Thoroughly updated, this edition offers new, faster techniques for solving differential equations generated by the emergence of high-speed computers.

    The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

    For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    During a police investigation (concluded in 1996), however, the author admitted that his claims were untrue. The investigation proved that the book was fraudulent, that the purported SAS "execution squads" did not exist, and that the book is not a memoir but a "work of fiction."'Paul Bruce' was the pseudonym of Paul Inman, a former mechanic in the British Army's Corps of Royal Electrical and Mechanical Engineers, and he was never a member of the SAS (Special Air Service). 'The Nemesis File: The True Story of an SAS Execution Squad,' therefore, is a work of sensational fiction which only served to exacerbate the sectarian divide in Northern Ireland through which Inman and the publisher (John Blake, a former tabloid editor) could financially profit.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    He has proven his ability to scientists exploring the nature of mediumship and has astounded them with the consistency and accuracy of his messages. Spirit Messenger is Gordon's first book, originally published in 2004, and in it he describes the development of his mediumistic skills and the training that he undertook to develop his extraordinary gifts. Since its publication, many people have asked Gordon for advice on how to develop their own psychic and mediumistic ability, and so he has added teaching, tips and practical exercises. Gordon tells you how to: recognize psychic abilities in children and remember your own psychic childhood experiences understand the difference between psychic awareness and tuning in to the spirit world develop your ability to hear messages from spirit learn the difference between your imagination and a true message.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    The revised edition is updated with a greater focus on digital recording techniques, the most powerful tools available to the home recordist. There are chapters devoted to instrument recording, humanizing drum patterns, mixing with plug-ins and virtual consoles, and a new section on using digital audio skills. And since, many true "Guerrillas" still record to analog tape, we have retained the best of that world. This edition features many more graphics than in the original edition, further enforcing Guerrilla Home Recording's reputation as the most readable, user-frienly recording title on the market.

    Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility.In Visions of Infinity, celebrated mathematician Ian Stewart provides a fascinating overview of the most formidable problems mathematicians have vanquished, and those that vex them still. He explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. The three-century effort to prove Fermat's last theorem—first posited in 1630, and finally solved by Andrew Wiles in 1995—led to the creation of algebraic number theory and complex analysis. The Poincaré conjecture, which was cracked in 2002 by the eccentric genius Grigori Perelman, has become fundamental to mathematicians' understanding of three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which Stewart refers to as the “Holy Grail of pure mathematics,” and the P/NP problem, which straddles mathematics and computer science, could easily remain unproved for another hundred years.An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematicians the world over are rising to the challenges set by their predecessors—and how the enigmas of the past inevitably surrender to the powerful techniques of the present.

    The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    1986 BILL JAMES SOFTCOVER

    A reference book that reads like a magazine, the Almanac contains “everything under the Sun, including the Moon”—facts, feature articles, and advice that are “useful, with a pleasant degree of humor.”   The 2013 edition, which marks the publication’s 221st anniversary, will feature     • weather predictions for every day and climatic trends for each season, plus hints of how a low sunspot cycle could influence conditions in the coming years     • the most accurate astronomical data in the solar system, with best-viewing recommendations for every month     • safe and easy home remedies for each season’s most common—and uncomfortable—aches and ailments     • fail-safe gardening tips to ensure a hefty harvest, ideas for using vegetable plants as ornamentals, plus gardening by the Moon     • delicious recipes for homebaked cakes, cookies, and pies; plus readers’ best bacon dishes     • amusing and enlightening articles on raising children, kisses, and why pets bite (and how to stop them)and much, much more!   Added value this year:     • 80 full-color pages     • full-color national weather maps of winter and summer forecasts