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By Martin Grohe
This groundbreaking, yet accessible book contains original results on the interaction between graph theory and computational complexity using methods from finite model theory. As well as a wealth of new, previously unpublished results, the author also gives an account of the established results in the area.
Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, drawn from many years of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for...
By Josef Lauri
An in-depth coverage of selected areas of graph theory, focusing on symmetry properties of graphs. This second edition expands on several topics found in the first and is ideal for students wishing to learn the basic concepts. The broad collection of results provided also makes this book valuable to researchers.
By Robin Wilson
Combinatorics is a large branch of mathematics involving the counting, selecting, and arranging of objects. Robin Wilson explores the field, looking at problems such as the shortest routes from A to B, to the number of Sudoku puzzles possible.
By Gabor Lugosi
An accessible account of the rich theory surrounding concentration inequalities in probability theory, with applications from machine learning and statistics to high-dimensional geometry. This book introduces key ideas and presents a detailed summary of the state-of-the-art in the area, making it ideal for independent learning and as a reference.
Includes access to student companion website. Updated to align to the latest 2013 ACM/IEEE Computer Science curricula, Discrete Structures, Logic, and Computability, Fourth Edition is designed for the one- to two-term Discrete Mathematics course. The structure of the book supports the spiral method of learning, by first introducing basic information,...
Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers.
This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is...
By Joel Tropp
Offers an invitation to the field of matrix concentration inequalities. The book begins with some history of random matrix theory; describes a flexible model for random matrices that is suitable for many problems; and discusses the most important matrix concentration results.