Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability 1st Edition by Bela Bollobas (PDF)

Description

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is the book from which I learnt Combinatorics the Erdosian way. One of the most pleasing qualities of the book is the bite-sized chapters. Perhaps this is one of the first books to start this trend.An earlier reviewer mentions the Ramsey theory chapter which I too would recommend. The chapters on Intersecting hypergraphs, Kruskal-Katona theorem, Littlewood–Offord problem, Four–functions theorem are other gems which come to mind readily. The proofs are crisp and the way the theorems are motivated means that they are not too demanding for a beginning graduate.This is the best and fastest introduction to the way Hungarian Combinatorists operate. An indispensable addition to any aspiring Combinatorist’s book shelf.

⭐This book provides an excellent introduction to a wide variety of extremely active areas of combinatorics. It focuses on the “gems” of the field — proofs and results which are simultaneously deep, central, and beautiful. One particular feature is the section on infinte Ramsey theory which presents this beautiful but taxing area in an exceptionally clear fashion. There are many good exercises.

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