Ian Stewart – författare

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 other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.

The fourth book in the Science of Discworld series, and this time around dealing with THE REALLY BIG QUESTIONS, Terry Pratchett’s brilliant new Discworld story Judgement Day is annotated with very big footnotes (the interleaving chapters) by mathematician Ian Stewart and biologist Jack Cohen, to bring you a mind-mangling combination of fiction, cutting-edge science and philosophy.Marjorie Daw is a librarian, and takes her job – and indeed the truth of words – very seriously. She doesn’t know it, but her world and ours – Roundworld – is in big trouble. On Discworld, a colossal row is brewing…The Wizards of Unseen University feel responsible for Roundworld (as one would for a pet gerbil). After all, they brought it into existence by bungling an experiment in Quantum ThaumoDynamics. But legal action is being brought against them by Omnians, who say that the Wizards’ god-like actions make a mockery of their noble religion.As the finest legal brains in Discworld (a zombie and a priest) gird their loins to do battle – and when the Great Big Thing in the High Energy Magic Laboratory is switched on – Marjorie Daw finds herself thrown across the multiverse and right in the middle of the whole explosive affair. As God, the Universe and, frankly, Everything Else is investigated by the trio, you can expect world-bearing elephants, quantum gravity in the Escher-verse, evolutionary design, eternal inflation, dark matter, disbelief systems – and an in-depth study of how to invent a better mousetrap.

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics.The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries.Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Roundworld is in trouble again, and this time it looks fatal. Having created it in the first place, the wizards of Unseen University feel vaguely responsible for its safety. They know the creatures who lived there escaped the impending Big Freeze by inventing the space elevator - they even intervened to rid the planet of a plague of elves, who attempted to divert humanity onto a different time track. But now it's all gone wrong - Victorian England has stagnated and the pace of progress would embarrass a limping snail. Unless something drastic is done, there won't be time for anyone to invent spaceflight and the human race will be turned into ice-pops. Why, though, did history come adrift? Was it Sir Arthur Nightingale's dismal book about natural selection? Or was it the devastating response by an obscure country vicar called Charles Darwin, whose bestselling Theology of Species made it impossible to refute the divine design of living creatures? Either way, it's no easy task to change history, as the wizards discover to their cost. Can the God of Evolution come to humanity's aid and ensure Darwin writes a very different book? And who stopped him writing it in the first place?

Symmetry plays a crucial role across various scales in physics-from the fundamental particles that comprise matter to the intricate shapes of snowflakes. The ubiquity of these symmetries poses a pivotal question: if life arises as an emergent property from physics, what prevents symmetry from also explaining the architectures of biological, or even artificial, life? This book addresses the question by introducing a new geometry for 'living' networks, drawing inspiration from Grothendieck's fibrations in category theory. The traditional, restrictive symmetry groups of physics are replaced with symmetry fibration, a novel notion which is both local and adaptable to evolutionary pressures. This provides an effective framework for understanding biological complexity, translating the once inscrutable AI 'black box' into an interpretable 'colored box' rich with symmetry. Featuring numerous cutting-edge applications from genomics, neuroscience and AI, this text is ideal for graduate students and researchers in mathematical biology, machine learning and network science.

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. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy's theorem and Cauchy's residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years'' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students'' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of ''nonstandard analysis'', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. 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.

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors'' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy''s theorem and Cauchy''s residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.

The writers behind New Scientist explore the baffling concept of nothingness from the fringes of the universe to our minds'' inner workings.It turns out that nothing is as curious or as enlightening as nothingness itself. What is nothing? Where can it be found? The writers of the world''s top-selling science magazine investigate—from the big bang, dark energy, and the void, to superconductors, vestigial organs, hypnosis, and the placebo effect. And they discover that understanding nothing may be the key to understanding everything:- What came before the big bang—and will our universe end?- How might cooling matter down almost to absolute zero help solve our energy crisis?- How can someone suffer from a false diagnosis as though it were true?- Does nothingness even exist if squeezing a perfect vacuum somehow creates light?- Why is it unfair to accuse sloths—animals who do nothing—of being lazy?- And more!Contributors Paul Davies, Jo Marchant, and Ian Stewart, along with two former editors of Nature and sixteen other leading writers and scientists, marshal up-to-the-minute research to make one of the most perplexing realms in science dazzlingly clear. Prepare to be amazed at how much more there is to nothing than you ever realized.

The fantastic first book in the Sunday Times bestselling Science of Discworld seriesWhen a wizardly experiment goes adrift, the wizards of Unseen University find themselves with a pocket universe on their hands: 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@terryandrobProfessor 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.

The programming language C occupies an unusual position midway between conventional high-level and assembly languages, allowing the programmer to combine the best features of both. This book is an introduction to the language itself, and to the special style of thinking that goes with it. Anyone wishing to learn C is likely to have some experience in a high-level language such as BASIC or Pascal, and it seems sensible to make use of that experience. We therefore assume some facility with conventional notation for computer arith­ metic, and simple notions (such as looping and branching) common to most high-level languages. However, that cannot be the whole story. One cannot learn to speak colloquial French by thinking in English and performing a routine translation. No more can one learn to program in colloquial C by thinking in BASIC and performing a routine translation. However, when learning French it is normal to assume familiarity with English, building on that in the early stages, thereby creating the confidence necessary to provide that mot juste to which nothing corresponding exists in English. Our approach to C is similar. In particular we do not introduce at the very beginning some of the features of C which eventually lead to more efficient and elegant code-for example, the ability to do several things, apparently at once. Initially, such constructs can be confusing. Once the reader has acquired some facility with the language it then becomes possible to bring these features into play in a natural manner.

The fantastic first book in the Sunday Times bestselling Science of Discworld seriesWhen a wizardly experiment goes adrift, the wizards of Unseen University find themselves with a pocket universe on their hands: 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@terryandrobProfessor 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.

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermat’s Last Theorem, Fifth 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, initially 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 Fifth EditionPell's Equation x^2-dy^2=1: all solutions can be obtained from a single `fundamental' solution, which can be found using continued fractions.Galois theory of number field extensions, relating the field structure to that of the group of automorphisms.More material on cyclotomic fields, and some results on cubic fields.Advanced properties of prime ideals, including the valuation of a fractional ideal relative to a prime ideal, localisation at a prime ideal, and discrete valuation rings.Ramification theory, which discusses how a prime ideal factorises when the number field is extended to a larger one.A short proof of the Quadratic Reciprocity Law based on properties of cyclotomic fields. ThisValuations and p-adic numbers. Topology of the p-adic integers.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.

Since 1973, Galois theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students.New to the Fifth EditionReorganised and revised Chapters 7 and 13New exercises and examplesExpanded, updated referencesFurther historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and AbelA new final chapter discussing other directions in which Galois theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representationsThis bestseller continues to deliver a rigorous, yet engaging, treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.

Is the universe around us a figment of our imagination? Or are our minds figments of reality? In this refreshing new look at the evolution of mind and culture, bestselling authors Ian Stewart and Jack Cohen eloquently argue that our minds necessarily evolved inextricably within the context of culture and language. They go beyond conventional reductionist ideas to look at how the mind is the response of an evolving brain trying to grapple with a complex environment. Along the way they develop new and intriguing insights into the nature of evolution, science and humanity.

Is the universe around us a figment of our imagination? Or are our minds figments of reality? In this refreshing new look at the evolution of mind and culture, bestselling authors Ian Stewart and Jack Cohen eloquently argue that our minds necessarily evolved inextricably within the context of culture and language. They go beyond conventional reductionist ideas to look at how the mind is the response of an evolving brain trying to grapple with a complex environment. Along the way they develop new and intriguing insights into the nature of evolution, science and humanity.

Acclaimed The Science of Discworld centred around an original Pratchett story about the wizards of Discworld. In it they accidentally witnessed the creation and evolution of our universe, a plot which was interleaved with a Cohen & Stewart non-fiction narrative about Big Science. In The Science of Discworld II: The Globe our authors join forces again to see just what happens when the wizards meddle with history in a battle against the elves for the future of humanity on Earth. London is replaced by a dozy Neanderthal village. The Renaissance is given a push. The role of fat women in art is developed. And one very famous playwright gets born and writes The Play. Weaving together a fast-paced Discworld novelette with cutting-edge scientific commentary on the evolution and development of the human mind, culture, language, art, and science, The Globe presents a fascinating and brilliantly original view of the world we live in. The scene of the final epic battle is the first production of A Midsummer's Night Dream at the Globe Theatre.

Since the dramatic discovery of the mathematical concept of chaos in 1989, the controversy of its contents has settled down. This revised edition of Does God Play Dice? takes a fresh look at its achievements and potential. With a new preface and three completely new chapters, it includes the latest practical applications of chaos theory, such as developing intelligent heart pacemakers. All this provides a fascinating new answer to Einstien's question which provided the title of this book.

Since the dramatic discovery of the mathematical concept of chaos in 1989, the controversy of its contents has settled down. This revised edition of Does God Play Dice? takes a fresh look at its achievements and potential. With a new preface and three completely new chapters, it includes the latest practical applications of chaos theory, such as developing intelligent heart pacemakers. All this provides a fascinating new answer to Einstien's question which provided the title of this book.

Do we live in a simple or a complex universe? Jack Cohen and Ian Stewart explore the ability of complicated rules to generate simple behaviour in nature through 'the collapse of chaos'. 'The most startling, thought-provoking book I've read all year. I was pleased to learn that most of the things I thought I knew were wrong' -- Terry Pratchett

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Welcome back to Ian Stewart''s magical world of mathematics! This is a strange world of never-ending chess games, empires on the moon, furious fireflies, and, of course, disputes over how best to cut a cake. Each quirky tale presents a fascinating mathematical puzzle -- challenging, fun, and also introducing the reader to a significant mathematical problem in an engaging and witty way.

Welcome to Ian Stewart''s strange and magical world of mathematics! In Math Hysteria, Professor Stewart presents us with a wealth of magical puzzles, each one spun around an amazing tale: Counting the Cattle of the Sun; The Great Drain Robbery; and Preposterous Piratical Predicaments; to name but a few. Along the way, we also meet many curious characters: in short, these stories are engaging, challenging, and lots of fun!

From the mathematics of mazes, to cones with a twist, and the amazing sphericon - and how to make one - Ian Stewart is back with more mathematical stories and puzzles that are as quirky as they are fascinating, and each from the cutting edge of the world of mathematics.We find out about the mathematics of time travel, explore the shape of teardrops (which are not tear-drop shaped, but something much, much more strange!), dance with dodecahedra, and play the game of Hex, amongst many more strange and delightful mathematical diversions.