AaronRobertson
Fundamentals of Ramsey Theory
Fundamentals of Ramsey Theory
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- More about Fundamentals of Ramsey Theory
The author presents a contemporary overview of Ramsey theory, covering all main results and introducing new topics. The book is accessible and reader-friendly, with a focus on motivation and discussion. It includes exercises and applications and is intended for students and mathematicians interested in learning about Ramsey theory.
Format: Hardback
Length: 241 pages
Publication date: 18 June 2021
Publisher: Taylor & Francis Ltd
Ramsey theory is a captivating subject that the author explores in this modern overview. He offers insights from various angles, incorporating intuition and intricate proofs, in a manner that sets this book apart from most others on the topic. This comprehensive guide encompasses all significant results in Ramsey theory, as well as previously unpublished findings.
The presentation is both thorough and user-friendly, making it accessible to readers of all levels. The book delves into integer, graph, and Euclidean Ramsey theory, employing numerous combinatorial proofs. Rather than merely presenting a sequence of theorems and proofs, the author actively motivates topics and discussions to engage the reader. Each chapter includes a section of exercises to further enhance the learning experience.
This up-to-date book presents Ramsey theory from multiple perspectives, allowing readers to choose the flavor that resonates with them best. Additionally, the book offers:
A chapter exploring diverse approaches to Ramsey theory, such as utilizing topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of integers.
A chapter dedicated to the probabilistic method, as it plays a pivotal role in Ramsey-type numbers.
A unique chapter highlighting applications of Ramsey theory.
Exercises in each chapter to reinforce understanding and application of the material.
The intended audience for this book consists of students and mathematicians eager to delve into the world of Ramsey theory. A foundational undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a course in combinatorics are assumed.
A preface, list of figures, list of tables, symbols, 1. Introduction, 2. Integer Ramsey Theory, 3. Graph Ramsey Theory, 4. Euclidean Ramsey Theory, 5. Other Approaches to Ramsey Theory, 6. The Probabilistic Method, 7. Applications, 8. Bibliography, and 9. Index are included to enhance the reading experience.
Weight: 528g
Dimension: 164 x 241 x 26 (mm)
ISBN-13: 9781138364332
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