New Perspectives in Algebraic Combinatorics
by Louis J. Billera, at al.
Publisher: Cambridge University Press 1999
Number of pages: 345
The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which contains expository contributions by some of the most respected researchers in the field. It will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.
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by Gian-Carlo Rota
In 1998, Gian-Carlo Rota gave his famous course at MIT. John N. Guidi took notes in a verbatim manner conveying the substance of the course. Topics covered included sets, relations, enumeration, order, matching, matroids, and geometric probability.
by Klaus Truemper - Leibniz
Matroids were introduced in 1935 as an abstract generalization of graphs and matrices. Matroid decomposition covers the area of the theory dealing with decomposition and composition of matroids. The exposition is clear and simple.
by Richard P. Stanley - MIT
The standard guide to the topic for students and experts alike. The material in Volume 1 was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics.
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This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.