It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike."A positively joyful exploration of mathematics."-Publishers Weekly, starred review"Each [trick] is more dazzling than the last."-Physics World

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader's interest. You'll find many unique features that help you grasp the material, such as worked-out examples, summary tables, thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory course

    . . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun. In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.

    Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. Among the many fascinating curiosities in these pages, you will discover the strange link between limericks and rabbits, an apparently 'fair' coin game where the odds are massively in your favour, why tourist boards can't agree on where the centre of Britain is, and how simple paper folding can lead to a Jurassic Park monster. With plenty of ideas you'll want to test out for yourself, this engaging and refreshing look at mathematics is for everyone.

    McGinnis's practical, easy-to-follow strategy offers twelve characteristics of optimists that show how they stave off disappointment and keep motivation high. Enjoy success, better health, happy relationships, and perhaps a longer life with this powerful book.

    A necessary addition to your reading." --David Maister, author of Managing the Professional Service Firm"Professional Services Marketing will certainly become the bible of the field in short order! Without a doubt, the most useful compendium of marketing insight for the practicing professional services firm executive...BRAVO!" --Leonard A. Schlesinger, President, Babson College, and coauthor of The Service Profit Chain"It's no longer sufficient to be a good 'expert for hire'--you need a brand and a powerful marketing engine behind you. Professional Services Marketing is a gold mine of research based strategies, best practices, and specific techniques that will help you consistently win in the client marketplace and outshine your competition. It's thoughtful, funny, and filled with the how-to so often missing in business books." --Andrew Sobel, coauthor of Clients for Life"Schultz and Doerr offer tactics and information in an easy-to-read, concise, and enjoyable format. Professional Services Marketing should be a required resource in every professional marketer's tool box!" --R. Granville Loar, Executive Director, Association for Accounting Marketing"This book is an excellent resource for anyone involved in professional services. It is especially timely in our current challenging economic conditions, and the ideas and guidance are relevant for the better times to come as well." --Josh Lee, Partner, Monitor Group"Smart. Practical. Comprehensive. This is the one book that won't collect dust on my shelf." --Kevin McMurdo, Chief Marketing Officer, Perkins Coie"Professional Services Marketing is the first book to directly address the challenges of the professional services marketer. This book is filled with practical wisdom and research on best practices and processes specifically for this industry. A must-read for anyone in a professional services firm!" --Paul Dunay, Global Director of Integrated Marketing, BearingPoint

    Advertising and entrepreneurial rockstar Sally Hogshead reveals 100 Radical Truths for closing the gap between your current reality and your utmost potential, including: # 15: Aspire to be the dumbest person in the room # 31: You can be comfortable, or outstanding, but not both # 67: Mistakes are tuition # 96: Expressing your truest self is the ultimate competitive advantage # 100: Make your memoirs worth reading With groundbreaking research and startling new ideas for success, Radical Careering will become the indispensable owner’s manual to your future. Get ready to turbocharge your career with smarter goals, higher market value, and killer results. "Radical Careering is a jolt to the old way of thinking about careers; a handbook of new thinking that will help you survive, strive and thrive in the radically new world of work." --Jeff Taylor, founder and Chief Monster, Monster.com “An innovative how-to-manual for anyone wanting to be more successful and satisfied in their career.” --Andy Spade, CEO and co-founder, Kate Spade “Take inventory of your strengths, identify your passions, then do everything in your power to carve your career toward them. Only then will you, and everyone else, see the best of you. Want to know how? Read this book.” -- Marcus Buckingham, author of The One Thing You Need to Know, and Now, Discover Your Strengths “Hogshead’s powerful strategies will teach you how to drive your own success, by having the fearlessness, daily courage, and curiosity to jump in the deep end and swim with real purpose.” --Lee Ann Daly, Executive VP of Marketing, ESPN “This book is so genius. It’s amazing to read on the page what I’ve always believed to be true. The ideas in this book will save your ass again and again. Drive is a radical careerist’s best friend.” --Liz Phair

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.