|
Showing 1 - 4 of
4 matches in All Departments
This elegant little book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries. Many famous mathematicians have worked on the problem, but the proof eluded fomulation until the 1950s, when it was finally cracked with a brute-force approach using a computer. The book begins by discussing the history of the problem, and then goes into the mathematics, both pleasantly enough that anyone with an elementary knowledge of geometry can follow it, and still with enough rigor that a mathematician can also read it with pleasure. The authors discuss the mathematics as well as the philosophical debate that ensued when the proof was announced: Just what is a mathematical proof, if it takes a computer to provide one -- and is such a thing a proof at all?
This book describes the construction and the properties of
CW-complexes. These spaces are important because firstly they are
the correct framework for homotopy theory, and secondly most spaces
that arise in pure mathematics are of this type. The authors
discuss the foundations and also developments, for example, the
theory of finite CW-complexes, CW-complexes in relation to the
theory of fibrations, and Milnor's work on spaces of the type of
CW-complexes. They establish very clearly the relationship between
CW-complexes and the theory of simplicial complexes, which is
developed in great detail. Exercises are provided throughout the
book; some are straightforward, others extend the text in a
non-trivial way. For the latter; further reference is given for
their solution. Each chapter ends with a section sketching the
historical development. An appendix gives basic results from
topology, homology and homotopy theory. These features will aid
graduate students, who can use the work as a course text. As a
contemporary reference work it will be essential reading for the
more specialized workers in algebraic topology and homotopy theory.
This book discusses a famous problem that helped to define the
field now known as topology: What is the minimum number of colors
required to print a map so that no two adjoining countries have the
same color? This problem remained unsolved until the 1950s, when it
was finally cracked using a computer. This book discusses the
history and mathematics of the problem, as well as the
philosophical debate which ensued, regarding the validity of
computer generated proofs.
This book describes the construction and the properties of
CW-complexes. These spaces are important because firstly they are
the correct framework for homotopy theory, and secondly most spaces
that arise in pure mathematics are of this type. The authors
discuss the foundations and also developments, for example, the
theory of finite CW-complexes, CW-complexes in relation to the
theory of fibrations, and Milnor's work on spaces of the type of
CW-complexes. They establish very clearly the relationship between
CW-complexes and the theory of simplicial complexes, which is
developed in great detail. Exercises are provided throughout the
book; some are straightforward, others extend the text in a
non-trivial way. For the latter; further reference is given for
their solution. Each chapter ends with a section sketching the
historical development. An appendix gives basic results from
topology, homology and homotopy theory. These features will aid
graduate students, who can use the work as a course text. As a
contemporary reference work it will be essential reading for the
more specialized workers in algebraic topology and homotopy theory.
|
You may like...
Hampstead
Diane Keaton, Brendan Gleeson, …
DVD
R66
Discovery Miles 660
|