From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1

This volume is a collection of survey papers in combinatorics that have grown out of lectures given in the workshop on Probabilistic Combinatorics at the Paul Erdös Summer Research Center in Mathematics in Budapest. The papers, reflecting the many facets of modern-day combinatorics, will be appreciated by specialists and general mathematicians alike: assuming relatively little background, each paper gives a quick introduction to an active area, enabling the reader to learn about the fundamental results and appreciate some of the latest developments. An important feature of the articles, very much in the spirit of Erdös, is the abundance of open problems.

Product Description: Can a Christian escape from a lion? How quickly can a rumor spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear...read more

Product Description: Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling...read more

Product Description: The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory...read more

This is a new edition of a now classic text. The addition of two new sections, numerous new results and over 150 references mean that this represents an up-to-date account of random graph theory. Suitable for mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. (view table of contents)

This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging. (view table of contents)

Product Description: The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics...read more (view table of contents, read Amazon.com's description)

Product Description: Combinatorics has not been an established branch of mathematics for very long: the last quarter of a century has seen an explosive growth in the subject. This growth has been largely due to the doyen of combinatorialists, Paul Erdos, whose penetrating insight and insatiable curiosity has provided a huge stimulus for workers in the field...read more

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Product 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...read more