This title, now in its second edition, is an introduction to the psychological system known as transactional analysis (TA). It is aimed at the general reader as well as at TA trainees and practitioners.

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: Mihailescu'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.

How to Read Bridges is a practical introduction to looking at the structure and purpose of bridges. It is a guide to reading the structural clues embedded in every bridge that allows their variety and ingenuity to be better appreciated. Small enough to carry in your pocket and serious enough to provide real answers, this comprehensive guide analyses and explores all types of bridges from around the world from the first millennium to the present day. The book also explores fundamental concepts of bridge design, key materials and engineering techniques whilst providing an accessible visual guide with intelligent text, using detailed illustrations and cross-sections of technical features.

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.

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 Schroedinger's cat. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration -- and explanation -- of life on earth.

The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications.

From the reviews:

" The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

New to the Fourth Edition Reorganised and revised chapter seven and thirteen New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A 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 representations.

'Stewart is Britain's most brilliant and prolific populariser of maths' Alex Bellos 'The instructive equivalent of a Michelin-starred tasting menu' Tim Radford Many people think mathematics is useless. They're wrong. In the UK, the 2.8 million people employed in mathematical science occupations contributed GBP208 billion to the economy in a single year - that's 10 per cent of the workforce contributing 16 per cent of the economy. What's the Use? asks why there is such a vast gulf between public perceptions of mathematics and reality. It shows how mathematics is vital, often in surprising ways, behind the scenes of daily life. How politicians pick their voters. How an absurd little puzzle solved 300 years ago leads to efficient methods for kidney transplants. And how a bizarre, infinitely wiggly curve helps to optimise deliveries to your door.

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 Poincare 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...

This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

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.

* 41 in-depth essays cover current economic theory and applied economics in a single, comprehensive volume
* Interfaces section considers economics as it relates to other disciplines
* Extensive notes, bibliographies and suggestions for further reading; detailed index of Topics and People
A treasure-house of stimulating argument and vast amounts of, mostly, well marshalled information. The market for general survey volumes, while already crowded, should surely find room for this offering.' - The World Economy
The work under review scores very high marks.' - The Economic Journal
The chapters are written by people who are excellently qualified and frequently well-known in their field ... The book's strengths lie in the range of contributors, the very high quality of most of the contributors and its emphasis on applied economics. For these reasons alone it is an important book, which will be invaluable both to students and to economists wishing to learn about developments in other branches of their discipline.' - Economica

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 Poincare 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.

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.

Which mathematician elaborated a crucial concept the night before he died in a duel? Who funded his maths and medical career through gambling and chess? Who learned maths from her wallpaper?

Ian Stewart presents the extraordinary lives and amazing discoveries of twenty-five of history's greatest mathematicians from Archimedes and Liu Hui to Benoit Mandelbrot and William Thurston. His subjects are the inspiring individuals from all over the world who have made crucial contributions to mathematics. They include the rediscovered geniuses Srinivasa Ramanujan and Emmy Noether, alongside the towering figures of Muhammad al-Khwarizmi (inventor of the algorithm), Pierre de Fermat, Isaac Newton, Carl Friedrich Gauss, Nikolai Ivanovich Lobachevsky, Bernhard Reimann (precursor to Einstein), Henri Poincaré, Ada Lovelace (arguably the first computer programmer), Kurt Gödel and Alan Turing.

Ian Stewart's vivid accounts are fascinating in themselves and, taken together, cohere into a riveting history of key steps in the development of mathematics.

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.

Peppered with wit and controversial topics, this is a refreshing new look at the co-evolution of mind and culture. Bestselling authors Ian Stewart and Jack Cohen (The Collapse of Chaos, 1994) eloquently argue that our minds evolved within an inextricable link with culture and language. They go beyond conventional views of the function and purpose of the mind to look at the ways that the mind is the response of an evolving brain that is constantly adjusting to a complex environment. Along the way they develop new and intriguing insights into the nature of evolution, science, and humanity that will challenge conventional views on consciousness. The esteemed authors tantalize the reader with these bold new outlooks while putting a revolutionary spin on such classic philosophical problems as the nature of free will and the essence of humanity. This clearly written and enjoyable book will inspire any educated reader to critically evaluate the existing notions of the nature of the human mind.

* 41 in-depth essays cover current economic theory and applied economics in a single, comprehensive volume
* Interfaces section considers economics as it relates to other disciplines
* Extensive notes, bibliographies and suggestions for further reading; detailed index of Topics and People

`A treasure-house of stimulating argument and vast amounts of, mostly, well marshalled information. The market for general survey volumes, while already crowded, should surely find room for this offering.' - The World Economy
`The work under review scores very high marks.' - The Economic Journal
`The chapters are written by people who are excellently qualified and frequently well-known in their field ... The book's strengths lie in the range of contributors, the very high quality of most of the contributors and its emphasis on applied economics. For these reasons alone it is an important book, which will be invaluable both to students and to economists wishing to learn about developments in other branches of their discipline.' - Economica

Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

Like its wildly popular predecessors Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures, Professor Stewart's brand-new book is a miscellany of over 150 mathematical curios and conundrums, packed with trademark humour and numerous illustrations.In addition to the fascinating formulae and thrilling theorems familiar to Professor Stewart's fans, the Casebook follows the adventures of the not-so-great detective Hemlock Soames and his sidekick Dr John Watsup (immortalised in the phrase 'Watsup, Doc?'). By a remarkable coincidence they live at 222B Baker Street, just across the road from their more illustrious neighbour who, for reasons known only to Dr Watsup, is never mentioned by name. A typical item is 'The Case of the Face-Down Aces', a mathematical magic trick of quite devilish cunning... Ranging from one-liners to four-page investigations from the frontiers of mathematical research, the Casebook reveals Professor Stewart at his challenging and entertaining best.

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.

Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of -- real, imaginary, rational, irrational, positive and negative -- along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes, Sudoku, Rubik's cube, music, primes and pi. You may be surprised to find you live in eleven-dimensional space, that of the twenty-three people on a football pitch two are more likely than not to share the same birthday, and that forty-two is a very interesting number. Professor Stewart's Incredible Numbers will delight everyone who loves numbers -- including those who currently think they don't.

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."