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001 978-0-8176-8092-3
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020 _a9780817680923
_9978-0-8176-8092-3
024 7 _a10.1007/978-0-8176-8092-3
_2doi
050 4 _aQA164-167.2
072 7 _aPBV
_2bicssc
072 7 _aMAT036000
_2bisacsh
082 0 4 _a511.6
_223
100 1 _aSoifer, Alexander.
_eeditor.
245 1 0 _aRamsey Theory
_h[electronic resource] :
_bYesterday, Today, and Tomorrow /
_cedited by Alexander Soifer.
250 _a1.
264 1 _aBoston, MA :
_bBirkhäuser Boston :
_bImprint: Birkhäuser,
_c2011.
300 _aXIV, 190p. 28 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics ;
_v285
505 0 _aHow This Book Came into Being -- Table of Contents -- Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts -- Eighty Years of Ramsey R(3, k). . . and Counting! -- Ramsey Numbers Involving Cycles -- On the function of Erdὅs and Rogers -- Large Monochromatic Components in Edge Colorings of Graphs -- Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications -- Open Problems in Euclidean Ramsey Theory -- Chromatic Number of the Plane and Its Relatives, History, Problems and Results: An Essay in 11 Parts -- Euclidean Distance Graphs on the Rational Points -- Open Problems Session.
520 _aRamsey theory is a relatively “new,” approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible. Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike. Contributors: J. Burkert, A. Dudek, R.L. Graham, A. Gyárfás, P.D. Johnson, Jr., S.P. Radziszowski, V. Rödl, J.H. Spencer, A. Soifer, E. Tressler.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aCombinatorics.
650 0 _aDiscrete groups.
650 1 4 _aMathematics.
650 2 4 _aCombinatorics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aConvex and Discrete Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817680916
830 0 _aProgress in Mathematics ;
_v285
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8092-3
912 _aZDB-2-SMA
999 _c105090
_d105090