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.

    Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.

    From the sudden expansion of a cloud of gas to the cooling of hot metal--everything is moved or restrained by four simple laws. Written by Peter Atkins, one of the world's leading authorities on thermodynamics, this powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth (so named because the first two laws were well established before scientists realized that a third law, relating to temperature, should precede them--hence the jocular name zeroth), and proceeds through the First, Second, and Third Laws, offering a clear account of concepts such as the availability of work and the conservation of energy. Atkins ranges from the fascinating theory of entropy (revealing how its unstoppable rise constitutes the engine of the universe), through the concept of free energy, and to the brink, and then beyond the brink, of absolute zero. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Konrad Lorenz was gifted with a similar power of understanding the animal world. He was that rare beast, a brilliant scientist who could write (and indeed draw) beautifully. He did more than any other person to establish and popularize the study of how animals behave, receiving a Nobel Prize for his work. King Solomon's Ring, the book which brought him worldwide recognition, is a delightful treasury of observations and insights into the lives of all sorts of creatures, from jackdaws and water-shrews to dogs, cats and even wolves. Charmingly illustrated by Lorenz himself, this book is a wonderfully written introduction to the world of our furred and feathered friends, a world which often provides an uncanny resemblance to our own. A must for any animal-lover!

    This title is intended for those who might enjoy an engaging dialogue on abstract mathematical ideas, and those who might wish to experience how new mathematics is created.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Like artists and poets, they are free spirits who resist the restrictions their cultures impose on them. In their pursuit of Nature’s truths, they are guided as much by imagination as by reason, and their greatest theories have the uniqueness and beauty of great works of art.Dyson argues that the best way to understand science is by understanding those who practice it. He tells stories of scientists at work, ranging from Isaac Newton’s absorption in physics, alchemy, theology, and politics, to Ernest Rutherford’s discovery of the structure of the atom, to Albert Einstein’s stubborn hostility to the idea of black holes. His descriptions of brilliant physicists like Edward Teller and Richard Feynman are enlivened by his own reminiscences of them. He looks with a skeptical eye at fashionable scientific fads and fantasies, and speculates on the future of climate prediction, genetic engineering, the colonization of space, and the possibility that paranormal phenomena may exist yet not be scientifically verifiable.Dyson also looks beyond particular scientific questions to reflect on broader philosophical issues, such as the limits of reductionism, the morality of strategic bombing and nuclear weapons, the preservation of the environment, and the relationship between science and religion. These essays, by a distinguished physicist who is also a lovely writer, offer informed insights into the history of science and fresh perspectives on contentious current debates about science, ethics, and faith.

    Why is glass see-through? What makes elastic stretchy? Why does a paper clip bend? Why does any material look and behave the way it does? These are the sorts of questions that Mark Miodownik a globally-renowned materials scientist has spent his life exploring In this book he examines the materials he encounters in a typical morning, from the steel in his razor and the graphite in his pencil to the foam in his sneakers and the concrete in a nearby skyscraper.

    Evo Devo Evolutionary Developmental Biology is the new science that has finally cracked open the box. Within the pages of his rich and riveting book, Sean B. Carroll explains how we are discovering that complex life is ironically much simpler than anyone ever expected.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.