Ian Stewart

Torry: The Life and Career of a Football Great is the story of the remarkable Torry Gillick, a Scottish international footballer revered both in Glasgow and Liverpool. On the pitch, Gillick won every possible honour in Scottish football with Rangers across two spells at Ibrox, and was the only player signed twice by the legendary Bill Struth. At Everton, he was a key player in their famous league title triumph in 1939, making the club the last champions before World War Two. Gillick was a character and an entertainer, his skills and goals earning him a place in the Hall of Fame at both clubs. But his story is about more than his wonderful football career; it is one of a family man whose life was blighted by tragedy and heartache, but who always emerged stronger and who earned respect and friendship in and out of football.

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.

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.

In the world of Latin Jazz/Latin American music, John Ben tez is considered to be one of the greatest bassists alive today. With five GRAMMY awards to his name and performance credits ranging from Tito Puente to Chick Corea, his impact on the music world is unquestionable. "The John Ben tez Bass Method Volume 1" is the first in a comprehensive book series forged from unique teaching methods developed over years of private instruction. "Volume 1 - Freedom In The Clave: A Rhythmic Approach To Bass Playing" is a vast collection of rhythmic independence exercises designed to strengthen a student's overall rhythmic confidence and awareness in regards to the clave, thus facilitating higher degrees of creativity and expression during performance. The book also contains five note-for-note transcriptions from various albums in Ben tez's discography to demonstrate how this master musician puts his own concepts to work in real time. Volume 1 is a highly useful, one-of-a-kind method for bassists and other inquisitive instrumentalists alike.

An exploration of ten intriguing areas of mathematics, from prime numbers and graph theory to fractals and knots This engaging book invites readers to dive into ten intriguing topics often left out of the standard curriculum yet essential to the mathematical enterprise. It guides the mathematically curious—undergraduates emerging from their comfort zones, high school students bored by what they are taught in math classes, general readers hungry for a challenge—through concepts and problems that encourage the active, hands-on learning that leads to real understanding. In ten chapters, readers meet prime numbers, graph theory, Pick’s Theorem, continued fractions, curves of constant diameter, computer logic, projective geometry and perspective, fractals, knots and links, and catastrophe theory, including the broader mathematical and historical setting. Along the way, they build their cognitive toolkit, encountering such ideas as theorem, proof, and algorithm organically and in context. Each chapter includes two problem sets, with answers provided in a final chapter. The authors, both prominent educators and mathematicians, invite readers to think deeply about the problems they investigate and to enjoy the process of searching for solutions.

An exploration of ten intriguing areas of mathematics, from prime numbers and graph theory to fractals and knots This engaging book invites readers to dive into ten intriguing topics often left out of the standard curriculum yet essential to the mathematical enterprise. It guides the mathematically curious—undergraduates emerging from their comfort zones, high school students bored by what they are taught in math classes, general readers hungry for a challenge—through concepts and problems that encourage the active, hands-on learning that leads to real understanding. In ten chapters, readers meet prime numbers, graph theory, Pick’s Theorem, continued fractions, curves of constant diameter, computer logic, projective geometry and perspective, fractals, knots and links, and catastrophe theory, including the broader mathematical and historical setting. Along the way, they build their cognitive toolkit, encountering such ideas as theorem, proof, and algorithm organically and in context. Each chapter includes two problem sets, with answers provided in a final chapter. The authors, both prominent educators and mathematicians, invite readers to think deeply about the problems they investigate and to enjoy the process of searching for solutions.

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.

By bringing together behavioural science, organisational psychology, and real-world case studies from global corporations, government, and the military, this book explains why leaders do what they do – it offers a model that is at once deeply human and immediately practical. This book challenges that outdated paradigm by revealing the hidden psychological patterns, schemas, that shape how individuals think, behave, and collaborate at work. These schemas operate below the level of conscious awareness, influencing how we make decisions, respond to pressure, handle conflict, and engage with power. They determine whether people step forward as leaders, contribute as effective teammates, or withdraw as silent followers. At the heart of the book is a simple but powerful premise: • Leadership is not a role you hold. It is a schema-driven behaviour you adopt in a moment. • Teaming is not a personality trait. It is a schema that shapes how you collaborate. • Followership is not passive obedience. It is an active schema that can drive loyalty, dissent, or disengagement. This is not another leadership style model, it is a cognitive framework that explains why styles emerge in the first place and shows readers how to develop role agility across the challenges of modern organisational life.

By bringing together behavioural science, organisational psychology, and real-world case studies from global corporations, government, and the military, this book explains why leaders do what they do – it offers a model that is at once deeply human and immediately practical. This book challenges that outdated paradigm by revealing the hidden psychological patterns, schemas, that shape how individuals think, behave, and collaborate at work. These schemas operate below the level of conscious awareness, influencing how we make decisions, respond to pressure, handle conflict, and engage with power. They determine whether people step forward as leaders, contribute as effective teammates, or withdraw as silent followers. At the heart of the book is a simple but powerful premise: • Leadership is not a role you hold. It is a schema-driven behaviour you adopt in a moment. • Teaming is not a personality trait. It is a schema that shapes how you collaborate. • Followership is not passive obedience. It is an active schema that can drive loyalty, dissent, or disengagement. This is not another leadership style model, it is a cognitive framework that explains why styles emerge in the first place and shows readers how to develop role agility across the challenges of modern organisational life.

Many of the deepest and most important areas of mathematics have arisen from questions about extremes - shortest lines, smallest areas, densest packings, fewest colours. Mathematicians have been grappling with such issues for centuries, and some go back thousands of years. The isoperimetric problem, for example - which asks for the shortest path enclosing a given area - dates back to the mythological founding of the city of Carthage. By contrast, it was only in 2017 that the densest ways to pack identical spheres into a space of 24 dimensions was finally proved. Many of these problems are more than mere thought experiments. The origins of the Travelling Salesperson Problem - find the shortest route that visits a given set of cities - are self-explanatory. The Plateau problem, about the geometry of soap bubbles, now has applications as diverse as cosmology and biological development. Reaching for the Extreme tells the stories of these and other similar problems: their historical roots, the struggles to solve them, and the uses that can be made of the results, when such uses exist.

From bestselling author and mathematician Ian Stewart, the fascinating story of the extreme problems that have driven math forward from antiquity to today "Stewart has a genius for explanation."--New Scientist Many of the deepest and most important areas of mathematics have emerged from questions about extremes--the shortest path between two points on a curved surface, the smallest area spanning a wire, or the fewest colors needed to make a map. Mathematicians have been pushing restlessly toward extremes for thousands of years. The isoperimetric problem, for example--which asks for the shortest route enclosing a given area--can be traced to ancient Carthage. By contrast, it was only in 2017 that the densest ways to pack identical spheres into a 24-dimensional space was proven. In Reaching for the Extreme, bestselling author Ian Stewart, one of the world's most popular writers on mathematics, presents a dazzling, wide-ranging tour of math's outer limits. Stewart tells the stories of sixteen superlative problems--their history, the struggles to solve them, and the uses of some of the results. From the biggest number to the smallest, the fastest fall to the weirdest symmetry, and the best fold to the shortest proof, these questions are either pure thought experiments or are motivated by real-world challenges. The Plateau problem, about the geometry of soap bubbles, led to the notion of a minimal surface--now used in cosmology, biology, and other fields. Meanwhile, the 2023 discovery of a single tile shape that covers the infinite plane without repeating the same pattern has no application--yet. Reaching for the Extreme illuminates how mathematicians drive knowledge forward by reaching for the edges and solving some of the world's most fascinating problems.

A new history of the Celts that reveals how this once-forgotten people became a pillar of modern national identity in Britain, Ireland, and FranceBefore the Greeks and Romans, the Celts ruled the ancient world. They sacked Rome, invaded Greece, and conquered much of Europe, from Ireland to Turkey. Celts registered deeply on the classical imagination for a thousand years and were variously described by writers like Caesar and Livy as unruly barbarians, fearless warriors, and gracious hosts. But then, in the early Middle Ages, they vanished. In The Celts, Ian Stewart tells the story of their rediscovery during the Renaissance and their transformation over the next few centuries into one of the most popular European ancestral peoples. The Celts shows how the idea of this ancient people was recovered by scholars, honed by intellectuals, politicians, and other thinkers of various stripes, and adopted by cultural revivalists and activists as they tried to build European nations and nationalisms during the eighteenth and nineteenth centuries. Long-forgotten, the Celts improbably came to be seen as the ancestors of most western Europeans—and as a pillar of modern national identity in Britain, Ireland, and France. Based on new research conducted across Europe and in the United States, The Celts reveals when and how we came to call much of Europe “Celtic,” why this idea mattered in the past, and why it still matters today, as the tide of nationalism is once again on the rise.

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.

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.

Vy uvidite, kak svjazany matematicheskie otkrytija proshlykh vekov i segodnjashnie tekhnologiiVy uznaete, chto obschego mezhdu preobrazovaniem Fure, otkrytiem struktury DNK i sovremennymi meditsinskimi skaneramiVam zakhochetsja vsem rasskazat, chto kompjuternaja grafika - eto novoe primenenie staroj matematikiVy ne smozhete ne dumat o tom, chto Vselennaja "sostoit" iz matematikiShirokoe rasprostranenie kompjuterov mozhet sozdat vpechatlenie, chto matematika uzhe i ne nuzhna, chto segodnjashnie tekhnologii pozvoljajut proizvodit samye slozhnye vychislitelnye operatsii za doli sekundy. Eto naivnoe predstavlenie pobudilo izvestnogo populjarizatora nauki Iena Stjuarta pokazat chitateljam ne samye ochevidnye zaslugi ljubimoj distsipliny, ved ee rol otnjud ne svoditsja k raschetam, i blagodarja kompjuteram, osvobozhdajuschim nas ot monotonnoj raboty, my prosto nachinaem zanimatsja matematikoj inache. Imenno matematika stoit za vsemi preobrazujuschimi tekhnologijami, kotorye delajut XXI vek sovershenno nepokhozhim na predshestvujuschuju epokhu. Bez matematiki nemyslimy i tsifrovaja fotografija, i sovremennaja svjaz, i sputnikovaja navigatsija, bez nee ne obojtis pri prognozirovanii posledstvij klimaticheskikh izmenenij. Etot rjad mozhno prodolzhat i prodolzhat, ne zabyv upomjanut gumanitarnye oblasti i iskusstvo, politiku i internet-bezopasnost. Slovom, schitaet avtor, potrebnost v etoj nauke universalna, ona - osnova osnov.

In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book's main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of "admissible" ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.