This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
Описание: This Book Is A Unique Work Which Provides An In-Depth Exploration Into The Mathematical Expertise, Philosophy, And Knowledge Of H W Gould. It Is Written In A Style That Is Accessible To The Reader With Basic Mathematical Knowledge, And Yet Contains Material That Will Be Of Interest To The Specialist In Enumerative Combinatorics. This Book Begins With Exposition On The Combinatorial And Algebraic Techniques That Professor Gould Uses For Proving Binomial Identities. These Techniques Are Then Applied To Develop Formulas Which Relate Stirling Numbers Of The Second Kind To Stirling Numbers Of The First Kind. Professor Gould'S Techniques Also Provide Connections Between Both Types Of Stirling Numbers And Bernoulli Numbers. Professor Gould Believes His Research Success Comes From His Intuition On How To Discover Combinatorial Identities.This Book Will Appeal To A Wide Audience And May Be Used Either As Lecture Notes For A Beginning Graduate Level Combinatorics Class, Or As A Research Supplement For The Specialist In Enumerative Combinatorics.
Автор: Feng Yuefeng Название: Combinatorial Extremization ISBN: 9814730025 ISBN-13(EAN): 9789814730020 Издательство: World Scientific Publishing Рейтинг: Цена: 6336.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad.
Автор: Feng Yuefeng Название: Combinatorial Extremization ISBN: 9814723169 ISBN-13(EAN): 9789814723169 Издательство: World Scientific Publishing Рейтинг: Цена: 3326.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad.
Описание: This book discusses cryptographic and combinatorial properties of Boolean functions. Boolean functions are very easy to understand (but deep in analysis) and the subject covers significant amount of material in digital circuits, communication theory, VLSI design, computer science, coding theory and Mathematics. Boolean function is considered as one of the most basic building blocks in cryptographic system design. The properties that make a Boolean function suitable for a cryptographic system, are mostly combinatorial. We discuss these properties (e.g., balancedness, nonlinearity, correlation immunity, propagation characteristics, algebraic immunity) in detail. For each of the properties, existing research results and the recent contributions in the literature will be presented. The basic material will always contain hardcore theoretical results. However, we present the materials in a way that a person with undergraduate level mathematical background can access it. Implementation details related to these properties (e.g., how to check in writing a program whether a Boolean function is correlation immune) will be detailed.In addition to theoretical construction techniques for Boolean functions with different combinatorial and cryptographic properties, the book will concentrate on different state-of-the-art search techniques. In some cases these search techniques provide better results than the construction techniques for low number of input variables and they are quite interesting as the size of the complete set of Boolean functions is super exponential in the number of input variables. Different symmetries in the set of Boolean functions will also be presented in detail. The author will present the inherent beauty of Boolean functions that he has experienced in his research career.
Автор: Quarteroni Alfio Название: Scientific Computing with MATLAB and Octave ISBN: 3642124291 ISBN-13(EAN): 9783642124297 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Поставка под заказ.
Название: Combinatorial and global optimization ISBN: 9810248024 ISBN-13(EAN): 9789810248024 Издательство: World Scientific Publishing Рейтинг: Цена: 15048.00 р. Наличие на складе: Поставка под заказ.
Описание: Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, and biological and computer science. This is a selection of refereed papers based on talks presented at a conference on "Combinatorial and Global Optimization" held at Crete.
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