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This book grew out of a course of lectures given to third year
undergraduates at Oxford University and it has the modest aim of
producing a rapid introduction to the subject. It is designed to be
read by students who have had a first elementary course in general
algebra. On the other hand, it is not intended as a substitute for
the more voluminous tracts such as Zariski-Samuel or Bourbaki. We
have concentrated on certain central topics, and large areas, such
as field theory, are not touched. In content we cover rather more
ground than Northcott and our treatment is substantially different
in that, following the modern trend, we put more emphasis on
modules and localization.
This book is designed to be read by students who have had a first
elementary course in general algebra. It provides a common
generalization of the primes of arithmetic and the points of
geometry. The book explains the various elementary operations which
can be performed on ideals.
These notes are based on the course of lectures I gave at Harvard
in the fall of 1964. They constitute a self-contained account of
vector bundles and K-theory assuming only the rudiments of
point-set topology and linear algebra. One of the features of the
treatment is that no use is made of ordinary homology or cohomology
theory. In fact, rational cohomology is defined in terms of
K-theory.The theory is taken as far as the solution of the Hopf
invariant problem and a start is mode on the J-homomorphism. In
addition to the lecture notes proper, two papers of mine published
since 1964 have been reproduced at the end. The first, dealing with
operations, is a natural supplement to the material in Chapter III.
It provides an alternative approach to operations which is less
slick but more fundamental than the Grothendieck method of Chapter
III, and it relates operations and filtration. Actually, the
lectures deal with compact spaces, not cell-complexes, and so the
skeleton-filtration does not figure in the notes. The second paper
provides a new approach to K-theory and so fills an obvious gap in
the lecture notes.
These notes are based on the course of lectures I gave at Harvard
in the fall of 1964. They constitute a self-contained account of
vector bundles and K-theory assuming only the rudiments of
point-set topology and linear algebra. One of the features of the
treatment is that no use is made of ordinary homology or cohomology
theory. In fact, rational cohomology is defined in terms of
K-theory.The theory is taken as far as the solution of the Hopf
invariant problem and a start is mode on the J-homomorphism. In
addition to the lecture notes proper, two papers of mine published
since 1964 have been reproduced at the end. The first, dealing with
operations, is a natural supplement to the material in Chapter III.
It provides an alternative approach to operations which is less
slick but more fundamental than the Grothendieck method of Chapter
III, and it relates operations and filtration. Actually, the
lectures deal with compact spaces, not cell-complexes, and so the
skeleton-filtration does not figure in the notes. The second paper
provides a new approach to K-theory and so fills an obvious gap in
the lecture notes.
This book grew out of a course of lectures given to third year
undergraduates at Oxford University and it has the modest aim of
producing a rapid introduction to the subject. It is designed to be
read by students who have had a first elementary course in general
algebra. On the other hand, it is not intended as a substitute for
the more voluminous tracts such as Zariski-Samuel or Bourbaki. We
have concentrated on certain central topics, and large areas, such
as field theory, are not touched. In content we cover rather more
ground than Northcott and our treatment is substantially different
in that, following the modern trend, we put more emphasis on
modules and localization.
Although the Fields Medal does not have the same public recognition
as the Nobel Prizes, they share a similar intellectual standing. It
is restricted to one field - that of mathematics - and an age limit
of 40 has become an accepted tradition. Mathematics has in the main
been interpreted as pure mathematics, and this is not so
unreasonable since major contributions in some applied areas can be
(and have been) recognized with Nobel Prizes. The restriction to 40
years is of marginal significance, since most mathematicians have
made their mark long before this age.A list of Fields Medallists
and their contributions provides a bird's eye view of mathematics
over the past 60 years. It highlights the areas in which, at
various times, greatest progress has been made. This volume does
not pretend to be comprehensive, nor is it a historical document.
On the other hand, it presents contributions from 22 Fields
Medallists and so provides a highly interesting and varied
picture.The contributions themselves represent the choice of the
individual Medallists. In some cases the articles relate directly
to the work for which the Fields Medals were awarded. In other
cases new articles have been produced which relate to more current
interests of the Medallists. This indicates that while Fields
Medallists must be under 40 at the time of the award, their
mathematical development goes well past this age. In fact the age
limit of 40 was chosen so that young mathematicians would be
encouraged in their future work.The Fields Medallists' Lectures is
now available on CD-ROM. Sections can be accessed at the touch of a
button, and similar topics grouped together using advanced keyword
searches.
Although the Fields Medal does not have the same public recognition
as the Nobel Prizes, they share a similar intellectual standing. It
is restricted to one field - that of mathematics - and an age limit
of 40 has become an accepted tradition. Mathematics has in the main
been interpreted as pure mathematics, and this is not so
unreasonable since major contributions in some applied areas can be
(and have been) recognized with Nobel Prizes. The restriction to 40
years is of marginal significance, since most mathematicians have
made their mark long before this age.A list of Fields Medallists
and their contributions provides a bird's eye view of mathematics
over the past 60 years. It highlights the areas in which, at
various times, greatest progress has been made. This volume does
not pretend to be comprehensive, nor is it a historical document.
On the other hand, it presents contributions from 22 Fields
Medallists and so provides a highly interesting and varied
picture.The contributions themselves represent the choice of the
individual Medallists. In some cases the articles relate directly
to the work for which the Fields Medals were awarded. In other
cases new articles have been produced which relate to more current
interests of the Medallists. This indicates that while Fields
Medallists must be under 40 at the time of the award, their
mathematical development goes well past this age. In fact the age
limit of 40 was chosen so that young mathematicians would be
encouraged in their future work.The Fields Medallists' Lectures is
now available on CD-ROM. Sections can be accessed at the touch of a
button, and similar topics grouped together using advanced keyword
searches.
Although the Fields Medal does not have the same public recognition
as the Nobel Prizes, they share a similar intellectual standing. It
is restricted to one field - that of mathematics. The medal is
awarded to the best mathematicians who are 40 or younger, every
four years.A list of Fields Medallists and their contributions
provides a bird's-eye view of the major developments in mathematics
over the past 80 years. It highlights the areas in which, at
various times, the greatest progress has been made.The third
edition of Fields Medallists' Lectures features additional
contributions from: John W Milnor (1962), Enrico Bombieri (1974),
Gerd Faltings (1986), Andrei Okounkov (2006), Terence Tao (2006),
Cedric Villani (2010), Elon Lindenstrauss (2010), Ngo Bao Chau
(2010), Stanislav Smirnov (2010).
Although the Fields Medal does not have the same public recognition
as the Nobel Prizes, they share a similar intellectual standing. It
is restricted to one field - that of mathematics. The medal is
awarded to the best mathematicians who are 40 or younger, every
four years.A list of Fields Medallists and their contributions
provides a bird's-eye view of the major developments in mathematics
over the past 80 years. It highlights the areas in which, at
various times, the greatest progress has been made.The third
edition of Fields Medallists' Lectures features additional
contributions from: John W Milnor (1962), Enrico Bombieri (1974),
Gerd Faltings (1986), Andrei Okounkov (2006), Terence Tao (2006),
Cedric Villani (2010), Elon Lindenstrauss (2010), Ngo Bao Chau
(2010), Stanislav Smirnov (2010).
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Idempotency (Paperback)
Jeremy Gunawardena; Foreword by John M Taylor, Michael Atiyah
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R1,913
Discovery Miles 19 130
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Ships in 10 - 15 working days
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Certain nonlinear optimization problems arise in such areas as the
theory of computation, pure and applied probability, and
mathematical physics. These problems can be solved through linear
methods, providing the usual number system is replaced with one
that satisfies the idempotent law. Only recently has a systematic
study of idempotency analysis emerged, triggered in part by a
workshop organized by Hewlett-Packard's Basic Research Institute in
the Mathematical Sciences (BRIMS), which brought together for the
first time many leading researchers in the area. This volume, a
record of that workshop, includes a variety of contributions, a
broad introduction to idempotency, written especially for the book,
and a bibliography of the subject. It is the most up-to-date survey
currently available of research in this developing area of
mathematics; the articles cover both practical and more theoretical
considerations, making it essential reading for all workers in the
area.
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Idempotency (Hardcover)
Jeremy Gunawardena; Foreword by John M Taylor, Michael Atiyah
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R4,567
Discovery Miles 45 670
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Ships in 10 - 15 working days
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Certain nonlinear optimization problems arise in such areas as the theory of computation, pure and applied probability, and mathematical physics. These problems can be solved through linear methods, providing the usual number system is replaced with one that satisfies the idempotent law. Only recently has a systematic study of idempotency analysis emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together for the first time many leading researchers in the area. This volume, a record of that workshop, includes a variety of contributions, a broad introduction to idempotency, written especially for the book, and a bibliography of the subject. It is the most up-to-date survey currently available of research in this developing area of mathematics; the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.
Deals with an area of research that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.
Although the Fields medal does not have the same public recognition
as the Nobel prizes, they share a similar intellectual standing. It
is restricted to one field - that of mathematics - and an age limit
of 40 has become an accepted tradition. Mathematics has in the main
been interpreted as pure mathematics, and this is not so
unreasonable since major contributions in some applied areas can
(and have been) recognized with Nobel prizes. The restriction to 40
years is of marginal significance, since most mathematicians have
made their mark long before this age. A list of Fields medallists
and their contributions provide an overview of mathematics over the
past 60 years. It highlights the areas in which, at various times,
greatest progress has been made. This CD-ROM does not pretend to be
comprehensive, nor is it an historical document. On the other hand,
it presents contributions from 22 Fields medallists and so provides
a highly interesting and varied picture. The contributions
themselves represent the choice of the individual medallists. In
some cases the articles relate directly to the work for which the
Fields medals were awarded. In other cases new articles have been
produced which relate to more current interests of the medallists.
This indicates that while Fields medallists must be under 40 at the
time of the award, their mathematical development goes well past
this age. In fact the age limit of 40 was chosen so that young
mathematicians would be encouraged in their future work.
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