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The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.

Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.

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This book introduces graph theory, a subject with a wide range of applications in real-work situations. This book is designed to be easily accessible to the novice, assuming no more than a good grasp of algebra to understand and relate to the concepts presented. Using many examples, illustrations, and figures, it provides an excellent foundation for the basic knowledge of graphs and their applications.This book includes an introductory chapter that reviews the tools necessary to understand the concepts of graphs, and then goes on to cover such topics as trees and bipartite graphs, distance and connectivity, Eulerian and Hamiltonian graphs, graph coloring, matrices, algorithms, planar graphs, and digraphs and networks.Graph theory has a wide range of applications; this book is useful for those in the fields of anthropology, computer science, chemistry, environmental conservation, fluid dynamics, psychology, sociology, traffic management, telecommunications, and business managers and strategists. ... Read more

Customer Reviews (1)

It's a very good intro text.
Good choice of topics. Easy to read. The concepts are well motivated. The book is full of applications. An undergraduate will be able to follow the proofs. They are clear. I also liked the homework exercises. This is a student-friendly book, as the title suggests. ... Read more

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Provides a solid background in the basic topics of graph theory.Does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. DLC: Graph theory. ... Read more

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The book presents the solutions to two problems: the first is the construction of expanding graphs – graphs which are of fundamental importance for communication networks and computer science; the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres. Both problems were partially solved using the Kazhdan property (T) from representation theory of semi-simple Lie groups. Later, complete soultions were obtained for both problems using the Ramanujan conjecture from analytic number theory. The author, who played an important role in these developments, explains the two problems and their solutions from a perspective which reveals why all these seemingly unrelated topics are so interconnected. The unified approach shows interrelations between different branches of mathematics such as graph theory, measure theory, Riemannian geometry, discrete subgroups of Lie groups, representation theory and analytic number theory.

Special efforts were made to make the book accessible to graduate students in mathematics and computer science. A number of problems and suggestions for further research are presented.

Reviews:

"This exciting book marks the genesis of a new field. It is a field in which one passes back and forth at will through the looking glass dividing the discrete from the continuous. (...) The book is a charming combination of topics from group theory (finite and infinite), combinatorics, number theory, harmonic analysis." - Zentralblatt MATH

"The Appendix, written by J. Rogawski, explains the Jacquet-Langlands theory and indicates Deligne’s proof of the Petersson-Ramanujan conjecture. It would merit its own review. (...) In conclusion, this is a wonderful way of transmitting recent mathematical research directly "from the producer to the consumer." - MathSciNet

"The book is accessible to mature graduate students in mathematics and theoretical computer science. It is a nice presentation of a gem at the border of analysis, geometry, algebra and combinatorics. Those who take the effort to glance what happens behind the scene won’t regret it." - Acta Scientiarum Mathematicarum

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A comprehensive look at the emerging science of networks

Network science helps you design faster, more resilient communication networks; revise infrastructure systems such as electrical power grids, telecommunications networks, and airline routes; model market dynamics; understand synchronization in biological systems; and analyze social interactions among people.

This is the first book to take a comprehensive look at this emerging science. It examines the various kinds of networks (regular, random, small-world, influence, scale-free, and social) and applies network processes and behaviors to emergence, epidemics, synchrony, and risk. The book's uniqueness lies in its integration of concepts across computer science, biology, physics, social network analysis, economics, and marketing.

The book is divided into easy-to-understand topical chapters and the presentation is augmented with clear illustrations, problems and answers, examples, applications, tutorials, and a discussion of related Java software. Chapters cover:

• Origins

• Graphs

• Regular Networks

• Random Networks

• Small-World Networks

• Scale-Free Networks

• Emergence

• Epidemics

• Synchrony

• Influence Networks

• Vulnerability

• Net Gain

• Biology

This book offers a new understanding and interpretation of the field of network science. It is an indispensable resource for researchers, professionals, and technicians in engineering, computing, and biology. It also serves as a valuable textbook for advanced undergraduate and graduate courses in related fields of study. ... Read more

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This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties.The first part of the book is a self-contained presentation of thebasic combinatorics of Young tableaux, including the remarkable constructions of "bumping" and "sliding", and several interesting correspondences.In Part II the author uses these results to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials.Much of this material has never before appeared in book form.There are numerous exercises throughout, with hints and answers provided. Researchersin representation theory and algebraic geometry as well as in combinatorics will find this book interesting and useful, while students will find the intuitive presentation easy to follow. ... Read more

Customer Reviews (1)

A Fine Synthesis of Combinatorics, Geometry, and Algebra
With his usual lucidity, Fulton brings together the surprisingly wide area of mathematics concerned with Young tableaux.These are combinatorial patterns which index basis vectors of group representations (either of the symmetric group or the general linear group).These vectors can be seen as Plucker coordinate functions on non-linear representations, namely homogeneous spaces (Grassmannians and flag varieties).Thus, Young tableaux form an invaluable tool to examine these representations and varieties in concrete detail.Fulton also gives a good exposition of the combinatorial operations on tableaux which reflect the crystal basis structure from quantum GL(n), though Fulton does not explicitly discuss quantum groups.Other good expositions of these topics, from a more algebraic and combinatorial point of view, are Sagan's newly revised "The Symmetric Group", and Stanley's "Enumerative Combinatorics", Vol 2. ... Read more

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In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory. ... Read more

Customer Reviews (1)

An excellent introduction to mathematical logic
This is an outstanding undergraduate treatment of the following topics at the core of modern mathematics: set theory, equivalence and ordering relations, cardinals, ordinals, sentential and quantifier logic, and just enough recursion theory to derive the paradoxical undecidability theorems.

The treatment is thoroughly contemporary (eg, Hintikka sets) but not too difficult, because this text emerged out of the philosophy rather than the mathematics classroom. The text is written in the mathematical tradition, consisting of many terse numbered subsections, each containing a definition, theorem, remark, or problem. The organisation of the subject, and the index, are excellent. The author chooses an unusual pedagogic strategy: to present a bit of axiomatic set theory BEFORE the chapters on logic and metamathematics. A benefit of this choice is that the metalanguage employed to exposit these topics can draw freely on elementary set theoretic concepts. This strategy is, of course, a consequence of the triumph of model theory over proof theory.

Except for the omission of Boolean algebra, this is the finest contemporary treatment I know of the propositional calculus.

The book ends with a concise and elegant treatment of the classic limitative results inherent in any formalization of arithmetic. Tarski indefinability is proved quite early on, right after the proof of the diagonal lemma and before the axiomatic systems of arithmetic are set out in order of increasing strength, RR=>Q=>P. The famous theorem of Matyasevich (recursively enumerable relations are diophantine) is stated without proof, then invoked to make stronger and simpler the proof of Godelian incompleteness.

This book is filled with the sort of shrewd philosophical asides too seldom included in textbooks, and that when spoken are the hallmark of a good experienced teacher. ... Read more

Product Description
This book considers a graph as a mathematical structure on aset of elements with a binary relation, and provides the mostclassical and important theory and application of graphs. It coversbasic concepts, trees and graphic spaces, plane graphs and planargraphs, flows and connectivity, matchings and independent sets,coloring theory, graphs and groups. These topics, both theoretical andapplied, are treated with some depth and with some suggestions forfurther reading. The treatment of material particularly lays stress ondigraphs, the mutual connections among these topics and theequivalence of some well-known theorems. All theorems are statedclearly, together with full and concise proofs. A number of examples,more than 350 figures and more than 500 exercises are given to helpthe reader understand and examine the materials covered in the book.

Audience: The book is particularly suitable as a textbook ofgraph theory for senior or beginning postgraduate students who aremajoring in pure and applied mathematics, operation research, computerscience, designing and analysis of networks, electronics, scientificmanagement and others. It is also suitable as a reference book forthose readers who are engaged and interested in graph theory and forall researchers who use graph theory as a mathematical tool. ... Read more

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Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem—a proof that revolutionized the field of graph theory—and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.
... Read more

Customer Reviews (2)

A recognized Classical text
This book had much that I needed to know about graph theory.
It is well written and includes much of the information needed.

It has three problems in notation that bother me:
1) Bn for Bouquets is like the Bn used for Braid groups.
2) definitions of "stars" are more the classical star than
the current usage as central point with radial connections.
3)The book doesn't distinguish well enough
between "graphs" with are symmetrical adjacency matrices
and "digraphs" and ends up confusing the issue it should clarify.

The book also shorts the reader on matrix theory connected to the graphs.
It tends to use an older approach to graphs that has to be adapted to modern computer mathematical systems.

Excellent
This book is written at a graduate level.It is written, for the most part, clearly and methodically.There are about 300 problems throughout the text, but there are no solutions in this book for those problems.

Titles of the 6 Chapters (with the number of pages in each chapter): 1) Introduction (to graph theory), 55; 2) Voltage Graphs and Covering Spaces, 40; 3) Surfaces and Graph Embeddings, 68; 4) Imbedded Voltage Graphs and Current Graphs, 54; 5) Map Colorings, 35; and 6) The Genus of a Group, 71.

This book is sufficient for self-study. ... Read more

Product Description
The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Königsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Dénes König published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been successfully applied in other areas of mathematics. However, the same methods were often incapable of providing satisfactory answers to questions arising in geometric applications.

In the spirit of König, geometric graph theory focuses on combinatorial and geometric properties of graphs drawn in the plane by straight-line edges (or more generally, by edges represented by simple Jordan arcs). It is an emerging discipline that abounds in open problems, but it has already yielded some striking results which have proved instrumental in the solution of several basic problems in combinatorial and computational geometry. The present volume is a careful selection of 25 invited and thoroughly refereed papers, reporting about important recent discoveries on the way Towards a Theory of Geometric Graphs. ... Read more

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Advanced textbook outlining combinatorial group theory, with emphasis on connections with topology, logic, and arguments of a primitive geometric nature. Also briefly mentions a number of topics not belonging to combinatorial group theory, such as groups acting on trees and linear groups. Softcover. ... Read more

Customer Reviews (3)

A reprint at last!
A text truly deserving the designation "classic"; bravo to Springer for reprinting this book!This seminal text provides a clear exposition of the topic, along with numerous jumping-off points for exploring interesting outgrowths and tangents.A must-have text for anyone interested in the subject.

Great book
A "must read" for everybody who is interested in combinatorial aspects of algebra. You can read whole book or some chapters (free groups, free constructions, diagrams, 1-relator, ...). I don't think it's forabsolute beginners, but if you want, you understand it. It would be greatif this book were reprinted with some complements (which could be writtenby Ol'shanskii, Gersten, Sapir,Shupp, Stallings, Guba, S.Ivanov,Baumslag, Lysyonok ...)

A very good textbook
It's an absolute pity that this book is out of print, since it's one of the few good recent textbooks about combinatorial group theory. One can only hope it will be reprinted soon... ... Read more

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The authors help you "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on your needs, the authors will lead you to mathematical understanding and, ultimately, success in class.

Customer Reviews (2)

Math Class Books
College Algebra: Graphs and Models with Graphing Calculator Manual Package (4th Edition)
This is a great book.It walks you through step by step.All the vocaulary and formulas and important items are highlighted. Awesome book!

Not reliable
I paid for student copy but, he shipped me an instructor copy making it difficult to resell ... Read more

Product Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz andWatts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At about the same time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. While this literature is extensive, many of the papers are based on simulations and nonrigorous arguments. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature of this book is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter. ... Read more

Customer Reviews (1)

Good text for technical readers
The author presents very interesting material and I really learned a lot from reading this book. I've read a lot of texts and papers on the subject of random graphs (both technical and for the general public) and most authors do a good job in making this subject interesting and enjoyable, but often lack a rigorous presentation of the subject. In that sense Durrett's book does an excellent job in providing this missing element from other books. On the negative side, the exposition in Durrett' sbook is not self-contained and the author relies too much on the notation and results from his previously published books.If you don't have those books the reading pace will be seriously hampered.Also, in trying to motivate the subject in Chapter 1, the author introduces a lot of cryptic notation and concepts that are not explained until later on. I know this is supposed to be a monograph, but at least the author should try to live up to the series mission of providing a clear presentation of the subjects. In summary, a great book if you are already familiar with the subject and are fairly mathematical sophisticated, but don't use this book as an introductory text or to get motivation on the subject. ... Read more

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This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches. ... Read more

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Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails.

The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition.

· New edition of the "Classic" book on the topic
· Wonderful introduction to a rich research area
· Leading author in the field of algorithmic graph theory
· Beautifully written for the new mathematician or computer scientist
· Comprehensive treatment ... Read more

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An extraordinary variety of disciplines rely on graphs to convey their fundamentals as well as their finer points. With this concise and well-written text, anyone with a firm grasp of general mathematics can follow the development of graph theory and learn to apply its principles in methods both formal and abstract. The work of a distinguished mathematician, this text uses practical examples to illustrate the theory's broad range of applications, from the behavioral sciences, information theory, cybernetics, and other areas, to mathematical disciplines such as set and matrix theory. 1966 ed. 109 b/w illus.
... Read more

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This book is a concept-oriented treatment of the structure theory of association schemes. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type.