|
Showing 1 - 5 of
5 matches in All Departments
Topology is a relatively young and very important branch of
mathematics. It studies properties of objects that are preserved by
deformations, twistings, and stretchings, but not tearing. This
book deals with the topology of curves and surfaces as well as with
the fundamental concepts of homotopy and homology, and does this in
a lively and well-motivated way. There is hardly an area of
mathematics that does not make use of topological results and
concepts. The importance of topological methods for different areas
of physics is also beyond doubt. They are used in field theory and
general relativity, in the physics of low temperatures, and in
modern quantum theory. The book is well suited not only as
preparation for students who plan to take a course in algebraic
topology but also for advanced undergraduates or beginning
graduates interested in finding out what topology is all about. The
book has more than 200 problems, many examples, and over 200
illustrations.
by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian
and Kleinian I1'OUps are of Il'eat interest from at least two
points of view: history, of course, but also as an inspiration for
further mathematical proll'ess. The papers are historic as the
climax of the ceometric theory of functions initiated by Riemann,
and ideal representatives of the unity between analysis, ceometry,
topololY and alcebra which prevailed during the 1880's. The rapid
mathematical prOll'ess of the 20th century has been made at the
expense of unity and historical perspective, and if mathematics is
not to disintell'ate altogether, an effort must sometime be made to
find its , main threads and weave them tocether 81ain. Poincare's
work is an excellent example of this process, and may yet prove to
be at the core of a . new synthesis. Certainly, we are now able to
gather up , some of the loose ends in Poincare, and a broader
synthesis seems to be actually taking place in the work of
Thurston. The papers I have selected include the three Il'eat
memoirs in the first volumes of Acta Math. -tice, on* Fuchsian
groups, Fuchsian , functions, and Kleinian groups (Poincare [1882
a,b,1883]). These are the papers which made his reputation and they
include many results and proofs which are now standard. They are
preceded by an , unedited memoir written by Poincare in May 1880 at
the height of his , creative ferment.
Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not tearing. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. There is hardly an area of mathematics that does not make use of topological results and concepts. The importance of topological methods for different areas of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low temperatures, and in modern quantum theory. The book is well suited not only as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book has more than 200 problems, many examples, and over 200 illustrations.
by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian
and Kleinian I1'OUps are of Il'eat interest from at least two
points of view: history, of course, but also as an inspiration for
further mathematical proll'ess. The papers are historic as the
climax of the ceometric theory of functions initiated by Riemann,
and ideal representatives of the unity between analysis, ceometry,
topololY and alcebra which prevailed during the 1880's. The rapid
mathematical prOll'ess of the 20th century has been made at the
expense of unity and historical perspective, and if mathematics is
not to disintell'ate altogether, an effort must sometime be made to
find its , main threads and weave them tocether 81ain. Poincare's
work is an excellent example of this process, and may yet prove to
be at the core of a . new synthesis. Certainly, we are now able to
gather up , some of the loose ends in Poincare, and a broader
synthesis seems to be actually taking place in the work of
Thurston. The papers I have selected include the three Il'eat
memoirs in the first volumes of Acta Math. -tice, on* Fuchsian
groups, Fuchsian , functions, and Kleinian groups (Poincare [1882
a,b,1883]). These are the papers which made his reputation and they
include many results and proofs which are now standard. They are
preceded by an , unedited memoir written by Poincare in May 1880 at
the height of his , creative ferment.
|
|