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The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.
It wasnt that uncommon for kids from the Baby Boomer generation to have big dreams. Growing up during the Happy Days of the 1950 era in sunny Los Angeles, California, we listened to Judy sing Somewhere Over The Rainbow knowing in our hearts we would find our pot of gold someday. Similar to the dreams of American pioneers traveling west in their covered wagons to California in search for gold, many spiritual pioneers are making a new journey in a different direction.
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