John Wiley, 1987. — 296 p. — (Wiley-Interscience series in discrete mathematics and optimization). — ISBN: 0-471-90825-8. Over the past thirty years there has been an increasing number of contributions to the topic of searching, both in theoretically as well as in applications- oriented journals. It is remarkable that very different kinds of problems are classified as search...
John Wiley & Sons, 1988. — 372 p. — (Wiley Teubner Series on Applicable Theory in Computer Science, Book 6). — ISBN: 0-471-92142-4. The purpose of this book is to give an introduction to the basic ideas (Chapter 1) and present a collection of the most interesting instances of search problems (Chapters 2-6). At the beginning the scope of combinatorial search is spelled out...
Springer, 1979. — 492 p. — ISBN: 3-540-61787-6. The present book covers most aspects of parts (a) and (b), but none of (c). The reasons for excluding (c) were twofold. First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on...
3rd ed. — Wiley, 2008. — 373 p. — (Wiley-Interscience Series in Discrete Mathematics and Optimization). — ISBN: 9780470170205 This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its...
Springer, 2001. — 200 p. — (Springer Undergraduate Mathematics Series). — ISBN: 1-85233-236-0. Counting and Binomial Coefficients. Recurrence. Introduction to Graphs. Travelling Round a Graph. tions and Colourings. The Inclusion-Exclusion Principle. Latin Squares and Hall's Theorem. Schedules and 1-Factorisations. Introduction to Designs. Solutions. Further Reading.
Dover Publications, 2010. — 251 p. — (Dover Books on Computer Science). — ISBN: 0486691152 OCR, electronic table of contents. This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them...
Cambridge University Press, 2 ed., Vol. 1, 1999 – 1100 p. - This is the first volume of a two-volume text on design theory. Since the first edition, there has been extensive development of the theory. In particular, the growing importance of discrete mathematics to many parts of engineering and science has made designs a useful tool for applications. The authors acknowledge...
Springer, 2018. — 308 p. — (Research in Mathematics Education). — ISBN: 978-3-319-90691-1. The emerging foundation of research on thinking about integers highlights students’ sophisticated reasoning about integers, demonstrated even by young children, and critical nonconventional conceptions that they can develop if integers are ignored. Understanding children’s thinking about...
North Holland, 1988, -419 p. Proceedings of the Cambridge Combinatorial Conference in Honour of Paul Erdös The 1988 Cambridge Combinatorial Conference was held at Trinity College, Cambridge, from 21 to 25 March 1988, under the auspices of the London Mathematical Society, the Department of Pure Mathematics and Mathematical Statistics of Cambridge University and Trinity College,...
Cambridge University Press, 1986, -187 p. This book is an expanded account of a first-year graduate course in combinatorics, given at Louisiana State University, Baton Rouge during the fall semester of 1985. The traditional ingredients of an initial combinatorics course seem to be combinatorial identities and generating functions, with some introductory design theory or graph...
Cambridge University Press, 2006, -336 p. The quality is average (pale text). Percolation theory was founded by Broadbent and Hammersley almost half a century ag: by now thousands of papers and many books have been devoted to the subject. The original aim was to open up to mathematical analysis the study of random physical processes such as the flow of through a disorders...
Basel: Birkhäuser, 2011. — 281 p. Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter...
Springer, 1997. — xxiii, 618 p. — (Grundlehren der mathematischen Wissenschaften, 315). — ISBN: 978-3-662-03338-8. The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search...
New Delhi: Hindustan Book Agency, 2009. — 189 p. The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for...
McGraw-Hill, 1994. — 597 p. Computer-aided design (CAD) of digital circuits has been a topic of great importance in the last two decades, and the interest in this field is expected to grow in the coming years. Computer-aided techniques have provided the enabling methodology to design efficiently and successfully large-scale high-performance circuits for a wide spectrum of...
Cambridge University Press, 1995, -254 p. Free-choice Petri nets have been around for more than twenty years, and are a successful branch of net theory. Nearly all the introductory texts on Petri nets devote some pages to them. This book is intended for those who wish to go further. It brings together the classical theorems of free-choice theory obtained by Commoner and Hack in...
Birkhäuser Basel, 2004. - 554 p. This book contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the 3rd International Colloquium on Mathematics and Computer Science that will be held in Vienna in September 2004. It addresses a large public in applied mathematics,...
Jones and Bartlett Publishers, 1992. - 352 p. This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is...
L'Enseignement Mathematique. University de Geneve, 1980, -128 p. In the present work we will discuss various problems in elementary number theory, most of which have a combinatorial flavor. In general, we will avoid classical problems, just mentioning references for the interested reader. We will almost never give proofs but on the other hand we will try to give as exact...
Berlin: Springer-Verlag, 1981. — 498 p. Some time ago a group of mathematicians and computer scientists (including the editors of this volume) thought of making a scientific pilgrimage to the birthplace of al-Khwarizmi, the outstanding ninth-century mathematician who gave Ms name to the word "algorithm".As his name indicates, al-Khwarizmi came from the Khorezm oasis, a...
Cambridge University Press, 2013. — 187 p. — ISBN: 1107666945 This title forms part of the completely new Mathematics for the IB Diploma series. This highly illustrated book covers topic 10 of the IB Diploma Higher Level Mathematics syllabus, the optional topic Discrete Mathematics. It is also for use with the further mathematics course. Based on the new group 5 aims, the...
Springer, 1979, -251 p. Since the early part of this century, logicians have been interested in decision procedures for theories in the predicate calculus. By a theory, we mean the set of sentences true about a particular structure, or the set of sentences true about every structure in a particular class of structures. One of the first decision procedures discovered was...
Elsevier Science Ltd, 1986. — 410 p. — (Studies in Logic and the Foundations of Mathematics). — ISBN: 0444878653, 9780444878656. Relation theory originates with Hausdorff (Mengenlehre 1914) and Sierpinski (Nombres transfinis, 1928) with the study of order types, specially among chains = total orders = linear orders. One of its first important problems was partially solved by...
Springer, 1998, -138 p. During the university reform of the 1970s, the classical Faculty of Science of the venerable Ludwig-Maximilians-Universität in Munich was divided into five smaller faculties. One was for mathematics, the others for physics, chemistry and pharmaceutics, biology, and the earth sciences. Nevertheless, in order to maintain an exchange of ideas between the...
Cambridge University Press, 1997. - 270 p. 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 the basic combinatorics of Young tableaux, including the...
Second Edition. — Taylor & Francis, 2001. — 767 p. ISBN: 0-7503-0652-1. Discrete Mathematics for New Technology provides an accessible introduction to discrete mathematics. The approach is comprehensive but maintains an easy-to-follow progression from the basic mathematical ideas to more sophisticated concepts. Although the theory is presented rigorously, it is illustrated by...
Pearson Education Australia, 1976. — 444 p. — ISBN: 0130392227, 9780130392220 The purpose of this book is to cover, in a mathematically precise manner, a variety of concepts, results, techniques, and applications of modern algebra that are of particular use to beginning students in the computer sciences. Abstract topics such as sets, relations, functions, Boolean algebras,...
Cambridge: Cambridge University Press, 2009. — 177 p. This thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members, What general methods are useful for listing...
2nd ed. — Prentice Hall, 2001. — 538 p. Adopting a user-friendly, conversational — and at times humorous — style, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique reader interest and bring clarity to even...
New York: Wiley, 1998. - 211 p. Ramsey theory has emerged as a cohesive subdiscipline of combinatorial analysis since about 1970. The present work comprises a self-contained exposition of the central results of Ramsey theory, describes recent developments in the field, and explores the influence of outside disciplines such as applications of topological dynamics and a...
Addison-Wesley, 1994. - 1026 p. Provides an introductory survey in both discrete & combinatorial mathematics. Intended for the beginning student designed to introduce a wide variety of applications & develop mathematical maturity of the student by studying an area that is so different form the traditional coverage in calculus & different equations.
Springer, 1988, -379 p. Historically, there is a close connection between geometry and optimization. This is illustrated by methods Like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the...
2nd edition. — Berlin: Springer, 1993. — 376 p. Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and...
Cambridge University Press, 2008. — 359 p. — ISBN13: 978-0-521-89885-0. Combinatory logic and λ-calculus were originally devised in the 1920s for investigating the foundations of mathematics using the basis concept of 'operation' instead of 'set'. They have since evolved into important tools for the development and study of programming languages. The authors' previous book...
Birkhäuser, 2003, -118 p. These notes had their origin in a postgraduate lecture series I gave at the Eidgenössiche Technische Hochschule (ETH) in Zürich in the Spring of 2000. I am very grateful to my hosts, the Forschungsinstitut für Mathematik at ETH, for providing the ideal opportunity to develop and present this material in what I hope is a reasonably coherent manner, and...
Cambridge University Press, 1994, -315 p. The origin of this book, whose first edition was published in 1968, is a series of notes by Paley and Zygmund that appeared in the 1930s, entitled 'On some series of functions' [167]. Paley and Zygmund, with the collaboration of Wiener in a subsequent paper, studied Fourier or Taylor series whose coefficients are independent random...
Mercury Learning and Information, 2021. — 382 p. This book covers discrete mathematics both as it has been established after its emergence since the middle of the last century and as its elementary applications to cryptography. It can be used by any individual studying discrete mathematics, finite mathematics, and similar subjects. Any necessary prerequisites are explained and...
Prentice Hall, 1996. - 524 p. Tying together discrete mathematical topics with a theme, this text stresses both basic theory and applications, offering students a firm foundation for more advanced courses. It limits the mathematics required (no calculus), and explains the small amount of linear algebra that is needed. The book uses algorithms and pseudocode to illustrate...
Cambridge University Press, 1995, -356 p. The central problem of complexity theory is the relation of deterministic and nondeterministic computations: whether Ρ equals NP, and generally whether the polynomial time hierarchy PH collapses. The famous Ρ versus NP problem is often regarded as one of the most important and beautiful open problems in contemporary mathematics, even by...
Boston; Basel; Stuttgart: Birkhäuser, 1986. – 413 p. ISBN: 978-0-8176-3173-4; ISBN: 978-1-4684-9199-9 (eBook); DOI 10.1007/978-1-4684-9199-9 This volume makes accessible some of the best results in matroid theory. Each paper is followed by a commentary providing background and a bibliography of related work. The volume is divided into five sections: origins and basic concepts;...
John Wiley, 1998, -163 p. This book is designed as a textbook. Its aim is to introduce various areas and applications in discrete mathematics via the use of Latin squares. Latin squares have been studied for centuries. They have a very fascinating history and, more important, many practical applications in areas of science, engineering, and statistics as well as being used...
Princeton University Press, 2019. — 402 p. — ISBN: 978-0-691-17929-2. A more intuitive approach to the mathematical foundation of computer science Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn....
World Scientific Publishing Company, 1995. - 450 p. This text provides a guide to dealing with 3-manifolds by computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex....
3nd Edition. — McGraw-Hill Companies, 2007. — 490 p. — ISBN: 0-07-151101-6. Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents...
McGraw-Hill College, 1985. — 448 p. — 2nd Sub edition — (McGraw-Hill Computer Science Series). — ISBN: 007038133X, 9780070381339 The second edition retains almost all the material in the first edition and includes three new chapters, namely, Chapter 2: Computability and Formal Languages, Chapter 7: Finite State Machines, and Chapter 8: Analysis of Algorithms, as well as several...
Cambridge University Press, 2002. — 515 p. — (Encyclopedia of Mathematics and its Applications, 90). — ISBN: 978-1107326019. Combinatorics on words is a field that has grown separately within several branches of mathematics, such as number theory, group theory or probability theory, and appears frequently in problems of theoretical computer science, as dealing with automata and...
Cambridge University Press, 1997, -254 p. This is the first book devoted to broad study of the combinatorics of words, that is to say, of sequences of symbols called letters. This subject is in fact very ancient and has cropped up repeatedly in a wide variety of contexts. Even in the most elegant parts of abstract pure mathematics, the proof of a beautiful theorem surprisingly...
Society for Industrial and Applied Mathematics, 1986, -96 p. There is little doubt that the present explosion of interest in the algorithmic aspects of mathematics is due to the development of computers — even though special algorithms and their study can be traced back all the way through the history of mathematics. Mathematics started out in Egypt and Babylon as a clearly...
Course Technology Inc, 2004. - 906 p. Discrete Mathematical Structures teaches students the mathematical foundations of computer science, including logic, Boolean algebra, basic graph theory, finite state machines, grammars, and algorithms. This required class for Computer Science students helps them understand mathematical reasoning for reading, comprehension, and construction...
John Wiley & Sons, 1993. - 538 p. Applauded by reviewers for its inviting, conversational style and outstanding coverage of logic and inductions, it introduces students to the topics and language of discrete mathematics and prepares them for future work in mathematics and/or computer science. Mattson develops students' mathematical thinking and overall maturity through careful...
Cambridge University Press, 1990, -443 p. The development of VLSI fabrication technology has resulted in a wide range of new ideas for application specific hardware and computer architectures, and in an extensive set of significant new theoretical problems for the design of hardware. The design of hardware is a process of creating a device that realises an algorithm, and many...
Cambridge University Press, 1996. — 125 p. This book is the first systematic and rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail, and discuss a number of related continuum models. Where appropriate, they make clear the connections between discrete percolation and continuum percolation. All...
Springer, 1989. — 138 p. One of the fundamental issues of complexity theory is to estimate the relative efficiency of different models of computation. A general program in doing this has been to take abstract models of computation, such as Turing machines, Random Access Machines, Boolean circuits or branching programs, and examine their behavior under certain resource...
Springer, 1980, -176 p. These notes present a calculus of concurrent systems. The presentation is partly informal, and aimed at practice; we unfold the calculus through the medium of examples each of which illustrates first its expressive power, and second the techniques which it offers for verifying properties of a system. A useful calculus, of computing systems as of anything...
Canadian Mathematical Monographs, 1970, -121 p. My object has been to gather together various combinatorial results on labelled trees. The basic definitions are given in the first chapter; enumerative results are presented in the next five chapters, classified according to the type of argument involved; some probabilistic problems on random trees are treated in the last...
2nd edition. — Prentice Hall of India, 1985. — 768 p. — ISBN: 8120315022 This is a lucidly written fine-tuned introduction to discrete mathematics. It is eminently suited for students persuing BCA, MCA and B.E./B.Tech courses. Considering the importance of the subject, quite a number of universities have sought to introduce discrete mathematics as a core subject in the...
Berlin: Springer, 1987. — 291 p. Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or...
New York: Springer, 1991. — 282 p. One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorics, and have been successfully applied...
Kluwer, 2003, -133 p. This proceedings is for the most part, a collection of papers presented in the three-day onference, held in Los Angeles, May 30 - June 1,2002, celebrating the 70th bIrthday of Professor Solomon W. Golomb. All contributions to the proceedings were peer-reviewed. Reflecting the interests of Professor Golomb, the major topics include sequences and...
Oxford University Press, 1992. — 542 p. Matroid theory examines and answers questions like these. Seventy-five years of study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and...
Addison-Wesley, 1994, -540 p. This book is an introduction to the theory of computational complexity at a level appropriate for a beginning graduate or advanced undergraduate course. Computational complexity is the area of computer science that contemplates the reasons why some problems are so hard to solve by computers. This field, virtually non-existent only 20 years ago, has...
Cambridge University Press, 2003, -497 p. Combinatorica has been perhaps the most widely used software for teaching and research in discrete mathematics since its initial release in 1990. Combinatorica is an extension to Mathematica, which has been used by researchers in mathematics, physics, computer science, economics, and anthropology. Combinatorica received a 1991 EDUCOM...
McGraw-Hill, 2006. - 1008 p. Sixth Edition Discrete Mathematics and its Applications, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused...
2nd ed. — Boca Raton: CRC Press, 2017. — 1612 p. Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual...
Crc press, 2000. - 1183 p. The Handbook of Discrete and Combinatorial Mathematics is the first book presenting a comprehensive collection of reference material for the essential areas of discrete mathematics as well as for important applications to computer science and engineering. Topics include logic and foundations, counting, number theory, abstract and linear algebra,...
Cambridge University Press, 2000, -272 p. This text surveys many of the topics taught in discrete and finite mathematics courses. The topics chosen are widely applied in present-day industry and, at the same time, are mathematically elegant. Chapter 1 begins with such preliminaries as sets, mathematical induction, functions, and the division algorithm of algebra. Chapters 2 and...
Springer, 1980, -152 p. The idea underlying this book is that a -comprehensive theory of computing may be developed based on the mathematics of relations. At present, research in each area of the theory of computation is pursued using whatever mathematical equipment appears most appropriate. While this may be the optimal strategy for one area taken in isolation, it is less than...
Little, Brown and Company, 1982. — 226 p. Computability theory is concerned primarily with determining what tasks can be accomplished by idealized computer programs. Formal language theory deals primarily with the ability of certain grammars to express the syntax of various types of languages. Both fields are branches of formal mathematics. The former theory has its roots in...
Academic Press, 1973. 218 p. In spite of the large number of existing mathematical tables, until now there has been no table of sequences of integers A bbrevia tions Description of the Book Description of a Typical Entry Arrangement Number of Terms Given What Sequences Are Included? How Are Arrays of Numbers Treated? Supplements How to Handle a Strange Sequence How to See if a...
New York: Franklin, Beedle & Associates, 2013. — 672 p. This book provides a distinct way to teach discrete mathematics. Since discrete mathematics is crucial for rigorous study in computer science, many texts include applications of mathematical topics to computer science or have selected topics of particular interest to computer science. This text fully integrates discrete...
Pergamon Press, 1961. — 580 p. — ISBN: 0080095682, 9780080095684 The following pages contain a reprinting of all the articles published by John von Neumann, some of his reports to government agencies and to other organizations, and reviews of unpublished manuscripts found in his files. The published papers, especially the earlier ones, are given herein in essentially...
Pergamon Press, 1961, 584 p. — ASIN: B00843PLXQ. Volume III : Rings of Operators — contains his work on, and closely related to, the theory of the rings of operators. On A Certain Topology for Rings of Operators. On RIngs of Operators. On rings of operators II. On rings of operators III. On rings of operators IV. On infinite direct products. On rings of operators. Reduction...
New York Oxford London Paris Pergamon Press, 1962. — 528 p. Volume IV : Continuous Geometry and other topics — includes the papers on continuous geometry, as well as papers written on a variety of mathematical topics. Also included in this volume are four papers on statistics, and reviews of a number of manuscripts found in his files.
Pergamon Press, 1961. — 672 p. OCR, table of contents. The following pages contain a reprinting of all the articles published by John von Neumann, some of his reports to government agencies and to other organizations, and reviews of unpublished manuscripts found in his files. The published papers, especially the earlier ones, are given herein in essentially chronological order....
New York Oxford London Paris Pergamon Press, 1963. — 550 p. — ASIN: B000V294MC Volume VI : Theory of Games, Astrophysics, Hydrodynamics and Meteorology. Papers on these topics, as well as a number of articles based on speeches delivered by von Neumann, are included in this volume.
Society for Industrial and Applied Mathematics, 2000, -419 p. Research on the complexity of Boolean functions has a more than fifty-year-old history. For a long time, research has been focused on circuits and the circuit complexity of Boolean functions. The open problems in circuit complexity are now so hard that not much progress has been made during the past 10 years....
Cambridge University Press, 1993, -164 p. These lecture notes are based on a series of lectures which I gave at the Advanced Research Institute of Discrete Applied Mathematics (ARIDAM VI) in June 1991. The lectures were addressed to an audience of discrete mathematicians and computer scientists. I have tried to make the material understandable to both groups; the result is that...
New York: Academic Press, 1976. — 443 p. The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. Aimed at advanced undergraduate and graduate students, this text is one of the earliest substantial works on matroid theory. Its author, D. J. A. Welsh, Professor of...
Springer, 2004, -256 p. Duration calculus (abbreviated to DC) represents a logical approach to the formal design of real-time systems. In DC, real numbers are used to model time, and Boolean-valued (i.e. {0,1}-valued) functions over time are used to model states of real-time systems. The duration of a state in a time interval is the accumulated presence time of the state in the...
North-Holland, 1981. — 391 p. The object of this book is to provide an account of results and methods for linear and combinatorial optimization problems over ordered algebraic structures. In linear optimization the set of feasible solutions is described by a system of linear constraints; to a large extent such linear characterizations are known for the set of feasible solutions...
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