This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

    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.

    Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves – or discover for the first time – that maths is relevant to almost everything we do.Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

    Amazingly, the story unveiled in it is true.In the world of math, the Poincaré Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize.George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincaré formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincaré sought to solve.In fact, Poincaré thought he had solved it back at the turn of the twentieth century, but soon realized his mistake. After four more years' work, he gave up. Across the generations from China to Texas, great minds stalked the solution in the wilds of higher dimensions. Among them was Grigory Perelman, a mysterious Russian who seems to have stepped out of a Dostoyevsky novel. Living in near poverty with his mother, he has refused all prizes and academic appointments, and rarely talks to anyone, including fellow mathematicians. It seemed he had lost the race in 2002, when the conjecture was widely but, again, falsely reported as solved. A year later, Perelman dropped three papers onto the Internet that not only proved the Poincaré Conjecture but enlightened the universe of higher dimensions, solving an array of even more mind-bending math with implications that will take an age to unravel. After years of review, his proof has just won him a Fields Medal--the 'Nobel of math'--awarded only once every four years. With no interest in fame, he refused to attend the ceremony, did not accept the medal, and stayed home to watch television.Perelman is a St. Petersburg hero, devoted to an ascetic life of the mind. The story of the enigma in the shape of space that he cracked is part history, part math, and a fascinating tale of the most abstract kind of creativity.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    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.

    Employing an irresistible cast of dragon-riding Vikings, lizard-throwing giants, and feuding aliens, the renowned illustrator Grady Klein and the award-winning statistician Alan Dabney teach you how to collect reliable data, make confident statements based on limited information, and judge the usefulness of polls and the other numbers that you're bombarded with every day. If you want to go beyond the basics, they've created the ultimate resource: "The Math Cave," where they reveal the more advanced formulas and concepts.Timely, authoritative, and hilarious, The Cartoon Introduction to Statistics is an essential guide for anyone who wants to better navigate our data-driven world.

    Provides a review of introductory noncalculus-based physics for those who do not have a strong background in mathematics.

    Our inaugural effort is OpenIntro Statistics. Probability is optional, inference is key, and we feature real data whenever possible. Files for the entire book are freely available at openintro.org, and anybody can purchase a paperback copy from amazon.com for under $10.The future for OpenIntro depends on the involvement and enthusiasm of our community. Visit our website, openintro.org. We provide free course management tools, including an online question bank, utilities for creating course quizzes, and many other helpful resources.CERTAIN CONTENT THAT APPEARS ON THIS SITE COMES FROM AMAZON SERVICES LLC. THIS CONTENT IS PROVIDED ‘AS IS’ AND IS SUBJECT TO CHANGE OR REMOVAL AT ANY TIME.Can’t find it here? Search Amazon.com Search: All Products Apparel & AccessoriesBabyBeautyBooksCamera & PhotoCell Phones & ServiceClassical MusicComputersComputer & Video GamesDVDElectronicsGourmet FoodHome & GardenMiscellaneousHealth & Personal CareJewelry & WatchesKitchen & HousewaresMagazine SubscriptionsMusicMusical InstrumentsSoftwareSports & OutdoorsTools & HardwareToys & GamesVHS Keywords:

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    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.

    She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye.In The Manga Guide to Calculus, you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).Mr. Seki teaches Noriko how to:Use differentiation to understand a function's rate of change Apply the fundamental theorem of calculus, and grasp the relationship between a function's derivative and its integral Integrate and differentiate trigonometric and other complicated functions Use multivariate calculus and partial differentiation to deal with tricky functions Use Taylor Expansions to accurately imitate difficult functions with polynomials Whether you're struggling through a calculus course for the first time or you just need a painless refresher, you'll find what you're looking for in The Manga Guide to Calculus.This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.

    For the media, statistics are routinely 'damning', 'horrifying', or, occasionally, 'encouraging'. Yet, for all their ubiquity, most of us really don't know what to make of statistics. Exploring the history, mathematics, philosophy and practical use of statistics, Eileen Magnello - accompanied by Bill Mayblin's intelligent graphic illustration - traces the rise of statistics from the ancient Babylonians, Egyptians and Chinese, to the censuses of Romans and the Greeks, and the modern emergence of the term itself in Europe. She explores the 'vital statistics' of, in particular, William Farr, and the mathematical statistics of Karl Pearson and R.A. Fisher.She even tells how knowledge of statistics can prolong one's life, as it did for evolutionary biologist Stephen Jay Gould, given eight months to live after a cancer diagnoses in 1982 - and he lived until 2002. This title offers an enjoyable, surprise-filled tour through a subject that is both fascinating and crucial to understanding our world.