Ebook: Ramsey Theory: Yesterday, Today, and Tomorrow

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.

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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. Gy?rf?s, P.D. Johnson, Jr., S.P. Radziszowski, V. R?dl, J.H. Spencer, A. Soifer, E. Tressler.

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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. Gy?rf?s, P.D. Johnson, Jr., S.P. Radziszowski, V. R?dl, J.H. Spencer, A. Soifer, E. Tressler.
Content:
Front Matter....Pages i-xiv
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts....Pages 1-26
Eighty Years of RamseyR(3, k)…and Counting!....Pages 27-39
Ramsey Numbers Involving Cycles....Pages 41-62
On the Function of Erd?s and Rogers....Pages 63-76
Large Monochromatic Components in Edge Colorings of Graphs: A Survey....Pages 77-96
Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications....Pages 97-113
Open Problems in Euclidean Ramsey Theory....Pages 115-120
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts ....Pages 121-161
Euclidean Distance Graphs on the Rational Points....Pages 163-176
Open Problems Session....Pages 177-189

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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. Gy?rf?s, P.D. Johnson, Jr., S.P. Radziszowski, V. R?dl, J.H. Spencer, A. Soifer, E. Tressler.
Content:
Front Matter....Pages i-xiv
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts....Pages 1-26
Eighty Years of RamseyR(3, k)…and Counting!....Pages 27-39
Ramsey Numbers Involving Cycles....Pages 41-62
On the Function of Erd?s and Rogers....Pages 63-76
Large Monochromatic Components in Edge Colorings of Graphs: A Survey....Pages 77-96
Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications....Pages 97-113
Open Problems in Euclidean Ramsey Theory....Pages 115-120
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts ....Pages 121-161
Euclidean Distance Graphs on the Rational Points....Pages 163-176
Open Problems Session....Pages 177-189
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