Robin Wilson – författare

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.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.

Can one prove that 1 + 1 = 2? How long is the coastline of Britain? Which US president proved Pythagoras' theorem on right-angled triangles? Who originated the quadratic equation we learned at school? In how many ways can you tile your bathroom? Is there a formula for prime numbers? How often are two winning lottery numbers consecutive? Who was the witch of Agnesi? What is 'the most important theorem in mathematics'? Who scratched mathematical equations on a Dublin bridge? What is a 'space-filling curve'? Must all infinities be the same size? These and many other questions are answered in this book which presents eighteen 'Stories' featuring famous mathematical equations and their historical development. The equations arise from geometry, arithmetic, algebra, calculus, combinatorics, number theory, and mathematical logic, and range over 4,000 years from early counting and circle measurement via Renaissance algebra to fractal geometry, and from the geometry of the ancient Greeks via the development of calculus to Boolean algebra and computing. The Stories are well illustrated with historical artefacts and explanatory diagrams.Presented in a straightforward, intelligible, and entertaining manner, Sum Stories is written for general readers of all ages with an interest in mathematics and its historical development.

The fourth edition of the Collins Cambridge IGCSE English Teacher’s Guide supports the Student’s Book, giving teachers everything they need to teach the Cambridge IGCSE and IGCSE (9–1) First Language English syllabuses (0500/0990).This Teacher’s Guide supports the syllabuses for examination from 2027.Exam Board: Cambridge International EducationLevel & Subject: Cambridge IGCSE First Language English (0500) and IGCSE (9–1) First Language English (0990)For examination from 2027We are working towards endorsement of this series for the Cambridge Pathway to support the syllabus (0500/0990) for examination from 2027. Revised and updated to support the 2027 syllabuses.Support student progress with teaching sequences that follow the structure of the Student's Book, moving from building key reading, writing and technical skills to applying these skills to a range of question types and tasks.Multiple schemes of work offer different routes through the course to suit the context of your classes.Save time on planning and preparation with pre-prepared lesson plans, answers, worksheets and PowerPoints for every topic of the Student's Book, plus extension and support activities.Adapt the resources to the needs of your classes with editable Word and PowerPoint files.Detailed guidance and annotated sample answers in the Teacher's Guide help you and your classes to make the most of the practice questions in the Student's Book.Written and developed by a team of experienced Cambridge IGCSE English teachers from a range of regions.

Lewis Carroll's books have delighted children and adults for generations, but behind their exuberant fantasy and delightful nonsense was the mind of a brilliant mathematician. Now his forgotten achievements in the world of numbers are brought to light by acclaimed author and mathematician Robin Wilson. Here he explores the curious imagination of a man whose pioneering work at Oxford University included investigations into voting patterns and tennis seeding, who dreamt up numerical conundrums in bed at night and who filled his writings with problems, paradoxes, puzzles and teasing games of logic. Taking us into a world of mock turtles and maps, gryphons and gravity, Lewis Carroll in Numberland reveals the singular mind of a genius.

Lewis Carroll's books have delighted children and adults for generations, but behind their exuberant fantasy and delightful nonsense was the mind of a brilliant mathematician. Now his forgotten achievements in the world of numbers are brought to light by acclaimed author and mathematician Robin Wilson. Here he explores the curious imagination of a man whose pioneering work at Oxford University included investigations into voting patterns and tennis seeding, who dreamt up numerical conundrums in bed at night and who filled his writings with problems, paradoxes, puzzles and teasing games of logic. Taking us into a world of mock turtles and maps, gryphons and gravity, Lewis Carroll in Numberland reveals the singular mind of a genius.

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal''s triangle? (it was not Pascal)Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.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.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing''s life and work.This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing''s life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing''s life and work.This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing''s life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

This is the story of the intellectual and social life of a community, and of its interactions with the wider world. For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This highly readable and beautifully illustrated book reveals the richness and influence of Oxford''s mathematical tradition and the fascinating characters that helped to shape it.The story begins with the founding of the University of Oxford and the establishing of the medieval curriculum, in which mathematics had an important role. The Black Death, the advent of printing, the Civil War, and the Newtonian revolution all had a great influence on the development of mathematics at Oxford. So too did many well-known figures: Roger Bacon, Henry Savile, Robert Hooke, Christopher Wren, Edmond Halley, Florence Nightingale, Charles Dodgson (Lewis Carroll), and G. H. Hardy, toname but a few. Later chapters bring us to the 20th century, with some entertaining reminiscences by Sir Michael Atiyah of the thirty years he spent as an Oxford mathematician.In this second edition the story is brought right up to the opening of the new Mathematical Institute in 2013 with a foreword from Marcus du Sautoy and recent developments from Peter M. Neumann.

This is the story of the intellectual and social life of a community, and of its interactions with the wider world. For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This highly readable and beautifully illustrated book reveals the richness and influence of Oxford''s mathematical tradition and the fascinating characters that helped to shape it.The story begins with the founding of the University of Oxford and the establishing of the medieval curriculum, in which mathematics had an important role. The Black Death, the advent of printing, the Civil War, and the Newtonian revolution all had a great influence on the development of mathematics at Oxford. So too did many well-known figures: Roger Bacon, Henry Savile, Robert Hooke, Christopher Wren, Edmond Halley, Florence Nightingale, Charles Dodgson (Lewis Carroll), and G. H. Hardy, toname but a few. Later chapters bring us to the 20th century, with some entertaining reminiscences by Sir Michael Atiyah of the thirty years he spent as an Oxford mathematician.In this second edition the story is brought right up to the opening of the new Mathematical Institute in 2013 with a foreword from Marcus du Sautoy and recent developments from Peter M. Neumann.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians.This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians.This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.

Who first presented Pascal''s triangle? (It was not Pascal.)Who first presented Hamiltonian graphs? (It was not Hamilton.)Who first presented Steiner triple systems? (It was not Steiner.)The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that wouldotherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings onpermutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler''s contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although itcan be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement forfurther research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Who first presented Pascal''s triangle? (It was not Pascal.)Who first presented Hamiltonian graphs? (It was not Hamilton.)Who first presented Steiner triple systems? (It was not Steiner.)The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that wouldotherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings onpermutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler''s contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although itcan be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement forfurther research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Can one prove that 1 + 1 = 2? How long is the coastline of Britain? Which US president proved Pythagoras' theorem on right-angled triangles? Who originated the quadratic equation we learned at school? In how many ways can you tile your bathroom? Is there a formula for prime numbers? How often are two winning lottery numbers consecutive? Who was the witch of Agnesi? What is 'the most important theorem in mathematics'? Who scratched mathematical equations on a Dublin bridge? What is a 'space-filling curve'? Must all infinities be the same size? These and many other questions are answered in this book which presents eighteen 'Stories' featuring famous mathematical equations and their historical development. The equations arise from geometry, arithmetic, algebra, calculus, combinatorics, number theory, and mathematical logic, and range over 4,000 years from early counting and circle measurement via Renaissance algebra to fractal geometry, and from the geometry of the ancient Greeks via the development of calculus to Boolean algebra and computing. The Stories are well illustrated with historical artefacts and explanatory diagrams.Presented in a straightforward, intelligible, and entertaining manner, Sum Stories is written for general readers of all ages with an interest in mathematics and its historical development.

Can one prove that 1 + 1 = 2? How long is the coastline of Britain? Which US president proved Pythagoras' theorem on right-angled triangles? Who originated the quadratic equation we learned at school? In how many ways can you tile your bathroom? Is there a formula for prime numbers? How often are two winning lottery numbers consecutive? Who was the witch of Agnesi? What is 'the most important theorem in mathematics'? Who scratched mathematical equations on a Dublin bridge? What is a 'space-filling curve'? Must all infinities be the same size? These and many other questions are answered in this book which presents eighteen 'Stories' featuring famous mathematical equations and their historical development. The equations arise from geometry, arithmetic, algebra, calculus, combinatorics, number theory, and mathematical logic, and range over 4,000 years from early counting and circle measurement via Renaissance algebra to fractal geometry, and from the geometry of the ancient Greeks via the development of calculus to Boolean algebra and computing. The Stories are well illustrated with historical artefacts and explanatory diagrams.Presented in a straightforward, intelligible, and entertaining manner, Sum Stories is written for general readers of all ages with an interest in mathematics and its historical development.

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a ''score for beauty''. While there were many worthy competitors, the winner was ''Euler''s equation''. In 2004 Physics World carried out a similar poll of ''greatest equations'', and found that among physicists Euler''s mathematical result came second only to Maxwell''s equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler''s equation reaches down into the very depths of existence". What is it that makes Euler''s identity, eiπ + 1 = 0, so special? In Euler''s Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a ''score for beauty''. While there were many worthy competitors, the winner was ''Euler''s equation''. In 2004 Physics World carried out a similar poll of ''greatest equations'', and found that among physicists Euler''s mathematical result came second only to Maxwell''s equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler''s equation reaches down into the very depths of existence". What is it that makes Euler''s identity, eiπ + 1 = 0, so special? In Euler''s Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the ''building blocks'' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation''s defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles''s proof of ''Fermat''s last theorem'' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.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.

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the ''building blocks'' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation''s defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles''s proof of ''Fermat''s last theorem'' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.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.

Charles Lutwidge Dodgson is best known for his ''Alice'' books, Alice''s Adventures in Wonderland and Through the Looking-Glass, written under his pen name of Lewis Carroll. Yet, whilst lauded for his work in children''s fiction and his pioneering work in the world of Victorian photography, his everyday job was a lecturer in Mathematics at Christ Church, Oxford University.The Mathematical World of Charles L. Dodgson (Lewis Carroll) explores the academic background behind this complex individual, outlining his mathematical life, describing his writings in geometry, algebra, logic, the theory of voting, and recreational mathematics, before going on to discuss his mathematical legacy.This is the first academic work that collects the research on Dodgson''s wide-ranging mathematical achievements into a single practical volume. Much material appears here for the first time, such as Dodgson''s personal letters and drawings, as well as the results of recent investigations into the life and work of Dodgson. Complementing this are many illustrations, both historical and explanatory, as well as a full mathematical bibliography of Dodgson''s mathematical publications.

Charles Lutwidge Dodgson is best known for his ''Alice'' books, Alice''s Adventures in Wonderland and Through the Looking-Glass, written under his pen name of Lewis Carroll. Yet, whilst lauded for his work in children''s fiction and his pioneering work in the world of Victorian photography, his everyday job was a lecturer in Mathematics at Christ Church, Oxford University.The Mathematical World of Charles L. Dodgson (Lewis Carroll) explores the academic background behind this complex individual, outlining his mathematical life, describing his writings in geometry, algebra, logic, the theory of voting, and recreational mathematics, before going on to discuss his mathematical legacy.This is the first academic work that collects the research on Dodgson''s wide-ranging mathematical achievements into a single practical volume. Much material appears here for the first time, such as Dodgson''s personal letters and drawings, as well as the results of recent investigations into the life and work of Dodgson. Complementing this are many illustrations, both historical and explanatory, as well as a full mathematical bibliography of Dodgson''s mathematical publications.

The Savilian Professorships in Geometry and Astronomy at Oxford University were founded in 1619 by Sir Henry Savile, distinguished scholar and Warden of Merton College. The Geometry chair, in particular, is the earliest University-based mathematics professorship in England, predating the first Cambridge equivalent by about sixty years.To celebrate the 400th anniversary of the founding of the geometry chair, a meeting was held at the Bodleian Library in Oxford, and the talks presented at this meeting have formed the basis for this fully edited and lavishly illustrated book, which outlines the first 400 years of Oxford''s Savilian Professors of Geometry.Starting with Henry Briggs, the co-inventor of logarithms, this volume proceeds via such figures as John Wallis, a founder member of the Royal Society, and Edmond Halley, via the 19th-century figures of Stephen Rigaud, Baden Powell, Henry Smith, and James Joseph Sylvester, to the 20th century and the present day.Oxford''s Savilian Professors of Geometry: The First 400 Years assumes no mathematical background, and should therefore appeal to the interested general reader with an interest in mathematics and the sciences. It should also be of interest to anyone interested in the history of mathematics or of the development of Oxford and its namesake university. To all of these audiences it offers portraits of mathematicians at work and an accessible exposition of historical mathematics in the context of its times.

August Möbius was one of the nineteenth century's most influential mathematicians and astronomers. Written by six distinguished contributors, this book explores the work of Möbius and his fellow-German scholars, in particular the achievements which act as a mirror for the work being undertaken by his contemporaries around the world.The background to Möbius's life and labours is provided by John Fauvel. Gert Schubring examines the mathematical community in nineteenth-century Germany, while Allan Chapman describes the revolution in astronomy that took place during the period. Jeremy Gray analyses Möbius's contribution to geometrical mechanics and Norman Biggs traces his role in the development of topological ideas. Finally, Ian Stewart explores the legacy Möbius left to mathematics in our own century.

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal)Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.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.

Who first presented Pascal's triangle? (It was not Pascal.)Who first presented Hamiltonian graphs? (It was not Hamilton.)Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work.This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work.This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.