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 malicious online rumor costs a company millions. A political sideshow derails the national news cycle and destroys a candidate. Some product or celebrity zooms from total obscurity to viral sensation. What you don't know is that someone is responsible for all this. Usually, someone like me.I'm a media manipulator. In a world where blogs control and distort the news, my job is to control blogs--as much as any one person can. In today's culture... 1) Blogs like "Gawker," "Buzzfeed" and the "Huffington Post" drive the media agenda. 2) Bloggers are slaves to money, technology, and deadlines. 3) Manipulators wield these levers to shape everything you read, see and watch--online and off.Why am I giving away these secrets? Because I'm tired of a world where blogs take indirect bribes, marketers help write the news, reckless journalists spread lies, and no one is accountable for any of it. I'm pulling back the curtain because I don't want anyone else to get blindsided. I'm going to explain exactly how the media "really" works. What you choose to do with this information is up to you.

    But as scientists break open the mind’s black box with the latest tools of neuroscience, they’re discovering that this is not how the mind works. Our best decisions are a finely tuned blend of both feeling and reason—and the precise mix depends on the situation. When buying a house, for example, it’s best to let our unconscious mull over the many variables. But when we’re picking a stock, intuition often leads us astray. The trick is to determine when to use the different parts of the brain, and to do this, we need to think harder (and smarter) about how we think.Jonah Lehrer arms us with the tools we need, drawing on cutting-edge research as well as the real-world experiences of a wide range of “deciders”—from airplane pilots and hedge fund investors to serial killers and poker players.Lehrer shows how people are taking advantage of the new science to make better television shows, win more football games, and improve military intelligence. His goal is to answer two questions that are of interest to just about anyone, from CEOs to firefighters: How does the human mind make decisions? And how can we make those decisions better?

    Our intellectual capacity, our introversion or extraversion, our vulnerability to mental illness, even whether we are a morning person - all of these aspects of our personality are profoundly shaped by our inherited DNA differences.In Blueprint, Robert Plomin, a pioneer in the field of behavioural genetics, draws on a lifetime's worth of research to make the case that DNA is the most important factor shaping who we are. Our families, schools and the environment around us are important, but they are not as influential as our genes. This is why, he argues, teachers and parents should accept children for who they are, rather than trying to mould them in certain directions. Even the environments we choose and the signal events that impact our lives, from divorce to addiction, are influenced by our genetic predispositions. Now, thanks to the DNA revolution, it is becoming possible to predict who we will become, at birth, from our DNA alone. As Plomin shows us, these developments have sweeping implications for how we think about parenting, education, and social mobility.A game-changing book by a leader in the field, Blueprint shows how the DNA present in the single cell with which we all begin our lives can impact our behaviour as adults.

    This is not a "how-to" book in any sense. Korn wants to get at the why of craft, in particular, and at the satisfactions of creative work, in general to understand their essential nature. How does the making of objects both reflect and refine our own identities? What is it about craft and creative work that makes them so rewarding? What is the nature of those rewards? How do the products of creative work inform society?

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.