Friday, April 19, 2013

A Walk Through Combinatorics 3rd Edition, Miklos Bona

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory 3rd Edition PDF Download Ebook. Miklos Bona encourages students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time.

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate.

The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.

The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.

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