In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    The author defines all terms, points out potential pitfalls in algebraic calculation, and makes problem solving a fun activity. New in this edition are painless approaches to understanding and graphing linear equations, solving systems of linear inequalities, and graphing quadratic equations. Barron’s popular Painless Series of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transforming details that might once have seemed boring or difficult into a series of interesting and mentally challenging ideas. Most titles in the series feature many fun-to-solve “Brain Tickler” problems with answers at the end of each chapter.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    In The Perfect Bet, mathematician and award-winning writer Adam Kucharski tells the astonishing story of how the experts have succeeded, revolutionizing mathematics and science in the process. The house can seem unbeatable. Kucharski shows us just why it isn't. Even better, he demonstrates how the search for the perfect bet has been crucial for the scientific pursuit of a better world.

    Make the bet more attractive for them: the game could have 10 or 20 rounds, and you’ll give them the privilege of starting first in every s-i-n-g-l-e round. “Piece of cake!” they will think and they will take the bet. Only to discover in despair, 10 or 20 rounds later, that it is impossible to beat you, even once. This book reveals a simple system that will help you never lose a single game from the moment you learn them. Let us repeat that.After reading this book and for the rest of your life, you will never, ever lose a game of Tic-Tac-Toe again! How is it possible never to lose in Tic-Tac-Toe? Tic-Tac-Toe is a “solved” game, meaning that there are mathematically proven strategies to defend yourself against losing. If you play with these optimal strategies in mind, you may win and you can’t lose. If your opponent also plays with the optimal strategies in mind, neither will win, and the game will always end in a draw.However, very few people really know these strategies.This book reveals an easy system of only 8 strategies that will make you a Tic-Tac-Toe Master. If you learn and start applying these 8 strategies, we guarantee that you will never lose a game of Tic-Tac-Toe again. Is it easy to learn these strategies? Very easy! These 8 strategies are presented in 8 mini chapters, with illustrations and step-by-step explanations. Even a kid can read this book and learn the strategies!In just 1 hour you will have learnt all 8 strategies and you will be ready to start applying them. Will I have to think too hard to apply these strategies? As a matter of fact, all you have to do is to memorize our simple system. As soon as you learn this system, every game will be a no-brainer for you. Our system tells you exactly how to play or how to respond to your opponent’s move. Simple as A-B-C.For example, if your opponent plays first and chooses a corner, our system tells you exactly how to respond in order to eliminate any chance of losing the game. Is this for real? Do you guarantee that I will never lose a TTT game again? YES!!! We challenge you to read this book and then immediately start playing Tic-Tac-Toe online, against a computer, applying everything you have learnt. You will discover that even a computer can’t beat you.Your new super powers in Tic-Tac-Toe will blow your mind! Start right now! Buy the book, learn the strategies and NEVER lose a Tic-Tac-Toe game again from that moment and for the rest of your life!Scroll to the top of the page and click the BUY WITH 1-CLICK Button!

    Cosmic Universe and Human History, microcosm and macrocosm, inorganic and living matter coexist and form a unique unity manifested in multiple forms. The Physical and the Mental constitute the form and the content of the World. The world does not consist of subjects and objects, the “subject” and the “object” are metaphysical abstractions of the single and indivisible Wholeness. Man’s finite knowledge separates the Whole into parts and studies fragmentarily the beings. The Wholeness is manifested in multiple forms and each form encapsulates the Wholeness. The rational explanation of the excerpts and the intuitive apprehension of the Wholeness are required to combine and create the open thought and the holistic knowledge. This means that the measurement should be defined by the ''measure'', but the responsibility for determining the ''measure'' depends on the man. This requires that man overcomes the anthropocentric arrogance and the narcissistic selfishness and he joins the Cosmic World in a friendly and creative manner.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    Comprehensive in scope and contemporary in coverage, this text introduces basic electronic and data communications fundamentals and explores their application.

    Luckily, algebra will help you solve each problem. By using simple addition, subtraction, mulitplication, and division, you'll discover that solving math mysteries isn't scary at all -- it's fun!

    Puzzlists need only an elementary knowledge of math and a will to resist looking up the answer before trying to solve a problem.Written in a light and witty style, Entertaining Mathematical Puzzles is a mixture of old and new riddles, grouped into sections that cover a variety of mathematical topics: money, speed, plane and solid geometry, probability, topology, tricky puzzles, and more. The probability section, for example, points out that everything we do, everything that happens around us, obeys the laws of probability; geometry puzzles test our ability to think pictorially and often, in more than one dimension; while topology, among the "youngest and rowdiest branches of modern geometry," offers a glimpse into a strange dimension where properties remain unchanged, no matter how a figure is twisted, stretched, or compressed.Clear and concise comments at the beginning of each section explain the nature and importance of the math needed to solve each puzzle. A carefully explained solution follows each problem. In many cases, all that is needed to solve a puzzle is the ability to think logically and clearly, to be "on the alert for surprising, off-beat angles...that strange hidden factor that everyone else had overlooked."Fully illustrated, this engaging collection will appeal to parents and children, amateur mathematicians, scientists, and students alike, and may, as the author writes, make the reader "want to study the subject in earnest" and explains "some of the inviting paths that wind away from the problems into lusher areas of the mathematical jungle." 65 black-and-white illustrations.

    Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions.

    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.

    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    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.

    Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.