000 | 03614nam a22004935i 4500 | ||
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001 | 978-0-8176-8092-3 | ||
003 | DE-He213 | ||
005 | 20140220083711.0 | ||
007 | cr nn 008mamaa | ||
008 | 101029s2011 xxu| s |||| 0|eng d | ||
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_a9780817680923 _9978-0-8176-8092-3 |
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024 | 7 |
_a10.1007/978-0-8176-8092-3 _2doi |
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050 | 4 | _aQA164-167.2 | |
072 | 7 |
_aPBV _2bicssc |
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072 | 7 |
_aMAT036000 _2bisacsh |
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082 | 0 | 4 |
_a511.6 _223 |
100 | 1 |
_aSoifer, Alexander. _eeditor. |
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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. |
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300 |
_aXIV, 190p. 28 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aProgress in Mathematics ; _v285 |
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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 |