Ramsey Theory on the Integers (Student Mathematical Library, Vol. 24) (Student Mathematical Library, V. 24)

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 something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. In addition to being the first truly accessible book on Ramsey theory, 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 subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike 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 Something Quite Rare For A Book At This Level: A Glimpse Into The World Of Mathematical Research And The Opportunity To Begin Pondering Unsolved Problems Themselves. This Book On Ramsey Theory, 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 Subarea Of Ramsey Theory. The Result Is A Book That Will Engage Students, Teachers, And Researchers Alike.--jacket. Ch. 1. Preliminaries -- Ch. 2. Van Der Waerden's Theorem -- Ch. 3. Supersets Of Ap -- Ch. 4. Subsets Of Ap -- Ch. 5. Other Generalizations Of W(k:r) -- Ch. 6. Arithmetic Progressions (mod M) -- Ch. 7. Other Variations On Van Der Waerden's Theorem -- Ch. 8. Schur's Theorem -- Ch. 9. Rado's Theorem -- Ch. 10. Other Topics. Bruce M. Landman, Aaron Robertson. Includes Bibliographical References (p. 297-313) And Index. 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 something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity to begin pondering unsolved problems themselves. In addition to being the first truly accessible book on Ramsey theory, 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 subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike. Landman and Robertson introduce students to mathematical research using the theory with the goal of providing them both basic tools and inspiration to set them on the path to their own research. They also offer a resource for mathematicians who are interested in the combinatorial or number theoretic This book investigates the significance of Wittgenstein's philosophy for aesthetic understanding.