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Europe has talked itself into a refugee and security crisis. There
is, however, a misrecognition of the real challenge facing Europe:
the challenge of managing the relationship between Europeans and
the currently stigmatized 'others' which it has attracted. Making
the case against a 'Europe of walls', Robin Wilson instead proposes
a refounding of Europe built on the power of diversity and an ethos
of hospitality rather than an institutional thicket serving the
market. Providing a robust critique of the moral panic surrounding
migrants and security dominating the European public sphere, this
book explains why old models for managing cultural diversity in
Europe no longer work, and why their obsolescence has led to morbid
symptoms. Incorporating discussion of the eurozone crisis and the
associated insecurity and the rise of xenophobic populists, Wilson
provides an insider account of how the Council of Europe has, over
a decade and a half, developed a new paradigm of intercultural
integration. He builds theory into this model, drawing on work on
cosmopolitanism in the social sciences, also emphasizing the
empirical validity of the approach. With its handling of critical
issues currently facing Europe, this book is of interest not only
to academics across the social sciences, undergraduate students of
politics and sociology and postgraduate students of cultural and
European studies, but also to policy-makers and NGO practitioners.
Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.
Image, Text, Architecture brings a radical and detailed analysis of
the modern and contemporary architectural media, addressing issues
of architectural criticism, architectural photography and the role
of journal editors. It covers examples as diverse as an article by
British artist Paul Nash in The Architectural Review, 1940, an
early project by French architects Lacaton & Vassal published
in the journal 2G, 2001, and recent photography by Hisao Suzuki for
the Spanish journal El Croquis. At the intersection of image and
text the book also reveals the role of the utopian impulse within
the architectural media, drawing on theories of utopian discourse
from the work of the French semiotician and art theorist Louis
Marin, and the American Marxist critic Fredric Jameson. Through
this it builds a fresh theoretical approach to journal studies,
revealing a hitherto unexplored dimension of "latent" or
"unconscious" discourse within the media portrait of architecture.
The purpose of this enquiry is to highlight moments where a
different type of critical voice emerges on the architectural
journal page, indicating the possibility of a more progressive
engagement with the media as a platform for critical and
speculative thinking about architecture, and to rethink the
journals' role within architectural history.
Image, Text, Architecture brings a radical and detailed analysis of
the modern and contemporary architectural media, addressing issues
of architectural criticism, architectural photography and the role
of journal editors. It covers examples as diverse as an article by
British artist Paul Nash in The Architectural Review, 1940, an
early project by French architects Lacaton & Vassal published
in the journal 2G, 2001, and recent photography by Hisao Suzuki for
the Spanish journal El Croquis. At the intersection of image and
text the book also reveals the role of the utopian impulse within
the architectural media, drawing on theories of utopian discourse
from the work of the French semiotician and art theorist Louis
Marin, and the American Marxist critic Fredric Jameson. Through
this it builds a fresh theoretical approach to journal studies,
revealing a hitherto unexplored dimension of "latent" or
"unconscious" discourse within the media portrait of architecture.
The purpose of this enquiry is to highlight moments where a
different type of critical voice emerges on the architectural
journal page, indicating the possibility of a more progressive
engagement with the media as a platform for critical and
speculative thinking about architecture, and to rethink the
journals' role within architectural history.
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, ei + 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; 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.
Approximately fifty articles that were published in The
Mathematical Intelligencer during its first eighteen years. The
selection demonstrates the wide variety of attractive articles that
have appeared over the years, ranging from general interest
articles of a historical nature to lucid expositions of important
current discoveries. Each article is introduced by the editors.
"...The Mathematical Intelligencer publishes stylish,
well-illustrated articles, rich in ideas and usually short on
proofs. ...Many, but not all articles fall within the reach of the
advanced undergraduate mathematics major. ... This book makes a
nice addition to any undergraduate mathematics collection that does
not already sport back issues of The Mathematical Intelligencer."
D.V. Feldman, University of New Hamphire, CHOICE Reviews, June
2001.
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.
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.
How a new mathematical field grew and matured in America Graph
Theory in America focuses on the development of graph theory in
North America from 1876 to 1976. At the beginning of this period,
James Joseph Sylvester, perhaps the finest mathematician in the
English-speaking world, took up his appointment as the first
professor of mathematics at the Johns Hopkins University, where his
inaugural lecture outlined connections between graph theory,
algebra, and chemistry-shortly after, he introduced the word graph
in our modern sense. A hundred years later, in 1976, graph theory
witnessed the solution of the long-standing four color problem by
Kenneth Appel and Wolfgang Haken of the University of Illinois.
Tracing graph theory's trajectory across its first century, this
book looks at influential figures in the field, both familiar and
less known. Whereas many of the featured mathematicians spent their
entire careers working on problems in graph theory, a few such as
Hassler Whitney started there and then moved to work in other
areas. Others, such as C. S. Peirce, Oswald Veblen, and George
Birkhoff, made excursions into graph theory while continuing their
focus elsewhere. Between the main chapters, the book provides short
contextual interludes, describing how the American university
system developed and how graph theory was progressing in Europe.
Brief summaries of specific publications that influenced the
subject's development are also included. Graph Theory in America
tells how a remarkable area of mathematics landed on American soil,
took root, and flourished.
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.
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The Turing Guide (Paperback)
Jack Copeland, Jonathan Bowen, Mark Sprevak, Robin Wilson
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R757
R632
Discovery Miles 6 320
Save R125 (17%)
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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.
From Ancient Greek times, music has been seen as a mathematical
art, and the relationship between mathematics and music has
fascinated generations. This collection of wide ranging,
comprehensive and fully-illustrated papers, authorized by leading
scholars, presents the link between these two subjects in a lucid
manner that is suitable for students of both subjects, as well as
the general reader with an interest in music. Physical,
theoretical, physiological, acoustic, compositional and analytical
relationships between mathematics and music are unfolded and
explored with focus on tuning and temperament, the mathematics of
sound, bell-ringing and modern compositional techniques.
August Mobius was one of the 19th century's most influential
mathematicians and astronomers. Written by six distinguished
contributors, this book explores the work of Mobius and his
brilliant German contemporaries. The work emphasizes those
achievements which in many ways can be seen to reflect the exciting
advances taking place at the time throughout the entire scientific
world. The background to Mobius's life and labors is provided by
John Fauvel. Gert Schubring examines the mathematical community in
19th-century Germany, while Allan Chapman describes the revolution
in astronomy that took place during the period. Jeremy Gray
analyzes Mobius's contribution to geometrical mechanics and Norman
Biggs traces his role in the development of topological ideas.
Finally, Ian Stewart explores the legacy Mobius left to mathematics
in our own century. This stimulating volume will appeal to all
scientists in the fields that Mobius helped advance--physics,
mathematics, and astronomy--as well as general readers interested
in the history of science.
The third edition of the Collins Cambridge IGCSE (R) English
Teacher's Guide supports the Student's Book, giving teachers
everything they need to teach the Cambridge IGCSE (R) and IGCSE (R)
(9-1) First Language English syllabuses 0500 and 0990. This
Teacher's Guide supports the new syllabuses for first examination
in 2020. Exam Board: Cambridge Assessment International Education
Level & Subject: IGCSE First Language English (0500), IGCSE
(9-1) First Language English (0990) First teaching: September 2018
First examination: June 2020 This title has been endorsed by
Cambridge Assessment International Education. Revised and updated
to support the 2020 syllabuses and examination formats. Support
student progress with teaching sequences that follow the structure
of the Student Book, moving from building the key reading and
writing skills to applying these skills to specific exam questions
and coursework tasks. Save time on planning and preparation with
expert support from Julia Burchell, an experienced examiner and
trainer. The Teacher Guide includes a two-year scheme of work,
differentiated lesson plans, worksheets and PowerPoints for every
two- or four-page section of the Student Book, plus extension
activities for students aiming for the highest grades. Adapt the
resources to the needs of your classes with printable PDFs and
editable Word and PowerPoint files. Detailed guidance and annotated
sample answers in the Teacher Guide help you and your classes to
make the most of the practice examination papers in the Student
Book.
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, to name 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.
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.
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 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.
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.
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