Aaron Robertson - Böcker

Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an “inequality” version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdos-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated.This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.

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.

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.

'Renewed my faith in the human power to resist, imagine and make new, better worlds.’ Susanna Crossman, author of Home Is Where We Start'Compelling' TLS How do the disillusioned, the forgotten, and the persecuted not merely hold on to life but expand its possibilities and preserve its beauty? What, in other words, does utopia look like in black?These questions animate Aaron Robertson’s exploration of Black Americans’ efforts to remake the conditions of their lives. Writing in the tradition of Saidiya Hartman and Ta-Nehisi Coates, Robertson makes his way from his ancestral hometown of Promise Land, Tennessee, to Detroit – the city where he was born, and where one of the country’s most remarkable Black utopian experiments got its start. Founded by the brilliant preacher Albert Cleage Jr., the Shrine of the Black Madonna combined Afrocentric Christian practice with radical social projects. Central to this endeavour was the Shrine’s chancel mural of a Black Virgin and child, the icon of a nationwide liberation movement that would come to be known as Black Christian Nationalism.Alongside the Shrine’s story, Robertson reflects on a diverse array of Black utopian visions, from the Reconstruction era through the countercultural fervour of the 1960s and 1970s and into the present day. By doing so, Robertson showcases the enduring quest of collectives and individuals for a world beyond the constraints of systemic racism.The Black Utopians is the story of a movement and of a world still in the making – one that points the way toward radical alternatives for the future.A TIME Book of the YearA New York Times Book of the Year

This volume contains selected refereed papers based on lectures presented at the ‘Integers Conference 2007’, an international conference in combinatorial number theory that was held in Carrollton, Georgia in October 2007.The proceedings include contributions from many distinguished speakers, including George Andrews, Neil Hindman, Florian Luca, Carl Pomerance, Ken Ono and Igor E. Shparlinski. Among the topics considered in these papers are additive number theory, multiplicative number theory, sequences, elementary number theory, theory of partitions, and Ramsey theory.

Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.

Elwyn Berlekamp, John Conway, and Richard Guy wrote ‘Winning Ways for your Mathematical Plays’ and turned a recreational mathematics topic into a full mathematical fi eld. They combined set theory, combinatorics, codes, algorithms, and a smattering of other fi elds, leavened with a liberal dose of humor and wit. Their legacy is a lively fi eld of study that still produces many surprises. Despite being experts in other areas of mathematics, in the 50 years since its publication, they also mentored, talked, and played games, giving their time, expertise, and guidance to several generations of mathematicians. This volume is dedicated to Elwyn Berlekamp, John Conway, and Richard Guy. It includes 20 contributions from colleagues that refl ect on their work in combinatorial game theory.