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Fundamentals of Ramsey Theory

Robertson Aaron
Heftet / 2024 / Engelsk

Produktdetaljer

ISBN
9781032018027
Publisert
2024-08-26
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
470 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
G, 01
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
241

Forfatter
Robertson Aaron

Biographical note

Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.

Fundamentals of Ramsey Theory

Robertson Aaron
Heftet / 2024 / Engelsk
Robertson Aaron
Heftet / 2024 / Engelsk
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Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before.The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises.This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapterThe intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTSPrefaceList of FiguresList of TablesSymbols1. Introduction2. Integer Ramsey Theory3. Graph Ramsey Theory4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography IndexBiographyAaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Les mer
This up-to-date book introduces the field of Ramsey theory from several different viewpoints. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs.
Les mer
1. Introduction. 1.1. What is Ramsey Theory? 1.2. Notations and Conventions. 1.3. Prerequisites. 1.4. Compactness Principle. 1.5. Set Theoretic Considerations. 1.6. Exercises. 2. Integer Ramsey Theory. 2.1. Van der Waerden's Theorem. 2.2. Equations. 2.3. Hales-Jewett Theorem. 2.4. Finite Sums. 2.5. Density Results. 2.6. Exercises. 3. Graph Ramsey Theory. 3.1. Complete Graphs. 3.2. Other Graphs. 3.3. Hypergraphs. 3.4. Infinite Graphs. 3.5. Comparing Ramsey and van der Waerden Results. 3.6. Exercises. 4. Euclidean Ramsey Theory. 4.1. Polygons. 4.2. Chromatic Number of the Plane. 4.3. Four Color Map Theorem. 4.4. Exercises. 5. Other Approaches to Ramsey Theory. 5.1. Topological Approaches. 5.2. Ergodic Theory. 5.3. Stone-Čech Compactification. 5.4. Additive Combinatorics Methods. 5.5. Exercises. 6. The Probabilistic Method. 6.1. Lower Bounds on Ramsey, van der Waerden, and Hales-Jewett Numbers. 6.2. Turán's Theorem. 6.3. Almost-surely van der Waerden and Ramsey Numbers. 6.4. Lovász Local Lemma. 6.5. Exercises. 7. Applications. 7.1. Fermat's Last Theorem. 7.2. Encoding Information. 7.3. Data Mining. 7.4. Exercises. Bibliography. Index.
Les mer

Relaterte produkter

Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before.The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises.This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapterThe intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTSPrefaceList of FiguresList of TablesSymbols1. Introduction2. Integer Ramsey Theory3. Graph Ramsey Theory4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography IndexBiographyAaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Les mer
This up-to-date book introduces the field of Ramsey theory from several different viewpoints. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs.
Les mer
1. Introduction. 1.1. What is Ramsey Theory? 1.2. Notations and Conventions. 1.3. Prerequisites. 1.4. Compactness Principle. 1.5. Set Theoretic Considerations. 1.6. Exercises. 2. Integer Ramsey Theory. 2.1. Van der Waerden's Theorem. 2.2. Equations. 2.3. Hales-Jewett Theorem. 2.4. Finite Sums. 2.5. Density Results. 2.6. Exercises. 3. Graph Ramsey Theory. 3.1. Complete Graphs. 3.2. Other Graphs. 3.3. Hypergraphs. 3.4. Infinite Graphs. 3.5. Comparing Ramsey and van der Waerden Results. 3.6. Exercises. 4. Euclidean Ramsey Theory. 4.1. Polygons. 4.2. Chromatic Number of the Plane. 4.3. Four Color Map Theorem. 4.4. Exercises. 5. Other Approaches to Ramsey Theory. 5.1. Topological Approaches. 5.2. Ergodic Theory. 5.3. Stone-Čech Compactification. 5.4. Additive Combinatorics Methods. 5.5. Exercises. 6. The Probabilistic Method. 6.1. Lower Bounds on Ramsey, van der Waerden, and Hales-Jewett Numbers. 6.2. Turán's Theorem. 6.3. Almost-surely van der Waerden and Ramsey Numbers. 6.4. Lovász Local Lemma. 6.5. Exercises. 7. Applications. 7.1. Fermat's Last Theorem. 7.2. Encoding Information. 7.3. Data Mining. 7.4. Exercises. Bibliography. Index.
Les mer

Produktdetaljer

ISBN
9781032018027
Publisert
2024-08-26
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
470 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
G, 01
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
241

Forfatter
Robertson Aaron

Biographical note

Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.

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