美國排名第一
紐約大學數學科學研究所
創辦人瑞赫德．庫蘭特送給高等數學人才
一本從代數到微積分的系統性數學學習書
1941年出版至今，仍在Amazon.com獲得4.5顆星好評
．作者庫蘭特教授創辦的紐約大學數學研究所（Courant Institute of Mathematical Sciences）今年再度獲得US News選為排名第一位的應用數學類研究所。
．至今仍在亞馬遜網路書店獲得4.5顆星好評
《數學是什麼？》(What is Mathematics?) 是一本為初學者和學者、學生和老師、哲學家，和工程師而寫的數學名著。自1941年出版以來就得到包括愛因斯坦、赫曼．外爾 (Herman Weyl) 等一代科學大師在內的一致推崇。兩位原作者如今都已辭世，不過後繼有人。1996年在著名數學家伊恩．史都華手中把原著中多個相關的數學主題帶到切合當前的發展水平，因而有現在的第二版。通過平易近人，引人入勝的描述，這部閃爍出兩代作者才華的鉅著，把「反映出人類積極的意志，深思熟慮的推理，以及在美學上盡善盡美的祈求」的數學世界，栩栩如生地呈現在我們眼前。《數學是什麼？》文情並茂地給我們報導了一個非凡的故事，為我們對數學的瞭解打開了一扇窗。

Explores one of the most important concepts in mathematics and science
Examines the role of symmetry in mathematics, physics, chemistry, and biology
Considers the scientific applications of symmetry
Part of the bestselling Very Short Introductions series
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature.
It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory.
Readership: Students of mathematics, physics, and chemistry, as well as general readers interested in symmetry.

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover how infinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.

"You believe in a God who plays dice, and I in complete law and order." Albert Einstein The science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner. Perhaps God plays dice within a cosmic game of complete law and order. Does God Play Dice? reveals a strange universe in which nothing may be as it seems. Familiar geometrical shapes such as circles and ellipses give way to infinitely complex structures known as fractals, the fluttering of a butterfly's wings can change the weather, and the gravitational attraction of a creature in a distant galaxy can change the fate of the solar system.
This revised and updated edition includes three chapters on the prediction and control of chaotic systems. New information regarding the solar system and an account of complexity theory is also incorporated. It is a lucid and witty book which makes the complex mathematics of chaos accessible and entertaining.

An eminent teacher and writer explores an idea both simple and complex, both multidisciplinary and unifying--the story of symmetry.
At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry.
In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published.
Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions--groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe.

Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.
By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

Flatland is a unique, delightful satire that has charmed readers for over a century. Published in 1884 by the English clergyman and headmaster Edwin A. Abbott, it is the fanciful tale of A. Square, a two-dimensional being who is whisked away by a mysterious visitor to The Land of Three Dimensions, an experience that forever alters his worldview. Like the original, Ian Stewart’s commentary takes readers on a strange and wonderful journey. With clarity and wit, Stewart illuminates Abbott’s numerous Victorian references and touches on such diverse topics as ancient Babylon, Karl Marx, Mary Shelley’s Frankenstein , Mt. Everest, H.G. Wells, and phrenology. The Annotated Flatland makes fascinating connections between Flatland and Abbott’s era, resulting in a classic to rival Abbott’s own, and a book that will inspire and delight curious readers for generations to come.

The brilliant "sequel" to one of the all-time classics of popular mathematics. First there was Edwin A. Abbott's remarkable Flatland , published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth , this magnificent investigation into the nature of reality is destined to become a modern classic.

Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work.
New to the Fourth Edition
Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(√14) is Euclidean
Presents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844
Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last Theorem
Improves and updates the index, figures, bibliography, further reading list, and historical remarks
Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.

The fantastic first book in the Sunday Times bestselling Science of Discworld series When a wizardly experiment goes adrift, the wizards of Unseen University find themselves with a pocket universe on their Roundworld, where neither magic nor common sense seems to stand a chance against logic.The Universe, of course, is our own. And Roundworld is Earth. As the wizards watch their accidental creation grow, we follow the story of our universe from the primal singularity of the Big Bang to the internet and beyond.Through this original Terry Pratchett story (with intervening chapters from Cohen and Stewart) we discover how puny and insignificant individual lives are against a cosmic backdrop of creation and disaster. Yet, paradoxically, we see how the richness of a universe based on rules, has led to a complex world and at least one species that tried to get a grip of what was going on. Terry Pratchett is the acclaimed creator of the global bestselling Discworld series, the first of which, The Colour of Magic, was published in 1983. Raising Steam is his fortieth Discworld novel. His books have been widely adapted for stage and screen, and he is the winner of multiple prizes, including the Carnegie Medal, as well as being awarded a knighthood for services to literature. After falling out with his keyboard he now talks to his computer. Occasionally, these days, it answers back.www.terrypratchett.co.uk@terryandrob Professor Ian Stewart is the author of many popular science books. He is the mathematics consultant for New Scientist and a Professor of Mathematics at the University of Warwick. He was awarded the Michael Faraday Prize for furthering the public understanding of science, and in 2001 became a Fellow of the Royal Society. Dr Jack Cohen is an internationally-known reproductive biologist, and lives in Newent, Gloucestershire. Jack has a laboratory in his kitchen, helps couples get pregnant by referring them to colleagues, invents biologically realistic aliens for science fiction writers and, in his spare time, throws boomerangs. Jack, who has more letters to his name than can be repeated here, writes, lectures, talks and campaigns to promote public awareness of science, particularly biology. He is mostly retired.

Rahip, öğretmen, okul müdürü, Shakespeare ve Bacon uzmanı, dilbilim ve teoloji alanlarında ellinin üzerinde kitabın yazarı Edwin A. Abbott’ın en “tanınmış” yapıtı Düzülke Türkçede! Üstelik kısa, neşeli, bir ayağı matematiğe bir ayağı toplumsal eleştiriye basan, zamana başarıyla direnen ve bu özellikleri bir arada taşıması nedeniyle az rastlanır türden bir yapıt olan bu öncü-klasik, Ian Stewart’ın sunusu, kapsamlı açıklamaları ve kitabın sonuna eklediği “Matematikte Dördüncü Boyut” başlıklı yazısıyla zenginleşmiş olarak karşımızda: Açıklamalı Düzülke.Akıllı geometrik şekillerin, karelerin, üçgenlerin, beşgenlerin, çemberlerin yasadığı bir düzlemde geçen bir macerayı anlatan Düzülke, bilimkurgunun öncüsü yapıtlardan biri. Boyut, düzlem, uzay, çok boyutluluk gibi kavramlar üzerine zihin açıcı ve düşündürücü bir öykü.Öykünün anlatıcısı Bir Kare önce bize ikiboyutlu ülkesini tanıtıyor; sonra birlikte Çizgiülke ve Noktaülke’yi ziyaret ediyor, Uzayülke’de bir üst boyutu anlamaya çalışmanın güçlüklerini tadıyor ve daha yüksek boyutlar üzerine kafa yoruyoruz. Bunun yanı sıra, modern çağın temellerinin atıldığı bir dönem olan Victoria çağının İngiliz toplumuna yönelik zekice bir hicve de tanık oluyoruz. Abbott’ın içinde yaşadığı topluma ilişkin kaygılarının bir izdüşümünü Düzülke’de bulmak mümkün:Kadın haklarından, dar kafalı tutuculuğa, sınıfsal ayrımlaşma ve ayrıcılıklardan, farklılıklara tahammülsüzlüğe kadar pek çok konu, kimi zaman soyutlamalarına sarılıp sarmalanmış olarak, kimi zaman acımasız bir ironiyle ele alınıyor.Yaşayan en saygın popüler bilim yazarlarından olan matematik profesörü Ian Stewart’ın özgün metne düştüğü notlar ise yalnızca metnin yaslandığı matematiksel kavramları açıklamakla kalmıyor, okurun Düzülke’yi daha geniş, daha kapsayıcı bir bakış açısıyla ele almasının da yolunu açıyor:Abbott’ın Victoria çağına ilişkin sayısız göndermesini açıklayıp, yaşami ve entelektüel çevresiyle ilgili bilgiler veriyor; H.G. Wells’den, Karl Marx’a, Victoria çağı ispritizmacılarından, İslam matematikçilerine kadar pek çok farklı konu ve figüre değiniyor; ve en önemlisi de matematiğin ve fiziğin çok boyutluluk kavramına ulaşana dek geçirdiği aşamaları gözler önüne seriyor. Açıklamalı Düzülke, bir yandan matematiksel düşüncenin gündelik düşünüşün uzağında, kendine özgü bir biçimde işleyişini bütün açıklığıyla ortaya koyan, bir yandan da matematikle diğer disiplinler arasındaki ilişkiyi derleyip toparlayan bir yapıt.Stewart’ın notları zaten bir klasik olan ve ilk basımından beri kitapçılardan eksik olmayan bu yapıta eğlendirici ve öğretici bir katkı sağlamıs. Hem Abbott hayranlarının hem de Abbott’la yeni tanışacak olanların edinmesi gereken basım işte bu.Gregory McNamee, Publishers Weekly