TY - BOOK ID - 14301966 TI - Ramsey theory : yesterday, today, and tomorrow PY - 2011 SN - 0817680918 9786612973673 1282973673 0817680926 PB - New York : Springer, DB - UniCat KW - Graph coloring. KW - Graph theory. KW - Mathematics. KW - Ramsey numbers. KW - Ramsey theory -- History. KW - Ramsey theory. KW - Ramsey theory KW - Ramsey numbers KW - Graph theory KW - Graph coloring KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebra KW - History KW - Dynamics. KW - Ergodic theory. KW - Convex geometry. KW - Discrete geometry. KW - Combinatorics. KW - Dynamical Systems and Ergodic Theory. KW - Convex and Discrete Geometry. KW - Combinatorial analysis KW - Differentiable dynamical systems. KW - Discrete groups. KW - Groups, Discrete KW - Infinite groups KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Combinatorics KW - Mathematical analysis KW - Discrete mathematics KW - Convex geometry . KW - Geometry KW - Combinatorial geometry KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14301966 AB - Ramsey 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. ER -