Foundations Of Combinatorics With Applications

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Foundations Of Combinatorics With Applications

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Author : Edward A. Bender
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18

Foundations Of Combinatorics With Applications written by Edward A. Bender and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

Foundations Of Applied Combinatorics

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Author : Edward A. Bender
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1991

Foundations Of Applied Combinatorics written by Edward A. Bender and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises (some with solutions), notes, and references appear throughout the text. 75 figures. Appendixes.

Foundations Of Combinatorial Topology

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Author : L. S. Pontryagin
language : en
Publisher: Courier Corporation
Release Date : 2015-05-20

Foundations Of Combinatorial Topology written by L. S. Pontryagin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-20 with Mathematics categories.

Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.

Notes On Introductory Combinatorics

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Author : George Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

Notes On Introductory Combinatorics written by George Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Social Science categories.

In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

Combinatorics And Graph Theory

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Author : John Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03

Combinatorics And Graph Theory written by John Harris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.

There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.

Lessons In Enumerative Combinatorics

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Author : Ömer Eğecioğlu
language : en
Publisher: Springer Nature
Release Date : 2021-05-13

Lessons In Enumerative Combinatorics written by Ömer Eğecioğlu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-13 with Mathematics categories.

This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.

Foundations Of Logic And Mathematics

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Author : Yves Nievergelt
language : en
Publisher: Birkhäuser
Release Date : 2012-10-13

Foundations Of Logic And Mathematics written by Yves Nievergelt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-13 with Mathematics categories.

This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

Quantitative Graph Theory

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Author : Matthias Dehmer
language : en
Publisher: CRC Press
Release Date : 2014-10-27

Quantitative Graph Theory written by Matthias Dehmer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-27 with Computers categories.

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as: Comparative approaches (graph similarity or distance) Graph measures to characterize graphs quantitatively Applications of graph measures in social network analysis and other disciplines Metrical properties of graphs and measures Mathematical properties of quantitative methods or measures in graph theory Network complexity measures and other topological indices Quantitative approaches to graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.

Mathematical Foundations Of Computer Science

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Author : Peter A. Fejer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematical Foundations Of Computer Science written by Peter A. Fejer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science. This volume treats basic topics, mostly of a set-theoretical nature (sets, functions and relations, partially ordered sets, induction, enumerability, and diagonalization) and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation, and program verification. The material is treated in a straightforward, systematic, and rigorous manner. The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate students in mathematics as well as in computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source. In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming.