Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.

    A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text.

    G.H. Hardy - eccentric, charismatic and considered the greatest British mathematician of his age - receives a mysterious envelope covered with Indian stamps. Inside he finds a rambling letter from a self-professed mathematical genius who claims to be on the brink of solving the most important mathematical problem of his time. Hardy determines to learn more about this mysterious Indian clerk, Srinivasa Ramanujan, a decision that will profoundly affect not only his own life, and that of his friends, but the entire history of mathematics. Set against the backdrop of the First World War, and populated with such luminaries as D.H. Lawrence and Bertrand Russell, "The Indian Clerk" fashions from this fascinating period an utterly compelling story about our need to find order in the world.

    For all ages and all levels of difficulty, these puzzles range from those that can be solved in minutes to those that will beguile for hours.

    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.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone--from those who fumble over fractions to those who solve complex equations in their heads--winds up marveling at what numbers can do.Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach them.

    Rare Book

    . . in which Sydney Padua transforms one of the most compelling scientific collaborations into a hilarious series of adventures. Meet Victorian London’s most dynamic duo: Charles Babbage, the unrealized inventor of the computer, and his accomplice, Ada, Countess of Lovelace, the peculiar protoprogrammer and daughter of Lord Byron. When Lovelace translated a description of Babbage’s plans for an enormous mechanical calculating machine in 1842, she added annotations three times longer than the original work. Her footnotes contained the first appearance of the general computing theory, a hundred years before an actual computer was built. Sadly, Lovelace died of cancer a decade after publishing the paper, and Babbage never built any of his machines. But do not despair! The Thrilling Adventures of Lovelace and Babbage presents a rollicking alternate reality in which Lovelace and Babbage do build the Difference Engine and then use it to build runaway economic models, battle the scourge of spelling errors, explore the wilder realms of mathematics, and, of course, fight crime—for the sake of both London and science. Complete with extensive footnotes that rival those penned by Lovelace herself, historical curiosities, and never-before-seen diagrams of Babbage’s mechanical, steam-powered computer, The Thrilling Adventures of Lovelace and Babbage is wonderfully whimsical, utterly unusual, and, above all, entirely irresistible.(With black-and-white illustrations throughout.)

    He was brought up in India in the apparently vigorous but dying Raj and was sent by his family in the 1930s to Berlin -- though he could not speak a word of German -- to study medicine and dentistry. It was here, before he migrated to Britain, that Shanti's path first crossed that of his future wife. Helga Gerda Caro, known to everyone as "Henny" was also born in 1908, in Berlin, to a Jewish family -- cultured, patriotic, and intensely German. When the family decided to take Shanti as a lodger, Henny's first reaction was, "Don't take the black man!" But a friendship flowered, and when Henny fled Hitler's Germany for England just one month before war broke out, she was met at Victoria Station by the only person in the country she knew: Shanti. Vikram Seth has woven together their astonishing story, which recounts the arrival into this childless couple's lives of their great-nephew from India -- the teenage student Vikram Seth. The result is an extraordinary tapestry of India, the Third Reich and the Second World War, Auschwitz and the Holocaust, Israel and Palestine, postwar Germany and 1970s Britain. Two Lives is both a history of a violent century seen through the eyes of two survivors and an intimate portrait of their friendship, marriage, and abiding yet complex love. Part biography, part memoir, part meditation on our times, this is the true tale of two remarkable lives -- a masterful telling from one of our greatest living writers.

    No cloistered don, this tall, married Englishman was a freethinking intellectual. A nudist, he was devoted to quirky folk dancing. In 1937, while working as a biochemist at Cambridge, he fell in love with a visiting Chinese student, with whom he began a lifelong affair. His mistress persuaded him to travel to her home country, where he embarked on a series of expeditions to the frontiers of the ancient empire. He searched for evidence to bolster a conviction that the Chinese were responsible for hundreds of humankind's most familiar innovations—including printing, the compass, explosives, suspension bridges, even toilet paper—often centuries before others. His journeys took him across war-torn China, consolidating his admiration for the Chinese. After the war, he determined to announce what he'd discovered & began writing Science & Civilization in China, describing the country's long history of invention & technology. By the time he died, he'd produced, almost single-handedly, 17 volumes, making him the greatest one-man encyclopedist ever. Epic & intimate, The Man Who Loved China tells the sweeping story of China thru Needham's life. Here's a tale of what makes men, nations & humankind great—related by one of the world's best storytellers.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    One year later, a struggling writer named Edgar Allan Poe decided to take on the case-and sent his fictional detective, C. Auguste Dupin, to solve the baffling murder of Mary Rogers in "The Mystery of Marie Rog�t."

    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.

    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.