It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    In addition to the language skills of listening, speaking, reading, and writing, it covers the basics of English grammer. It also includes key topics such as technical reports, business correspondence, group discussions, interviews, and presentation strategies. With its up-to-date coverage and practical orientation, the book would prove to be an extremely useful text for students, while also serving as a ready reference for day-to-day communication.

    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.

    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.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    Have you ever opened a Kindle book to find that the font started out way too small or way too large? Have you tried to change to a different font while reading and discovered you couldn't? Have you jumped to a new chapter in a Kindle book and seen that the chapter heading lost its formatting? Has a Kindle completely ignored formatting you knew was in the book? According to Amazon, the simplest way to publish your Kindle book is to upload an HTML file you've saved from Microsoft Word or another app. By itself, that method can bring you maybe 80% of the way to a well-formatted, trouble-free ebook. But what about the other 20%? In this follow-up to his bestselling -From Word to Kindle, - Aaron Shepard takes your saved HTML as a starting point and tells how to quickly tweak and tune it to avoid common problems. Assuming no knowledge of HTML, he introduces the basics of the language, then reveals how to use find-and-replace and macros to touch up an entire book in seconds! If you're serious about Kindle publishing and you're technically inclined -- but not a full-fledged geek -- Aaron provides the tips you need to bring your Kindle book to the next level, making it something truly to be proud of. ///////////////////////////////////////////////// Aaron Shepard is a foremost proponent of the new business of profitable self publishing, which he has practiced and helped develop since 1998. He is the author of -Aiming at Amazon, - -POD for Profit, - -Perfect Pages, - and Amazon's #1 and #2 bestselling paid books on Kindle formatting, -From Word to Kindle- and -Pictures on Kindle.- ///////////////////////////////////////////////// CONTENTS Getting Started 1 WORKING WITH HTML HTML and Kindle HTML Export HTML Editing HTML Processing HTML Basics HTML Checking HTML Cleanup HTML Testing 2 HTML FIXES Fixes for Fonts Fixes for Paragraphs Fixes for Headings Fixes for Line Breaking Fixes for Pictures Fixes for Navigation ///////////////////////////////////////////////// SAMPLE Here are some of the things you can accomplish through changes in HTML. * Adjust bookmarks so headings retain proper formatting when jumped to. * Remove settings that stop the user from choosing their own. * Keep fonts from appearing much too small or much too large when the book is opened. * Make sure indents and other spacing stays relative to larger and smaller font sizes. * Avoid line breaks that leave short words dangling at the ends of lines or paragraphs. * Make up for features lost in translation from your word processor, like nonbreaking hyphens. * Stop -ghost hyphens- from appearing in the middle of words. * Keep pages of text from disappearing for some users. * Prevent the Kindle from applying its own defaults in place of your settings.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    

    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.

    Their goal: create a computer animated feature, despite predictions that it could never be done. An unprecedented catalog of blockbuster films later, the studio is honoring its history in this deluxe volume. From its fledgling days under George Lucas to ten demanding years creating Toy Story to the merger with Disney, each milestone is vibrantly detailed. Interviews with Pixar directors, producers, animators, voice talent, and industry insiders, as well as concept art, storyboards, and snapshots illuminate a history that is both definitive and enthralling.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular “Good Math” blog, you’ll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark’s book will both entertain and enlighten you.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    Most know Richard Feynman for the hilarious anecdotes and exploits in his best-selling books Surely You're Joking, Mr. Feynman! and What DoYou Care What Other People Think? But not always obvious in those stories was his brilliance as a pure scientist—one of the century's greatest physicists. With this book and CD, we hear the voice of the great Feynman in all his ingenuity, insight, and acumen for argument. This breathtaking lecture—"The Motion of the Planets Around the Sun"—uses nothing more advanced than high-school geometry to explain why the planets orbit the sun elliptically rather than in perfect circles, and conclusively demonstrates the astonishing fact that has mystified and intrigued thinkers since Newton: Nature obeys mathematics. David and Judith Goodstein give us a beautifully written short memoir of life with Feynman, provide meticulous commentary on the lecture itself, and relate the exciting story of their effort to chase down one of Feynman's most original and scintillating lectures.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.