Atnaujinkite slapukų nuostatas

El. knyga: Ramsey Theory: Yesterday, Today, and Tomorrow

2.00/5 (2 ratings by Goodreads)
Edited by
  • Formatas: PDF+DRM
  • Serija: Progress in Mathematics 285
  • Išleidimo metai: 29-Oct-2010
  • Leidėjas: Birkhauser Boston Inc
  • Kalba: eng
  • ISBN-13: 9780817680923
Kitos knygos pagal šią temą:
Ramsey Theory: Yesterday, Today, and TomorrowDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Progress in Mathematics 285
  • Išleidimo metai: 29-Oct-2010
  • Leidėjas: Birkhauser Boston Inc
  • Kalba: eng
  • ISBN-13: 9780817680923
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

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 theorys 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.

Recenzijos

As we learn from the preface, [ Ramsey Theory: Yesterday, Today and Tomorrow] grew out of an intentionally non-traditional conference on Ramsey theory. In accordance with that, the book itself is far from being a traditional textbook or reference book on the subjectWe learn far more about the history of Ramsey theory than from other sourcesthe promise of discussing the future is fulfilled by a very extensive list of open problems contributed by numerous participants. Sometimes it is not even clear what the best way of asking a certain question is, and we are shown the raw form of the problem, just as we would if we participated at a conferencethe book is undoubtedly a lot of fun. As one expects from a book on Ramsey theory, it is full of problems that are very easy to formulate, but terribly hard to solve[ the book] could well be used for a course using a seminar format, or for self-study by a graduate student familiarizing himself with the subject.      MAA Reviews

What This Book Is About and How It Came into Being vii
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts
1(26)
Alexander Soifer
1 Overture
1(1)
2 David Hilbert's 1892 Cube Lemma
2(1)
3 The Issai Schur 1916 Theorem
3(4)
4 The Baudet-Schur-Van der Waerden 1927 Theorem
7(1)
5 The Generalized 1928 Schur Theorem
8(1)
6 The Frank Plumpton Ramsey Principle
9(2)
7 The Paul, Gjorgy, and Esther Happy End Problem
11(3)
8 Richard Rado's Regularity
14(3)
9 Density and Arithmetic Progressions
17(5)
10 The Tibor Gallai Theorem
22(1)
11 De Bruijn-Erdos's 1951 Compactness Theorem
23(1)
12 Khinchin's Small Book of Big Impact
23(1)
13 Long Live the Young Theory!
24(3)
References
25(2)
Eighty Years of Ramsey R(3, k)...and Counting!
27(14)
Joel Spencer
1 Basics
27(1)
2 George, Esther, Paul
28(1)
3 Erdos Magic
29(1)
4 An Erdos Gem
30(1)
5 Upper Bounds
31(2)
6 The Lovasz Local Lemma
33(1)
7 Random Greedy Triangle-Free
34(1)
8 R(3, k) Resolved!
35(1)
9 Random Greedy Triangle-Free Redux
36(2)
10 Epilogue
38(3)
References
38(3)
Ramsey Numbers Involving Cycles
41(22)
Stanislaw P. Radziszowski
1 Scope and Notation
41(1)
2 Two-Color Numbers Involving Cycles
42(8)
2.1 Cycles
43(1)
2.2 Cycles Versus Complete Graphs
44(2)
2.3 Cycles Versus Wheels
46(1)
2.4 Cycles Versus Books
47(2)
2.5 Cycles Versus Other Graphs
49(1)
3 Multicolor Numbers for Cycles
50(5)
3.1 Three Colors
50(3)
3.2 More Colors
53(1)
3.3 Cycles Versus Other Graphs
54(1)
4 Hypergraph Numbers for Cycles
55(8)
References
56(7)
On the Function of Erdos and Rogers
63(14)
Andrzej Dudek
Vojtech Rodl
1 Introduction
63(1)
2 The Most Restrictive Case
64(5)
2.1 Proof of ƒs, s+1(n) ≤ O(n1-1/o(s4log s)) [ 1]
65(2)
2.2 Proof of Ω(n1/2) ≤ƒs, s+1(n) for s ≥2 [ 2]
67(1)
2.3 Proof of ƒs, s+1(n) ≤O(n2/3) for s ≥ 2[ 4]
67(2)
3 General Bounds
69(6)
3.1 Proof of Ω(nak(s)) ≤ƒs, s+k(n) [ 14, 15]
71(2)
3.2 Sketch of the Proof of ƒs, s+k(n)≤ O(n((k+1)/(2k+1))+ε) for s≥so =so(ε, k) [ 4]
73(2)
4 Concluding Remarks
75(2)
References
75(2)
Large Monochromatic Components in Edge Colorings of Graphs: A Survey
77(20)
Andras Gyarfas
1 Introduction
77(2)
1.1 A Remark of Erdos and Rado and Its Extension
77(1)
1.2 Colorings from Affine Planes
78(1)
1.3 Extending Colorings by Substitutions
79(1)
2 2-Colorings
79(4)
2.1 Type of Spanning Trees, Connectivity, Diameter
79(3)
2.2 Gallai-Colorings: Substitutions to 2-Colorings
82(1)
3 Multicolorings: Basic Results and Proof Methods
83(6)
3.1 Complete Bipartite Graphs: Counting Double Stars
83(2)
3.2 Fractional Transversals: Furedi's Method
85(1)
3.3 Fine Tuning
85(1)
3.4 When Both Methods Work: Local Colorings
86(2)
3.5 Hypergraphs
88(1)
4 Multicolorings: Type of Components
89(1)
4.1 Components with Large Matching
89(1)
4.2 Double Stars
90(1)
5 Variations
90(7)
5.1 Vertex-Coverings by Components
91(1)
5.2 Coloring by Group Elements
91(1)
5.3 Coloring Geometric Graphs
91(1)
5.4 Coloring Noncomplete Graphs
92(2)
References
94(3)
Szlam's Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications
97(18)
Jeffrey Burkert
Peter Johnson, Jr.
1 1973: A Volcano Erupts
97(1)
2 Some Definitions and More Background
98(3)
3 What Happened to the Rather Red Coloring Problem from 1973?
101(1)
4 Distance Graphs
102(2)
5 Szlam's Lemma, a Connection Between Rather Red Colorings and Chromatic Numbers
104(3)
6 van der Waerden Numbers, Cyclic van der Waerden Numbers, and a Lower Bound on Them Both
107(8)
References
112(3)
Open Problems in Euclidean Ramsey Theory
115(6)
Ron Graham
Eric Tressler
1 Introduction
115(2)
2 Ramsey Sets
117(1)
3 Unit Distance Graphs
117(2)
4 More General Distance Graphs
119(2)
References
119(2)
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts
121(42)
Alexander Soifer
1 The Problem
121(3)
2 The History
124(11)
3 Polychromatic Number of the Plane & Results Near the Lower Bound
135(3)
4 De Bruijn-Erdos Reduction to Finite Sets and Results Near the Lower Bound
138(3)
5 Polychromatic Number of the Plane & Results Near the Upper Bound
141(3)
6 Continuum of 6-Colorings of the Plane
144(4)
7 Chromatic Number of the Plane in Special Circumstances
148(1)
8 Colored Space
149(2)
9 Rational Coloring
151(2)
10 Axioms of Set Theory and the Chromatic Number of Graphs
153(3)
11 Predicting the Future
156(7)
References
157(6)
Euclidean Distance Graphs on the Rational Points
163(14)
Peter Johnson, Jr.
1 Definitions
163(1)
2 The Search for Χ(Rn, 1) Leads to the Search for Χ(Qn, 1)
164(3)
3 Distances Other Than 1?
167(5)
4 Problems
172(5)
References
174(3)
Open Problems Session
177
1 Problems Submitted
179(1)
William Gasarch
2 Problems Submitted
180(2)
Peter Johnson, Jr.
3 Problems on Topological Stability of Chromatic Numbers Submitted
182(1)
Dmytro Karabash
4 Problem on the Gallai-Ramsey Structure, Submitted
183(2)
Colton Magnant
5 Problems Involving Triangles, Submitted
185(4)
Stanislaw P. Radziszowski
6 Problems on Chromatic Number of the Plane and Its Relatives, Submitted
189
Alexander Soifer
Alexander Soifer is a Russian born and educated American mathematician, a professor of mathematics at the University of Colorado, an author of some 200 articles on mathematics, history of mathematics, mathematics education, film reviews, etc. He is Senior Vice President of the World Federation of National Mathematics Competitions, which in 2006 awarded him The Paul Erdos Award. 26 years ago Soifer founded and has since chaired the Colorado Mathematical Olympiad, and served on both the USSR and USA Mathematical Olympiads committees. Soifer's Erdos number is 1.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97808176809232e.html
Raktažodžiai: