Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

    Inside, you will find over 200 facts about the Titanic. There are facts about: • Building the Titanic • Crew of the Titanic • Passengers of the Titanic • Interior of the Titanic • Maiden voyage of the Titanic • Sinking of the Titanic • Survivors of the Titanic • Museums of the Titanic • Movies about the Titanic • Titanic’s legacy Ready? Let’s go back to Titanic…

    

    This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, -The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.- Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.In the paper, -On Computable Numbers, with an Application to the Entscheidungsproblem, - Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

    Here, Robert Solomon and Kathleen Higgins tell the story of philosophy's development with great clarity and refreshing wit. The authors begin with the most ancient religious beliefs of the east and west and bring us right up to the feminist and multicultural philosophies of the present. Along the way, they highlight major philosophers, from Plato and the Buddha to William James and Simone de Beauvoir, and explore major categories, from metaphysics and ethics to politics and logic. The book is enlivened as well by telling anecdotes and sparkling quotations. Among many memorable observations, we're treated to Thomas Hobbes' assessment that life is nasty, brutish, and short and Hegel's description of Napoleon as world history on horseback. Engaging, comprehensive, and delightfully written, A Passion for Wisdom is a splendid introduction to an intellectual tradition that reaches back over three thousand years.

    The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.

    Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

    On any given Saturday, in dozens of stadiums across America, you will find crowds in excess of 75,000 gathered to root on their teams. This book is their Bible???a rich and comprehensive reference guide to the game??'s history, tradition and lore. Based on three years of research by the nation??'s foremost football experts, the book features: ???? ???? ??Capsule histories for each of the 119 Division 1-A programs, the Ivy League schools and teams from the SWAC, MEAC and historically black colleges ??????????????Year-by-year schedules and records ??????????????Statistical leaders from every school ??????????????Fightsong lyrics ??????????????Box scores for every bowl game ever played ??????????????4-color insert illustrating the evolution of each school??'s helmet design ??????????????Weekly polls dating back to 1936 ??????????????Essays by the game??'s top wordsmiths (Dan Jenkins, Beano Cook, Chris Fowler, Gene Wojciechowski) ??????????????Plus a lively round table discussion with ESPN??'s popular Game Day Team (Fowler, LeeCorso and Kirk Herbstreit) Packed with tables and charts and designed in an easy-to-read style, the updated ESPN College Football Encyclopedia will continue to dazzle even the most knowledgeable fan.

    Over five decades, Star Trek's celebration of mankind's technical achievements and positive view of the future have earned it an enduring place in our global culture. Its scientific vision has also had a profound effect on the past thirty years of technological breakthroughs. Join William Shatner, the original captain of the Starship Enterprise, as he reveals how Star Trek has influenced and inspired some of our greatest scientific minds -- the people behind the future we will all share. In interviews with dozens of scientists we learn about the inventions that will revolutionise our lives and the discoveries that will make it truly possible to explore the last great frontier -- space. As one Nobel Laureate commented on being shown a wood and plastic model of the engine core from a Star Trek: The Next Generation starship: I'm working on that. From the technicalities of warp speed to real-life replicators to the likelihood of our being able to beam across continents, this always-informative book takes us on a fascinating and eye-opening voyage to

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.

    It grew to become a major political force in Italy, while its tentacles penetrated every aspect of life in the United States. Through drugs, it spread its influence to Britain, Canada and Australia. And through the gangster movies of Hollywood, including The Godfather and Goodfellas, it permeates popular culture.The History of the Mafia is full of blood-chilling characters, from Al Capone, who ran Chicago during Prohibition, and hitmen Louis Lekpe and Alberto Anastasia who founded Murder, Inc, to Totò Riina, 'boss of bosses', John Gotti, 'the Teflon don', and Bernardo 'The Tractor' Provenzano, who hid out from the law in a farmhouse for 43 years...These were extraordinary men who lived through extraordinary times. The History of the Mafia tells the story of their lives, their families, their codes, their crimes and their cold-blooded murders. A long and enthralling tale, drenched in blood and scored with betrayal.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.