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On The Foundation Of Combinatorial Theory
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Book Synopsis Combinatorial Theory by : Martin Aigner
Download or read book Combinatorial Theory written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
Book Synopsis Foundations of Combinatorics with Applications by : Edward A. Bender
Download or read book Foundations of Combinatorics with Applications written by Edward A. Bender and published by Courier Corporation. This book was released on 2013-01-18 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On the Foundations of Combinatorial Theory: Combinatorial Geometries by : Henry H. Crapo
Download or read book On the Foundations of Combinatorial Theory: Combinatorial Geometries written by Henry H. Crapo and published by MIT Press (MA). This book was released on 1970 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major aim of this book is to present the theory of combinatorial geometry in a form accessible to mathematicians working in disparate subjects.
Book Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung
Download or read book Combinatorics: The Rota Way written by Joseph P. S. Kung and published by Cambridge University Press. This book was released on 2009-02-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.
Book Synopsis Foundations of Combinatorial Topology by : L. S. Pontryagin
Download or read book Foundations of Combinatorial Topology written by L. S. Pontryagin and published by Courier Corporation. This book was released on 2015-05-20 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen
Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
Book Synopsis Problems in Combinatorics and Graph Theory by : Ioan Tomescu
Download or read book Problems in Combinatorics and Graph Theory written by Ioan Tomescu and published by Wiley-Interscience. This book was released on 1985-04-30 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the most important combinatorial structures and techniques. This is a book of problems and solutions which range in difficulty and scope from the elementary/student-oriented to open questions at the research level. Each problem is accompanied by a complete and detailed solution together with appropriate references to the mathematical literature, helping the reader not only to learn but to apply the relevant discrete methods. The text is unique in its range and variety -- some problems include straightforward manipulations while others are more complicated and require insights and a solid foundation of combinatorics and/or graph theory. Includes a dictionary of terms that makes many of the challenging problems accessible to those whose mathematical education is limited to highschool algebra.
Book Synopsis Combinatorics and Graph Theory by : John Harris
Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
Book Synopsis The History of Combinatorial Group Theory by : B. Chandler
Download or read book The History of Combinatorial Group Theory written by B. Chandler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.
Book Synopsis Notes on Introductory Combinatorics by : George Polya
Download or read book Notes on Introductory Combinatorics written by George Polya and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Path to Combinatorics for Undergraduates by : Titu Andreescu
Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
Book Synopsis Introduction to Combinatorics by : Martin J. Erickson
Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.
Book Synopsis Combinatorial Algebraic Topology by : Dimitry Kozlov
Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Book Synopsis Algebraic Combinatorics by : Eiichi Bannai
Download or read book Algebraic Combinatorics written by Eiichi Bannai and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
Book Synopsis Finite Operator Calculus by : Gian-Carlo Rota
Download or read book Finite Operator Calculus written by Gian-Carlo Rota and published by . This book was released on 1972 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lessons in Enumerative Combinatorics by : Ömer Eğecioğlu
Download or read book Lessons in Enumerative Combinatorics written by Ömer Eğecioğlu and published by Springer Nature. This book was released on 2021-05-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorics of Finite Sets by : Ian Anderson
Download or read book Combinatorics of Finite Sets written by Ian Anderson and published by Courier Corporation. This book was released on 2002-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
