Faculty Book: Alexander Kheyfits
A Primer in Combinatorics
(De Gruyter, 2010)
This textbook on combinatorics and graph theory, cornerstones of discrete mathematics, systematically employs the basic language of set theory. This approach is often useful for solving combinatorial problems, especially problems where one has to identify some objects, and significantly reduces the number of students’ errors. The book uses simple model problems to begin every section. Following their detailed analysis, the reader is led through the derivation of definitions, concepts, and methods for solving typical problems. Theorems are then formulated, proved, and illustrated by more problems of increasing difficulty. Topics covered include elementary combinatorial constructions, graphs and trees, hierarchical clustering algorithms, more advanced counting techniques, and existence theorems in combinatorial analysis. The textbook is suitable for undergraduate and entry-level graduate students as well as for self-education. Alexander Kheyfits (Assoc. Prof., Bronx Community) is on the doctoral faculty in physics.
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Submitted on: MAY 1, 2010