblical stories as symbolic diagrams for living that can "show you how to overcome difficulties and problems, and how to give expression to the deep aspirations that lie hidden in your soul." This power to reveal, inspire, and guide makes the Bible's teachings adaptable to everyone at every stage of spiritual development.Sensible, contemporary, and full of reassurance, Diagrams for Living offers sage counsel from a gifted teacher.

    Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, alwayschoosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum ofmathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issuesand has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

    Best known in recent years for producing U2's sensational albums, Eno began his career as a synthesizer player for Roxy Music. He has since released many solo albums, both rock and ambient, written music for film and television soundtracks, and collaborated with David Bowie, David Byrne, Robert Fripp, and classical and experimental composers. His pioneering ambient sound has been enormously influential, and without him today's rock would have a decidedly different sound. Drawing on Eno's own words to examine his influences and ideas, this book—featuring a new afterword and an updated discography and bibliography—will long remain provocative and definitive.

    Dillon.

    

    Describes how fractals were discovered, explains their unique properties, and discusses the mathematical foundation of fractals.