Ian Stewart

On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.

Selling over 25,000 copies across three editions, this book provides an unrivalled introduction to the core concepts and basic techniques of Transactional Analysis (TA). Ian Stewart guides the reader step-by-step through the successive stages in using TA to create therapeutic change, building understanding of the way the approach works in real-life practice. Key features of this new edition include: -a single extended case study running through the book -'Key ideas' panels to summarize the main ideas in each section -Detailed discussion of 'closing the escape hatches': TA's distinctive approach to resolving the issues of suicide, self-harm or violence -Practice Checklists offering suggested questions readers can use to appraise their own work with clients at strategic points in the text - Space for Reflection sections and Further Reading lists to conclude each chapter. This bestselling textbook offers trainee and practising psychotherapists and counsellors a concise, hands-on exploration of current concepts and techniques in Transactional Analysis. Ian Stewart is Co-Director of The Berne Institute, Nottingham. He is the author of Eric Berne (SAGE, 1992) and Developing Transactional Analysis Counselling (SAGE, 1996), and co-author of TA Today (2nd edn, Lifespace, 2012).

Selling over 25,000 copies across three editions, this book provides an unrivalled introduction to the core concepts and basic techniques of Transactional Analysis (TA). Ian Stewart guides the reader step-by-step through the successive stages in using TA to create therapeutic change, building understanding of the way the approach works in real-life practice. Key features of this new edition include: -a single extended case study running through the book -'Key ideas' panels to summarize the main ideas in each section -Detailed discussion of 'closing the escape hatches': TA's distinctive approach to resolving the issues of suicide, self-harm or violence -Practice Checklists offering suggested questions readers can use to appraise their own work with clients at strategic points in the text - Space for Reflection sections and Further Reading lists to conclude each chapter. This bestselling textbook offers trainee and practising psychotherapists and counsellors a concise, hands-on exploration of current concepts and techniques in Transactional Analysis. Ian Stewart is Co-Director of The Berne Institute, Nottingham. He is the author of Eric Berne (SAGE, 1992) and Developing Transactional Analysis Counselling (SAGE, 1996), and co-author of TA Today (2nd edn, Lifespace, 2012).

The seventeen equations that form the basis for life as we know it. Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations -- including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time -- Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

From Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere -- and they are fundamental to everyday life. Seventeen Equations that Changed the World examines seventeen ground-breaking equations that have altered the course of human history. He explores how Pythagoras's Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration -- and explanation -- of life on earth.

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.

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.

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. Can the God of Evolution come to humanity's aid and ensure Darwin writes a very different book?

Acclaimed The Science of Discworld centred around an original Pratchett story about the wizards of Discworld.

Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

A new partnership of biologists and mathematicians is picking apart the hidden complexity of animals and plants to throw fresh light on the behaviour of entire organisms, how they interact and how changes in biological diversity affect the planet's ecological balance. Mathematics offers new and sometimes startling perspectives on evolution and how patterns of inheritance and population work out over time-scales ranging from millions to hundreds of years - as well as what's going on to change us right now. Ian Stewart, in characteristically clear and entertaining fashion, explores these and a whole range of pertinent issues, including how far genes control behaviour and the nature of life itself. He shows how far mathematicians and biologists are succeeding in tackling some of the most difficult scientific problems the human race has ever confronted and where their research is currently taking us.

Welcome to a world that is not our own. Mankind's new home among the stars is more than they ever imagined when they left Earth. The settlers are surrounded by bizarre alien creatures that are often as deadly as they are amazing. Their lives are filled with the wonders of technology, but are held together by the strength of their resolve. Mankind walks this new world hand in hand with wafans, their sister race of sentient living machines, designed during the darker days of humanity's past. This is the world we live in, this is New Horizon. New Horizon is a roleplaying game that incorporates elements of science fiction, fantasy, utopian and dystopian fiction, and speculative fiction. New Horizon is a setting where advanced technologies and futuristic innovations are interweaved with the primeval roughness of an untamed world. It is a place where technology and nature are often seen struggling against one another, each protecting itself from the spread of the other.

It is only in recent times that infinite-dimensional Lie algebras have been the subject of other than sporadic study, with perhaps two exceptions: Cartan's simple algebras of infinite type, and free algebras. However, the last decade has seen a considerable increase of interest in the subject, along two fronts: the topological and the algebraic. The former, which deals largely with algebras of operators on linear spaces, or on manifolds modelled on linear spaces, has been dealt with elsewhere*). The latter, which is the subject of the present volume, exploits the surprising depth of analogy which exists between infinite-dimen­ sional Lie algebras and infinite groups. This is not to say that the theory consists of groups dressed in Lie-algebraic clothing. One of the tantalising aspects of the analogy, and one which renders it difficult to formalise, is that it extends to theorems better than to proofs. There are several cases where a true theorem about groups translates into a true theorem about Lie algebras, but where the group-theoretic proof uses methods not available for Lie algebras and the Lie-theoretic proof uses methods not available for groups. The two theories tend to differ in fine detail, and extra variations occur in the Lie algebra case according to the underlying field. Occasionally the analogy breaks down altogether. And of course there are parts of the Lie theory with no group-theoretic counterpart.

Welcome to a world that is not our own. Mankind's new home among the stars is more than they ever imagined when they left Earth. The settlers are surrounded by bizarre alien creatures that are often as deadly as they are amazing. Their lives are filled with the wonders of technology, but are held together by the strength of their resolve. Mankind walks this new world hand in hand with wafans, their sister race of sentient living machines, designed during the darker days of humanity's past. This is the world we live in, this is New Horizon. New Horizon is a roleplaying game that incorporates elements of science fiction, fantasy, utopian and dystopian fiction, and speculative fiction. New Horizon is a setting where advanced technologies and futuristic innovations are interweaved with the primeval roughness of an untamed world. It is a place where technology and nature are often seen struggling against one another, each protecting itself from the spread of the other.

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

Ian Stewart, author of the bestselling Professor Stewart's Cabinet of Mathematical Curiosities, presents a new and magical mix of games, puzzles, paradoxes, brainteasers, and riddles. He mingles these with forays into ancient and modern mathematical thought, appallingly hilarious mathematical jokes, and enquiries into the great mathematical challenges of the present and past. Amongst a host of arcane and astonishing facts about every kind of number from irrational or imaginary to complex or cuneiform, we find out: how to organise chaos; how matter balances anti-matter; how to turn a sphere inside out (without creasing it...); why you can't comb a hairy ball; how to calculate pi by observing the stars. And we get some tantalising glimpses of the maths of life and the universe. Mind-stretching, enlightening and endlessly amusing, Professor Stewart's new entertainment will stimulate, delight, and enthral.

School maths is not the interesting part. The real fun is elsewhere. Like a magpie, Ian Stewart has collected the most enlightening, entertaining and vexing 'curiosities' of maths over the years... Now, the private collection is displayed in his cabinet. There are some hidden gems of logic, geometry and probability -- like how to extract a cherry from a cocktail glass (harder than you think), a pop up dodecahedron, the real reason why you can't divide anything by zero and some tips for making money by proving the obvious. Scattered among these are keys to unlocking the mysteries of Fermat's last theorem, the Poincaré Conjecture, chaos theory, and the P/NP problem for which a million dollar prize is on offer. There are beguiling secrets about familiar names like Pythagoras or prime numbers, as well as anecdotes about great mathematicians. Pull out the drawers of the Professor's cabinet and who knows what could happen...