Fundamentals of Ramsey theory
- Boca Raton : CRC Press, 2021
- xiii, 241 p.; ill., 24 cm
- Discrete mathematics and its applications .
Includes bibliographical references and index.
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 chapter The 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.
9781138364332
Combinatorics Aruoutov-Folkman-Rado-Sanders' theorem Bonferroni inequalities Compactness principle de Bruijn-Erdos theorem Erdos-Ko-Rado theorem Euler's formula Fermat's last theorem Hindman's theorem Infinite Ramsey theorem Krylov-Bogoliubov theorem Lefmann's theorem Multiple Birkoff Recurrence theorem Redo's theorem for powers Steiner system Tychonoff's theorem Van der Waerden's theorem