A Textbook of Discrete Mathematics, Harish Mittal, Vinay Kumar Goyal, Deepak Kumar Goyal

Автор: Baik Jinho
Название: Combinatorics and Random Matrix Theory
ISBN: 0821848410 ISBN-13(EAN): 9780821848418
Издательство: Mare Nostrum (Eurospan)
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Цена: 112860.00 T
Наличие на складе: Нет в наличии.
Описание: Over the last fifteen years a variety of problems in combinatorics has been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a ``stochastic special function theory'' for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail.Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Автор: Karlin, Anna R.
Название: Game theory, alive /
ISBN: 1470419823 ISBN-13(EAN): 9781470419820
Издательство: Mare Nostrum (Eurospan)
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Цена: 66050.00 T
Наличие на складе: Невозможна поставка.
Описание: We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities.This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments.The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, engineering, or statistics. The importance of game-theoretic thinking transcends the academic setting-for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

Автор: Biggs
Название: Discrete mathematics 2/e
ISBN: 0198507178 ISBN-13(EAN): 9780198507178
Издательство: Oxford Academ
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Цена: 69690.00 T
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Описание: Includes chapters on statements and proof, logical framework, and natural numbers and the integers. This edition also features over 1000 tailored exercises and an accompanying website containing hints and solutions to all exercises. It is suitable for mathematicians and computer scientists seeking a first approach to this topic.

Автор: Stanic, Zoran,
Название: Regular Graphs A spectral Approach
ISBN: 3110351285 ISBN-13(EAN): 9783110351286
Издательство: Walter de Gruyter
Цена: 103550.00 T
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Описание:

Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specifi ed subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research.