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..

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    The National Security Agency grew out of the legendary codebreaking programs of World War II that turned the tide of Allied victory by cracking the famed Enigma machine and other seemingly impenetrable German and Japanese codes. But things became murky in the postwar years, when our intelligence community found itself targeting not battlefield enemies, but suspected spies, foreign leaders, and even American citizens. Now Stephen Budiansky--a longtime expert in cryptology--tells the fascinating story of how the NSA came to be, and of its central, often fraught and controversial role in the major events of the Cold War, from the Korean War to the Cuban Missile Crisis to Vietnam and beyond. He also guides us through the fascinating challenges faced by cryptanalysts, and how they broke some of the most complicated codes of the twentieth century. A riveting, essential history of the underbelly of the Cold War.

    Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein. Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.Calculus For Dummies is intended for three groups of readers:Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:Real-world examples of calculus The two big ideas of calculus: differentiation and integration Why calculus works Pre-algebra and algebra review Common functions and their graphs Limits and continuity Integration and approximating area Sequences and series Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression.

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

    The authors include such best sellers as Malcolm Gladwell, Seymour Hersh, and Jonathan Franzen - and the subjects range from the lives of short-order cooks to the secrets of college admissions.In all, there are nine stories:ANNALS OF TECHNOLOGY"The Bakeoff" by Malcolm Gladwell: Project Delta aims to create the perfect cookie. (Originally published Sept. 5, 2005)COMMENT"Mired" by Hendrik Hertzberg: Evolution vs. creationism vs. intelligent design. (Originally published Aug. 22, 2005)ANNALS OF MEDICINE"Bloodsuckers" by John Colapinto: Leeches are good for you after all. (Originally published July 25, 2005)BOOKS"A Cloud of Dust" by John Updike: A review of E. L. Doctorow's new novel, The March. (Originally published Sept. 12, 2005)THE TALK OF THE TOWN:"Watergate Days" by Seymour Hersh: The veteran investigative reporter writes about the revelation of the identity of "Deep Throat" and his own reporting experiences. (Originally published June 13 & 20, 2005)IN THE KITCHEN"The Egg Men" by Burkhard Bilger: What it takes to be a short-order cook in Las Vegas. (Originally published Sept. 5, 2005)A CRITIC AT LARGE"Getting In" by Malcolm Gladwell: The social logic of Ivy League admissions. (Originally published Oct. 10, 2005)ANNALS OF ADOLESCENCE"The Retreat" by Jonathan Franzen: Memories of a church youth group. (Originally published June 6, 2005)POP MUSIC"The Gift and the Curse" by Sasha Frere-Jones: The "vexing brilliance" of Jack White and the latest release by The White Stripes. (Originally published June 13 & 20, 2005)The articles in this collection were selected by Audible in cooperation with the editorial staff of The New Yorker. Narration by William Dufris, Todd Mundt, and Christine Marshall.(P) and ©2005 The New YorkerListening Length: 4 hours and 32 minutes

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    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.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    He was the undisputed finest high school player in America. He was the one NBA scouts drooled over, corporations dreamed of, event promoters begged for, and now fans clamor after. Never before had a high school basketball player been so highly touted or an eighteen-year-old athlete been the subject of such fascination. Maybe no basketball player in the world has had that level of attention.Now with the Cleveland Cavaliers, LeBron has become a certified NBA all-star. Love him or hate him, there is no denying that LeBron James is a force on the basketball court, and his rags to riches story is the stuff that dreams are made of.Ryan Jones has updated his smash hit book King James to incorporate everything that is LeBron: the controversy, the star power, the shoes, the cars, the hobnobbing with the world's most famous celebrities, and, of course, the game. This is a book for every fan of LeBron James and for anybody interested in reading about an NBA legend in the making.

    This proven magick works safely, without wands, herbs, incense or candles. There is no need to pay the spirits, and there is no karma or spiritual backlash. You get what you deserve, you get it fast and you get to spend it any way you want. Where the Magickal Cashbook gave just one method for attracting a small burst of money, and Wealth Magick worked on long-term career enhancement, Magickal Riches contains practical rituals that continually manifest money. Developed from ancient knowledge and modern occult technology, the major workings in this book have never been published before, in any form. The secrets of Magickal Riches have been crafted by The Gallery of Magick during the past thirty years. You will discover: *The Master Money Ritual, using a sigil that contains a pattern of magickal symbols. *How to find your Secret Source of Money, to provide new streams of unexpected income. *A Ritual To Increase Sales, for anybody who sells a product of any kind. *A Ritual For Buying and Selling that ensures that you get the best deal when you are buying or selling anything, from a small item to a house or business. *A ritual to Get Somebody To Pay Up. When you are owed money, use magick to get what belongs to you. *The Genius Rituals, with a set of unique sigils to call on intelligent and helpful spirits. *A ritual to Attract Money Through Perception, for trading shares, or to find out the best course of action in any money-making situation. *The Chance Money Attraction ritual, employing the power of Nitika in harmony with other genius spirits, to bring money out of the blue. *The Gambling Ritual, to increase your luck in lotteries and games of chance. *A secret technique, never revealed until now, for adding extra energy to your magickal workings. Damon Brand says, 'Creating money with magick is one of the most direct and exciting ways to experience the raw power of the occult.' If you are completely new to magick, be assured that this magick is safe and effective. It will work whether you believe in it or not. If you are an experienced occultist, you will discover many new secrets for manifesting money. This exceptional work gives you all the knowledge, techniques, images and secret words that you need to unleash a flow of riches into your life.

     So why can it be so hard to achieve the results we crave? Working harder rarely has the desired effect. The answer is to work smarter, and with – not against – our natural strengths. Mindset with Muscle takes you on a different transformation journey. Rather than hitting the gym and obsessing about success, this book brings you ‘sets and reps for the brain’. When you read this book, and implement Jamie Alderton’s proven strategies, you will be able to: Develop your brain and build new habits that hard-wire you for success Map out exactly what you need to do in order to achieve your physical, business and financial goals Move forward confidently and take action to build the business, body and lifestyle of your dreams Finally get in the best physical and mental shape of your life Know with certainty you can achieve whatever it is you set out to do Mindset with Muscle urges you to wake up and realise you have the choice in life to achieve pretty much anything you set your mind to.

    It's a great project for families and foodies alike, and all you need to start off is this book, a specialist mushroom growing kit, and a small space in which to grow them!In this book I aim to teach you the basics that you need to know to grow mushrooms at home. You'll take a step back in time and learn about the history of mushrooms as food, and why it has taken centuries for home mushroom growing to really catch on. I'll let you know exactly which are the best types of mushrooms for you to start with. If you aren't sure what tools you'll need, don't worry - this book has that covered too. And I'll explain how to make sure that your mushrooms grow quickly and pest free, and the best ways to harvest, preserve and store your crop.But where should you grow your mushrooms? That's a good question! Contained within the pages of this book are tips on how to set up a mushroom patch in your back yard, as well as how to grow them inside. Is it really better to grow them completely in the dark? You are about to find out!So, whether you like shiitakes, portobellos or oyster mushrooms, stop buying them in stores. I'll teach you how to grow your own and keep your entire family well supplied.In as little as a few weeks you can have the perfect fresh mushrooms grown and ready to eat. Yum!This easy to read, beginners book, summarizes the essential information I have learned over the years, and is written to help you decide if mycology is for you, and if so, which route to take.