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|a contents: Preface, Prolog:what this book is about, Notation, PART I:The classics, 1.Counting, 2.Advanced counting, 3.The principle, of inclusion and exclusion, 4.The pigeonhole principle, 5.Systems of distinct representatives, 6.Colorings, PART II:Extremal set theory, 7.Sunflowers, 8.Intersecting families, 9.Chains and antichains, 10.Blocking sets and the duality, 11.Density and universality, 12.Witness sets and isolation, 13.Designs, PART III:The linear algebra method, 14.The basic method, 15.Orthologonality and rank arguments, 16.Span programms, PART IV:The probabilistic method, 17.Basic tools, 18.Counting sieve, 19.The Lovasz Sieve, 20.Linearity of expectation, 21.The deletion method, 22.The second moment method, 23.The entropy function, 24.Random walks, 25.Randomized algorithms, 26.Derandomization, PART V:Fragments of ramsey theory, 27.Ramsey's theorem, 28.Ramseyan theorems for numbers, 29.The Hales-Jewett theorem, Epilog:what's next?, References, Name index, Subject index.
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