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.

    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.

    A biography of Brazilian soccer player Kaká detailing his life and career.

         Taoism isn’t a spiritual extracurricular activity, it’s an integral practice for living all of  life to the fullest.  The modern Taoist adept Eva Wong is your guide to living well according to the wisdom of this ancient system.  She uses the ancient texts to demonstrate the Taoist masters’ approach to the traditional four aspects of life--the public, the domestic, the private, and the spiritual—and shows how learning to balance them is the secret to  infusing your life with health, harmony, and deep satisfaction.​

    In this entertaining and ingenious book, Blastland reveals how in our quest to make the world more understandable, we lose sight of how unexplainable it often is. The result - from GDP figures to medicine - is that experts know a lot less than they think. Filled with compelling stories from economics, genetics, business, and science, The Hidden Half is a warning that an explanation which works in one arena may not work in another. Entertaining and provocative, it will change how you view the world.

    Get this Amazing #1 Amazon Top Release - Great Deal! You can read on your PC, Mac, smartphone, tablet or Kindle device. Bitcoin is not just a new word in the Internet age or technological and financial progress, it's a start of a new era on the Earth! Even 10 years ago we even couldn't imagine dreaming about digital money - you can't physically touch them but you can own and spend them. Today this is a reality! Bitcoin revolution covered the whole world like a huge wave, more and more people interested in this "Digital Gold". Over the past few years, Bitcoin has grown from something known only to a select few tech nerds into a revolutionary currency that has rapidly changed the way that we think about the concept of money. You no doubt see Bitcoin payments accepted in all kinds of places now, but, if you can believe it, it used to be a fairly complicated procedure for finding places that let you pay in Bitcoin. Anyway, to run the world you need to know everything. We can't guarantee that you will know EVERYTHING from this book, but we can guarantee you will have the notion of a new currency - Bitcoin. What is it? Where did it come from? How do you use it? Is it really just fake internet money created by drug dealers? That is precisely what we will be answering in this book. We’ll cover everything you need to know in order to get started with Bitcoin: understanding the Blockchain and Bitcoin transactions where to keep your Bitcoin (how to choose a secure wallet) buying Bitcoin investing in Bitcoin how to start accepting and using Bitcoin as a part of your business principles of Bitcoin mining the security of Bitcoin etc. Also, the author will share with you interesting facts about Bitcoin and will give you professional tips on the start of your way in Bitcoin family! Ready to take on the Bitcoin world yet? I hope so. I’d like to be the first to officially welcome you to the world of Bitcoin!

    40 illustrations throughout.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    Most of us have unfinished business that might make us feel like we walk around dragging a heavy ball with a chain connected to our ankle. When you declutter and possibly downsize, you can free yourself of weighty matters that tie you down physically, mentally, emotionally, and spiritually.Lighter Living explains why you might want to simplify your home and your life. It shows you how to declutter and then organize what you keep. Finally, you are given a vision for lifelong decluttering and how it can lead to well-being and peace of mind.