It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    

    The Times called it elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer praised it as absolutely scintillating. In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the Republic of Numbers, where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. Less than All, wrote William Blake, cannot satisfy Man. The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

     Buddhism is an agnostic religion. It neither acknowledges the existence of a god nor denies it. It simply teaches that we must live by a moral code because it is our nature to do so, regardless of whether a god exists or not. To choose good in the hopes of reward, while avoiding evil out of fear of punishment, is not true goodness. It is sheer hypocrisy — a selfish desire to do something in return for our own benefit. To understand the Four Noble Truths and the Eightfold Path, we first have to understand the word “dukkha.” This is often mistranslated into English as “suffering,” giving people the idea that Buddhism is a pessimistic religion. Nothing can possibly be further from the truth. While dukkha can certainly be understood to mean “suffering,” it would be more accurate to translate this word as “anxiety,” “stress,” or “dissatisfaction.” This book endeavors to explain the Buddha’s perspective on dukkha, and how one can live in spite of it, even striving to move beyond it. If you’re ready to learn more about dukkha and the path to liberation, let’s get started! Here Is A Preview Of What You'll Learn... About Buddhist Diversity Understanding Dukkha The Four Noble Truths The Eightfold Path Panna – Wisdom Śila – Ethical Conduct Samādhi – Concentration Nibbāna – Blown Out Much, much more! Download your copy today! Tags: eight-fold path, nirvana, the four noble truths and the eightfold path, four noble truths and eightfold path, buddhism, buddhist, theraveda buddhism, Eightfold Path, four noble truths, nibbana, eightfold path of buddhism, the eightfold path, noble eightfold path, eight fold path

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Over the next ten years the “Strange” books sold over 6,000,000 copies worldwide. Strange True Encounters & Unearthly Experiences is the first new book in the series in over three decades, and features: Robert M. Schoch, Ph.D. in Geology and Geophysics at Yale University on discoveries at Anatolia‘s Gobekli Tepe suggesting civilization is far older than previously believed. Gregory Sams on unfolding evidence that stars may be conscious. Janet Brennan on Europe’s mysterious Black Madonna statues. Martin Cadin, ex-member Federal Aviation Administration, on his personal experiments using telekinesis. Michio Kaku, Professor of Theoretical Physics at the City University of New York, on our ten-dimensional universe and paranormal phenomenon. Journalist Chris Friar on 19th century UFO sightings proving they are not a modern phenomenon. Actor Anthony Quinn on the “profound mystical experience” in the Sinai Desert that changed his life. Plus over a dozen other accounts, investigation and in-depth reports on the Ouija board, remote viewing, poltergeists, Kansas’ sacred sites, the U.S. warship that was saved by an angel, and much more. We believe this brand new entry in the “Strange” series – is in every way the equal of its predecessors. And will prove every bit as entertaining and enlightening as the earlier books did. (Asked where he got the ideas for his stories, Steven King credited FATE. “My mother used to read me FATE Magazine, which was about the paranormal, flying saucers…all that stuff. I was fascinated.”) Here is what Amazon readers have to say about classic reprints from FATE: “A book worth reading. I look forward to reading the other books in this series.” “FATE always comes through.” “Well written, short articles on a variety of paranormal events, many of which were unfamiliar to me. Interesting, unfamiliar and competently edited.” “Good stuff. Reminds us that stories like this have been happening for years. Not just a modern invention. Worth a read.” “Very good read. 5 stars.”

    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.

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    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.

    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.

    Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further."

    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.