London: Ellis Horwood, 1995. — 270 p. — ISBN: 0138340943. For too long ‘applied mathematics’ in schools and universities has meant ‘mechanics’. Although this area still has an important role to play, many students are turning away from it and are showing a growing interest in newer areas of applications of mathematics, such as those covered by the various syllabuses in A-level...
Salzburg: University of Salzburg, 2025. — 373 p. Computational Geometry and Applications Lab. Propositional and Predicate Logic. Definitions and Theorem Proving. Numbers and Basics of Number Theory. Principles of Elementary Counting and Combinatorics. Complexity Analysis and Recurrence Relations. Graph Theory. Cryptography.
Hannover: Gottfried Wilhelm Leibniz Universität Hannover, 2024. — 108 S. Dieses Skript entstand aus einer 4 + 2-Vorlesung im Sommersemester 2021 (14 Wochen) an der Leibniz Universität Hannover. Die Veranstaltung richtete sich hauptsächlich an Bachelor-Studierende der Mathematik sowie an Studierende im fachübergreifenden Bachelorstudiengängen (Lehramt). Es wurden Kenntnisse der...
Zürich: Die Eidgenössische Technische Hochschule (ETH) Zürich, 2023. — 90 p. Departement Informatik. Viele Disziplinen der Wissenschaft, insbesondere der Natur- und Ingenieurwissenschaften, beruhen in einer zentralen Weise auf der Mathematik. Einerseits erlaubt die Mathematik, Sachverhalte zu modellieren und damit den Diskurs von einer intuitiven auf eine präzise und formale...
Skript zur Vorlesung. — Aachen: Rheinisch-westfälische technische hochschule (RWTH) university, 96 S. — (Die Mathematik von Paul Erdös). Skript zur Vorlesung Diskrete Mathematik. Lehrstuhl II für Mathematik. Die Diskrete Mathematik ist die Mathematik der endlichen (evtl. noch abzählbar unendlichen) Mengen. "Diskret" bezeichnet dabei den Gegensatz zu "kontinuierlich". Die...
Wrocław: Wrocław University of Science and Technology, 2022. — 52 p. — ISBN: 978-83-7493-221-9. Discrete mathematical structures, in particular, such as mathematical logic and set theory, algebraic systems, formal languages, automata theory, graphs, number theory, coding theory, combinatorial analysis, discrete probability theory, Petri nets, and so on, underpin a large amount...
Wrocław: Wrocław University of Science and Technology, 2022. — 408 p. — ISBN: 978-83-7493-188-5. At the beginning of Chapter I, the classical propositional calculus is presented. The logical calculi considered here are based on a system of rules, which define the methods used in proofs from assumptions. The methodological problems in the deductive sciences are given only an...
4th ed. — CRC Press, 2025. — 497 p. Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second-year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the...
Dreamtech Press, 2020. — 256 p. In this book, we have attempted to cover all the topics normally taught in the course on Discrete Mathematics (Mathematical Foundation of Computer Science) in all undergraduate programs across most universities, so that teachers and students need not consult several textbooks.
Wiley, 2009. — 431 p. This book explains the basic principles of Discrete Mathematics and Structures in a clear systematic manner. A contemporary approach is adopted throughout the book. The book is divided into five sections. The first section discusses Set Theory, Relations and Functions, Probability and Counting Techniques; the second section is about Recurrence Relations...
Boca Raton: CRC Press, 2025. — 145 p. This book explores the problem of minimal valid graph coloring, first in the form of games and then of resolution algorithms. Emphasis is placed on deterministic, guaranteed, and non-guaranteed methods. Stochastic methods are then just mentioned because they are already widely described in previous publications. The study then details a...
Hoboken: Wiley, 1991. — 770 p. List of Standard Symbols. Suggested Course Coverage. One. Introduction and Preliminaries. What is Discrete Mathematics? Typical Problems. Comments about Typical Problems. Review of Logic. Two. Elementary Counting Techniques. Sets and Functions. Cardinalities of Sets. Applications to Counting Problems. Principle of Inclusion and Exclusion. Three....
Translated from Russian by R.S. Wadhwa, N.V. Wadhwa. — Moscow: Mir Publishers, 1989. — 417 p. This collection of problems is intended as an accompaniment to a course on discrete mathematics at the universities. Senior students and graduates specializing in mathematical cybernetics may also find the book useful. Lecturers can use the material for exercises during seminars. The...
Arcler Press, 2024. — 243 p. This book discusses the role of proofs in mathematics and Computer Science. In mathematics, a proof involves validating a proposition through logical deductions from axioms. Computer scientists focus on demonstrating program accuracy, given the increasing error susceptibility of software. A community of specialists aims to enhance program precision,...
Cambridge University Press, 2001. — 174 p. — ISBN: 0-521-64320-1. Communication is a fundamental and integral part of computing, whether between different computers on a network or between components within a single computer. In this book, Robin Milner introduces a new way of modeling communication that reflects its position. He treats computers and their programs as themselves...
Cambridge: Cambridge University Press, 2024. — 452 p. This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to...
Chapman and Hall/CRC, 2024. — 567 p. Vector Partitions, Visible Points, and Ramanujan Functions offer a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number...
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...
Springer Cham, 2024. — 297 p. — (Studies in Computational Intelligence, volume 1163). — eBook ISBN: 978-3-031-63053-8. Presents and elucidates novel metaheuristic algorithms that feature innovative search mechanisms. Provides a foundational framework for assessing the performance of metaheuristics. Offers practical insights into the performance of optimization algorithms on...
Springer-Verlag, 1991. — 446 p. Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) that 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,...
Singapore: World Scientific Publishing Company, 2024. — 819 p. — ISBN: 9811285780. Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course:...
Chapman & Hall, 2011. — 1016 p. Reflecting many of the recent advances and trends in this area, Discrete Structures with Contemporary Applications covers the core topics in discrete structures as well as an assortment of novel applications-oriented topics. The applications described include simulations, genetic algorithms, network flows, probabilistic primality tests, public...
Birkhäuser, 2024. — 179 p. — (Compact Textbooks in Mathematics). — ISBN: 3031553837. This compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Politècnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is...
Birkhäuser, 2024. - 179 p. - (Compact Textbooks in Mathematics). - ISBN: 3031553837. This compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Politècnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is...
Cambridge: Cambridge University Press, 2024. - 506 p. - ISBN: 1107174007. Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small,...
Springer, 2021. — 322 p. — ISBN: 9783030611149. This textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-computer Science majors; and as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer...
Chapman and Hall/CRC, 2017. — 945 p. Discrete Mathematics and Applications, Second Edition is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs,...
Springer, 2023. — 398 p. Whether you are looking for an introduction to the field of tree balance, a reference work on the multitude of available balance indices, or inspiration for your future research, this book offers all three. It delves into the significance of tree balance in phylogenetics and other research domains, where numerous indices have been introduced over the...
Springer, 2024. - 265 p. - (Synthesis Lectures on Mathematics & Statistics). - ISBN: 303130487X. This book is ideal for a first or second-year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions...
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...
2nd. ed. - Cambridge: Cambridge University Press, 2022. - 691 p. - ISBN: 1009150499. Computer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard...
New York; London: John Wiley & Sons, 1962. — 428 p. This book is intended both as a teaching tool on the senior level and as an up-to-date presentation of significant theoretical results. Reflecting my attitude toward teaching numerical analysis, the elementary parts of the book stress basic concepts and questions of intrinsic interest rather than a cookbook-like enumeration of...
Mercury Learning and Information, 2021. — 382 p. — ISBN: 978-1-68392-763-1. This book covers discrete mathematics both as it was established after its emergence in 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...
Scrivener Publishing, 2023. — ISBN: 978-1-119-89632-6. This second volume in a new series from Wiley-Scrivener is the first of its kind to present scientific and technological innovations by leading academicians, eminent researchers, and experts around the world in the areas of mathematical sciences and computing. Building on what was presented in volume one, the chapters focus...
Springer, 2023. — 648 p. This book is designed to meet the requirements of undergraduate and postgraduate students pursuing computer science, information technology, mathematical science, and physical science courses. No formal prerequisites are needed to understand the text matter except a very reasonable background in college algebra. The text contains in-depth coverage of...
Birkhäuser, 2023. — 198 p. This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak...
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...
Boca Raton: CRC Press, 2023. — 547 p. — (Textbooks in Mathematics). — ISBN: 1000917452. This book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one or the other, the book explores the rich and important connection...
Wiley-Scrivener, 2023 — 560 p. — eBook ISBN: 978-1-119-87981-7. This new edited volume from Wiley-Scrivener is the first of its kind to present scientific and technological innovations by leading academicians, eminent researchers, and experts around the world in the areas of mathematical sciences and computing. The chapters focus on recent advances in computer science, and...
Basel: Birkhäuser, 2023. — 191 p. Logicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets. This textbook presents these techniques in a unified way that should appeal to computer scientists. Specifically, the book explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly...
Springer, 2023. — 251 p. — (Artificial Intelligence: Foundations, Theory, and Algorithms). — ISBN: 978-981-99-0184-5. Artificial Intelligence (AI) is now everywhere and fuels both industry and daily life all over the world. We are in the era of “Big Data,” and huge sums of information can be obtained which are too cumbersome for people to process themselves. These Big Data are...
Berlin: de Gruyter, 2022. — 372 p. Ring theoretical foundations. Characters. Tensor products, Mackey formulas, and Clifford theory. Bilinear forms on modules. Brauer induction, Brauer’s splitting field theorem. Some homological algebra methods in ring theory. Some algebraic number theory. Some notions of integral representations. The solution to selected exercises.
Boca Raton: CRC Press/Chapman & Hall, 2023. — 238 p. Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the book consists of discussions and proofs of the results now universally known as...
London: Springer-Verlag, 2013. — 123 p. Probabilistic Group Theory, Combinatorics, and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods...
CRC Press, 2020. - 732 p. - (Chapman & Hall/CRC Cryptography and Network Security Series). - Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open...
Wiley, 2023. — 501 p. This first volume in a new multi-volume set gives readers the basic concepts and applications for diverse ideas and innovations in the field of computing together with its growing interactions with mathematics. This new edited volume from Wiley-Scrivener is the first of its kind to present scientific and technological innovations by leading academicians,...
Cambridge: Cambridge University Press, 1979. — 148 p. The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs, and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth...
10th Latin American Symposium. Arequipa, Peru, April 16-20, 2012. Proceedings. — Springer-Verlag Berlin Heidelberg, 2012. — 685 p. — ISBN: 978-3-642-29343-6, e-ISBN: 978-3-642-29344-3 This volume contains the papers presented at the 10th Latin American Symposium on Theoretical Informatics (LATIN 2012), held at the Universidad Cat´olica San Pablo (UCSP), in Arequipa, Peru....
New Mexico Tech Press, 2014. — 260 p. Concepts of discrete mathematics can help clarify a programmer's thinking about software design problems and can make many solutions obvious. Starting at an elementary level, this book teaches about fundamental structures of discrete mathematics and many simple but powerful programming techniques using those structures.
Academic Press/Elsevier, 2023. — 438 p. The Boolean functions may be iterated either asynchronously when their coordinates are computed independently of each other, or synchronously when their coordinates are computed at the same time. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their...
Monograph. 8th Edition. - Pearson Education Ltd., 2019. — 214 p. Solution Manual For Discrete Mathematics 8th Edition by Richard Johnsonbaugh 2018. Instructor's Manual to the Monograph "Johnsonbaugh R. Discrete Mathematics. 8th Edition". Solutions and Answers to Selected Exercises of the Johnsonbaugh R. "Discrete Mathematics. 8th Edition". Find step-by-step solutions and...
London: Academic Press, 2022. — 442 p. Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proof of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple...
Springer, 2023. — 225 p. — (Forum for Interdisciplinary Mathematics). — ISBN: 978-981-19-7013-9. In real-life situations, we come across problems that comprise imprecise or uncertain, simple or complex information that needs to be analyzed for various requirements. To tackle this situation, Zadeh 1965 formulated the concept of a fuzzy set, which in an imprecise environment...
Kluwer Academic Publishers, 2002. — 435 p. — (Fundamental Materials Research). — ISBN: 978-0-306-46115-6. Although rigidity has been studied since the time of Lagrange (1788) and Maxwell (1864), it is only in the last twenty-five years that it has begun to find applications in the basic sciences. The modern era started with Laman (1970), who made the subject rigorously in two...
Basel: Birkhäuser, 2009. — 136 p. The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, like finite or incidence geometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently...
American Mathematical Society, 2018. — 238 p. — (Problem Books 29). — ISBN13: 9781470443498. A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. Tanton provides a coherent guided tour of exploration and discovery of a rich mathematical...
William S. Veatch, 2021. — 200 p. Introduction to Drawing Inferences. A Quick Note About Domain Lattices. The Subset-Superset Two-Set Relationship. Relations - A Boolean Lattice of Ordered Pairs. The Boolean Algebra of Relations. Equivalence Relations and Partitions. Order Relations and Chains. Functions or Mappings. Incorporating the Concept of a Timeline. Propositions -...
John Wiley & Sons, Inc., 2023. — 354 p. — ISBN: 978-1119898917. Network Science Network Science offers comprehensive insight into network analysis and network optimization algorithms, with simple step-by-step guides and examples throughout, and a thorough introduction and history of network science, explaining the key concepts and the type of data needed for network analysis,...
Morgan & Claypool Publishers, 2014. — 124 p. A zero-suppressed decision diagram (ZDD) is a data structure to represent objects that typically contain many zeros. Applications include combinatorial problems, such as graphs, circuits, faults, and data mining. This book consists of four chapters on the applications of ZDDs. The first chapter by Alan Mishchenko introduces the ZDD....
Leanpub.com, 2022. — 280 p. About the Book Active Learning. Problem-based Learning. Python Programming Language. Mathematical Thinking in Computer Science. Proofs: Convincing Arguments. Warm Up. Existence Proofs. Finding an Example. How to Find an Example. Optimality. Computer Search. Recursion and Induction. Recursion. Induction. Logic. Examples and Counterexamples. Logic....
2nd Edition. — Springer, 2022. — 231 p. — (Texts and Readings in Mathematics 55). — ISBN13: 9789811913358. This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book...
University of Pennsylvania, 2022. - 713 p. This is a book about discrete mathematics that also discusses mathematical reasoning and logic . Since the publication of the first edition of this book a few years ago, we came to realize that for a significant number of readers, it is their first exposure to the rules of mathematical reasoning and to logic. As a consequence, the version...
Kinson Publishing, 2013. — 309 p. Number Theory and Modular Arithmetic. Integer Arithmetic. Prime Numbers and the Prime Decomposition Theorem. Modular Arithmetic. The Day of the Week. Linear Congruences. Modular Representation and the Euler ϕ-function. Public Key Encryption. Graph Theory. Basic Concepts. Graph Isomorphism. Walks, Paths, Circuits, and Cycles. Connectedness....
Philadelphia: Drexel University, 2022. — 1397 p. These notes are a detailed introduction to some of the basic objects of combinatorics and algebra : finite sums, binomial coefficients, permutations, and determinants ( from a combinatorial viewpoint – no linear algebra is presumed). To a lesser extent, modular arithmetic and recurrent integer sequences are treated as well. The...
Springer, 2022. — 375 p. — (Springer Monographs in Mathematics). — ISBN: 3030941507. The ever-growing applications and richness of approaches to the Riordan group are captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field . The concept of a Riordan array has played a unifying role in enumerative...
Cambridge: Cambridge University Press, 2022. — 262 p. The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a...
Studentlitteratur AB, 2015. — 332 p. This book is intended as a coursebook for the first course in discrete mathematics. A special aim of the book is to provide an understanding of the role of discrete mathematics in modeling. Phenomena that are mmodeledare picked from for instance computer science, electronics, and politics. An introductory chapter discusses what is meant by...
5th edition. Cengage Publishing, 2019, 984 p., ISBN13: 978-1337694193 Explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics but also the reasoning that underlies mathematical...
New York: Chapman and Hall/CRC, 2020. — 294 p. — (Textbooks in Mathematics). — ISBN: 0367225700, 9780367225704. Formal Methods in Computer Science gives students a comprehensive introduction to formal methods and their application in software and hardware specification and verification. The first part introduces some fundamentals in formal methods, including set theory,...
CRC, Taylor & Francis Group, 2021. — 270 p. — ISBN: 978-0-367-54988-6. Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations,...
4rd Edition. — McGraw-Hill, 2022. — 320 p. — ISBN: 978-1-26-425881-9. Study smarter and stay on top of your discrete mathematics course with the best-selling Schaum’s Outline — now with the NEW Schaum’s app and website! Schaum’s Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university...
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...
Springer, 2021. — 229 p. — (Undergraduate Topics in Computer Science). — ISBN: 978-3-030-87885-6. This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for...
New York: Wiley-Interscience, 1979. — 393 p. Elementary definitions and examples Green's relations Simple semigroups, Rees-Suschkewitsch theorem The prime decomposition theorem for finite monoids Free monoids, languages, and codes Automata, rational languages, and their syntactic monoids Star problems for rational languages Rational prefix codes Algebraic languages The Burnside...
Dartmouth: Dartmouth College, 2019. — 99 p. Basic Definitions History Lewis Carroll Identity Dodgson/Muir Identity The Matrix Tree Theorem Involution Principle Lewis Carroll and the Red Hot Potato Connecting Identities The Red Hot Potato algorithm Sets Involutions Example Proof of φ1 Identity Proofs Connection to Zeilberger Zeilberger’s Proof Alternate Definition of φ1...
Singapore: World Scientific, 2017. — 292 p. Kashiwara Crystals Crystals of Tableaux Stembridge Crystals Virtual, Fundamental, and Normal Crystals Crystals of Tableaux II Insertion Algorithms The Plactic Monoid Bicrystals and the Littlewood-Richardson Rule Crystals for Stanley Symmetric Functions Patterns and the Weyl Group Action The B_infinity Crystal Demazure Crystals The...
Sergei O. Kuznetsov, Ordered Sets for Data Analysis, Part 1: Relations, Orders, Lattices, Formal Concept Analysis Moscow: National Research University Higher School of Economics, 2019. — 93 p. This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to...
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...
Mercury Learning and Information, 2021. — 382 p. — ISBN: 978-1-68392-763-1. 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...
New York: Springer, 2014. — 708 p. This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory, and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the...
Brown University, 2018. — 51 p. This year-long class exposes students to six fundamental areas of mathematics. It is a team taught by six members of the faculty. Fall topics include logic, set theory, combinatorics, and analysis. Spring topics include number theory, algebra, and geometry. Approximately 4 weeks are devoted to each topic. The class emphasizes rigorous proofs and...
Chapman and Hall/CRC, 2019. — xxvi, 416 p. — (Discrete Mathematics and Its Applications). — ISBN: 978-0-367-23503-1. 50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern...
Springer, 2014. — xiv, 154 p. — (Universitext). — ISBN: 3-319-07964-6, 3-319-07965-4, 978-3-319-07964-6, 978-3-319-07965-3. The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily, and completely rigorously to graduate students and advanced undergraduates. The book takes several specific problems and solves them,...
8th Edition, Global Edition. — Pearson, 2019. — 772 p. — ISBN: 978-1-292-23370-3. For one- or two-term introductory courses in discrete mathematics. An accessible introduction to the topics of discrete math, this best-selling text also works to expand students’ mathematical maturity. With nearly 4,500 exercises, Discrete Mathematics provides ample opportunities for students to...
Blurb, Incorporated, 2020. — 235 p. — ISBN: 978-1714675845. Discrete math is a popular book topicstart Googling around and you'll nd a zillion dierent textbooks about it. Take a closer look, and you'll discover that most of these are pretty thick, dense volumes packed with lots of equations and proofs. They're prin- cipled approaches, written by mathematicians and (seemingly)...
New York: Prentice-Hall, 1997. — 212 p. The Prentice Hall Essence of Computing Series provides a concise, practical and uniform introduction to the core components of an undergraduate computer science degree. Acknowledging recent changes within Higher Education, this approach uses a variety of pedagogical tools-case studies, worked examples and self-test questions to underpin...
Whitman College, 2021. — 153 p. Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics. As the name suggests, however, it is broader than this: it is about combining things. Questions that arise include counting problems: "How many ways can these elements be combined ?" But there are other questions, such as...
Springer Open, 2019. - 125 p. - (Lecture Notes in Mathematics, 2243). - ISBN: 3030279677. This book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem . Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and...
CRC Press, 2021. — 256 p. — (Discrete Mathematics and Its Applications). — ISBN: 978-1138364332. Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers...
Copenhagen: IT University of Copenhagen, 2021. — 760 p. Network science is the field dedicated to the investigation and analysis of complex systems via their representations as networks. We normally model such networks as graphs : sets of nodes connected by sets of edges and a number of node and edge attributes. This deceptively simple object is the starting point of...
Packt Publishing, 2021. — 330 p. — ISBN: 9781838983147. A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key Features Apply the math of countable objects to practical problems in computer science Explore modern Python libraries such as...
Hoboken: Wiley, 2019. — 419 p. Presented in a comprehensive manner, this book provides a comprehensive foundation in algebraic approaches for the analysis of different types of social networks such as multiple, signed, and affiliation networks. The study of such configurations corresponds to the structural analysis within the social sciences, and the methods applied for the...
Cambridge Scholars Publishing 2019. — 621 p. — ISBN: 9781527537033. This book analyses selected algorithms for random and stochastic phenomena in the areas of basic probability, random variables, mathematical expectation, special probability and statistical distributions, random processes, and Markov chains. It also presents a novel approach, titled the Complex Probability...
Springer, 2021. — 322 p. — ISBN: 9783030611149. This textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer...
8th Edition. — McGraw-Hill Education, 2012. — 1118 p. — ISBN: 978-1-259-67651-2. A discrete mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical...
CRC Press, 2021. - 272 p. - ISBN: 9780367549886 Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean...
Springer, 3020. — 560 p. — ISBN: 978-3-030-58375-0. In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in...
Springer, 2020. — 159 p. — ISBN: 978-981-15-9900-2. This book discusses different types of distance functions defined in an n-D integral space for their usefulness in approximating the Euclidean metric. It discusses the properties of these distance functions and presents various kinds of error analysis in approximating Euclidean metrics. It also presents a historical...
New York: Springer, 2020. — 504 p. — (Springer Optimization and Its Applications, 165). — ISBN: 978-3-030-55856-7. Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and...
6 ed. — Pearson Prentice Hall, 2009. — 550 p. — ISBN: 9780132078450. Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field. This book is written at an...
Springer, 2020. — 207 p. — (Understanding Complex Systems). — ISBN ISBN 978-3-030-36102-0. This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a...
Hoboken: John Wiley & Sons, 2018. — 1209 p. On the point of this book Basic data types Logic Proofs Mathematical induction Analysis of algorithms Number theory Relations Counting Probability Graphs and trees.
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...
Metric Version. — Cengage Learning, Inc., 2020. — xxii+1036 p. — ISBN 978-0-357-11408-7. Susanna Epp's "Discrete Mathematics with Applications" provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics,...
Cambridge University Press, 2011. — 266 p. — (London Mathematical Society Lecture Note Series 382). — ISBN: 978-0-521-15433-8. This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower...
Springer 2020. — XIII+185 p. — ISBN: 978-3-030-37861-5, ISBN: 978-3-030-37860-8. Demonstrates the beauty of mathematics through a concise discussion of 9 topics in discrete math; Appealing to a wide readership from high school students to research mathematicians; Includes an appendices with basic tools used in the text and a healthy list of identities derived within the book....
Cambridge University Press, 2020. — 347 p. — ISBN: 978-1-108-47113-7. Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from...
Cambridge University Press, 2020. — 347 p. — ISBN: 978-1-108-47113-7. Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from...
Cambridge: Cambridge University Press, 2020. — 300 p. — ISBN: 1108471137. Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from...
Cambridge: Cambridge University Press, 2020. — 300 p. — ISBN: 1108471137. Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from...
Córdoba: Tiraboschi, 2019. — 150 p. Apuntes para el curso de la materia Matemática Discreta I, FAMAF, UNC, 2019. Unidades de contenidos: Números Enteros, Conteo, Divisibilidad, Aritmética Modular, Grafos, Árboles Apéndices: Permutaciones, El principio del tamiz, La función de Euler, Grafos planares.
2nd ed. — Springer, 2020. — 467 p. — (Undergraduate Topics in Computer Science). — ISBN: 3030342085. This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The...
New York: Springer, 2019. — 496 p. This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on...
Boca Raton: CRC Press, 2020. — 499 p. Combinatorics and Number Theory of Counting Sequencesis an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are...
Springer, 2019. — 237 p. — ISBN: 9811397449. This book covers all aspects of head-related transfer function (HRTF), from the fundamentals through to the latest applications, such as 3D sound systems. An introductory chapter defines HRTF, describes the coordinate system used in the book, and presents the most recent research achievements in the field. HRTF and sound localization...
2nd Ed. — CRC Press, 2019. — xlii, 658 p. — (Textbooks in mathematics). — ISBN: 978-1-138-05259-8. True PDF "Discrete Mathematics with Ducks", Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first...
Springer, 2019. — 107 p. — (Trends in Logic 50). — ISBN: 978-3-030-12095-5. This translation of Leo Esakia’s book on Heyting algebras has been in the making for a long time. The book was originally published in 1985 by the Georgian publishing house Metsniereba (Science). It was the first volume of Esakia’s planned two volume monograph on Heyting algebras. The book turned out to...
Z języka angielskiego przełożyli E. Sepko-Guzicka, W. Guzicki, P. Zakrzewski. — Warszawa: Wydawnictwo Naukowe PWN, 1996. — 902 s. — (in Polish). Oddajemy do rąk Czytelnika podręcznik matematyki dyskretnej — bardzo ważnego działu matematyki, który ma obecnie szerokie zastosowanie w informatyce. Podstawowy materiał wykładu jest zawarty w czterech pierwszych rozdziałach. Tematy...
Oxford: Oxford University Press, 2007. — 360 p. Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation, and has taught, influenced and inspired generations of students and researchers in mathematics. This volume summarizes and reviews the consistent themes from his work...
3rd. ed. (ver. 6) — University of Massachusetts Lowell, 2019. — 567 p. Applied Discrete Structures is designed for use in a university course in discrete mathematics spanning up two semesters. Its original design was for computer science majors to be introduced to the mathematical topics that are useful in computer science. It can also serve the same purpose for mathematics...
San Diego: UC San Diego, 2019. — 503 p. Boolean Functions & Computer Arithmetic Boolean Functions Exercises for Section Number Systems & Computer Arithmetic Computer Arithmetic Exercises for Section Multiple Choice Questions for Review Logic Propositional Logic Implication Exercises for Section Predicate Logic Exercises for Section Multiple Choice Questions for Review Number...
Minneapolis: University of Minnesota, 2019. — 1327 p. These notes are a detailed introduction to some of the basic objects of combinatorics and algebra: binomial coefficients, permutations and determinants (from a combinatorial viewpoint – no linear algebra is presumed). To a lesser extent, modular arithmetic and recurrent integer sequences are treated as well. The reader is...
2nd Edition. — Ohio, USA: The Education Publisher Inc., 2011. — 399 p. — (Graduate Textbook in Mathematics). — ISBN: 978-1-59973-154-4. Automorphism groups survey similarities on mathematical systems, which appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, • • • and theoretical physics, theoretical chemistry, etc.. In geometry,...
Rehoboth, USA: American Research Press, 2005. — 124 p. — (Graduate Textbook in Mathematics). — ISBN: 1-931233-92-6. A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are...
Berlin: Springer, 1991. — 213 p. With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the underlying mathematical object, and properties exploited by algorithms are often closely tied to classical structural analysis in mathematics. This connection between algorithms and structure is in...
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...
Boca Raton: CRC Press, 2018. — 308 p. The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by...
Amsterdam: North-Holland Publishing Company, 1982. — 197 p. — ISBN: 9783642008139. The watchdog technique for forcing convergence in algorithms for constrained optimization / R.M. Chamberlain et al.] Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization / D. Gabay A superlinearly convergent algorithm for constrained optimization...
5th Ed. — Cengage Learning, 2019. — xxii+1036 p. — ISBN 978-1-337-69419-3. Susanna Epp's "Discrete Mathematics with Applications" provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the...
Cambridge: Cambridge University Press, 1999. — 290 p. This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the early 1980s: the number of n × n alternating sign matrices, objects that...
Springer, 2016. — 255 p. — (Lecture Notes in Mathematics 2160). — ISBN: 978-3-319-39779-5. This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited...
3rd ed. — Independently published, 2019. — 407 p. — ISBN: 978-1792901690. This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics...
Springer, 2018. — 176 p. — (Springerbriefs in Computer Science). — ISBN: 3030020738. Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form more complex ones. Coming historically from algebraic topology, operads intervene now as important objects in computer...
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....
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....
New York: Springer, 1992. — 234 p. The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics. Decision Problems for Groups — Survey and Reflections The Word...
Hoboken: Wiley, 2006. — xii + 691 p. — ISBN: 9780471476023., 0471476021. Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through...
AMS, 2018. — 224 p. — (Student Mathematical Library). — ISBN: 9781470442903. This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but...
Chapman and Hall/CRC, 2018. — 604 p. — ISBN: 978-1498738910. The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts....
Springer, 2019. — 581 p. — (Foundations in Signal Processing, Communications and Networking 15). — ISBN: 978-3-030-00310-4. The fifth volume of Rudolf Ahlswede’s lectures on Information Theory focuses on several problems that were at the heart of a lot of his research. One of the highlights of the entire lecture note series is surely Part I of this volume on arbitrarily varying...
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...
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...
Chapman and Hall/CRC, 2019. — 284 p. The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were...
Chapman and Hall/CRC, 2019. — 534 p. Discrete Mathematics has permeated the whole of mathematics so much so it has now come to be taught even at the high school level. This book presents the basics of Discrete Mathematics and its applications to day-to-day problems in several areas. This book is intended for undergraduate students of Computer Science, Mathematics and...
Amsterdam: Elsevier, 1997. — 661 p. There is a strong case for electrical network topologists and submodular function theorists being aware of each other's fields. Presenting a topological approach to electrical network theory, this book demonstrates the strong links that exist between submodular functions and electrical networks. The book contains: a detailed discussion of...
Springer, 2019. — 235 p. 9th International Conference on Non-Integer Order Calculus and Its Applications, Łódź, Poland. This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that...
Springer, 2018. — 258 p. — ISBN: 3319978454. This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the...
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...
2nd Edition. — The McGraw-Hill Companies, Inc., 1987. — 369 p. — (Schaum's Outline Series). — ISBN: 0-07-037990-4. Computers appear in almost all fields of human endeavor, wherever data are collected and analyzed. Furthermore, with the development of inexpensive microcomputers, more and more individuals are buying and operating their own computer. For these reasons, certain...
Springer, 2018. — 515 p. — (Springer Optimization and Its Applications 131). — ISBN: 978-3-319-74325-7. A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers...
Springer, 2018. — 515 p. — (Springer Optimization and Its Applications 131). — ISBN: 3319743244. A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and...
Springer, 2018. — 189 p. — (Lecture Notes in Mathematics 2209). — ISBN: 3319740385. This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of...
Cambridge University Press, 2018. — 367 p. — ISBN: 978-1-107-15398-1. Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that common threads connect the different areas,...
Cambridge University Press, 2018. — 589 p. — (Cambridge Studies in Advanced Mathematics, 172). — ISBN: 978-1-107-18233-2. This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features...
Long Grove: Waveland Press, Inc., 1997. — 525 p. — ISBN: 978-0881339406. This highly regarded work fills the need for a treatment of elementary discrete mathematics that provides a core of mathematical terminology and concepts as well as emphasizes computer applications. Includes numerous elementary applications to computing and examples with solutions. Number Systems The...
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...
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...
Springer International Publishing AG, 2018. — 235 p. — (Advanced Courses in Mathematics - CRM Barcelona). — ISBN: 978-3-319-70156-1. Homological algebra is a ubiquitous subject: it is both an active field of research in its own right and a widespread toolbox for many mathematicians. As time passes, there is the danger that, while the amount of knowledge increases, it may split...
Cambridge University Press, 2008. — 290 p. Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and yet the use of sieve methods is still evolving. At one time it seemed that, as analytic tools improved, the use of sieves would decline, and only their role as an auxiliary device would survive. However, as probability and combinatorics have penetrated...
Berlin: Walter de Gruyter GmbH, 2016. — 354 p. This book is based on courses taught by the authors over many years at universities in Dortmund, Hamburg, Munich, and Stuttgart. Essentially, no knowledge beyond high school mathematics is required for reading this book. However, the density of the presentation suggests a certain amount of mathematical maturity, as, for example,...
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...
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...
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...
Springer, 2018. — 238 p. This book discusses Moore finite state machines (FSMs) implemented with field programmable gate arrays (FPGAs) including look-up table (LUT) elements and embedded memory blocks (EMBs). To minimize the number of LUTs in FSM logic circuits, the authors propose replacing a state register with a state counter. They also put forward an approach allowing...
Springer International Publishing AG, 2018. — 274 p. — (ICME-13 Monographs) — ISBN: 978-3-319-70307-7. This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete...
8th ed. — Pearson, 2017. — 768 p. — ISBN: 0321964683. For one- or two-term introductory courses in discrete mathematics. An accessible introduction to the topics of discrete math, this best-selling text also works to expand students mathematical maturity. With nearly 4,500 exercises, Discrete Mathematics provides ample opportunities for students to practice, apply, and...
2009. — 312 p. Computers and Computing: Numbers, Circuits, and Logic Circuits Logic Design of a Simple Processor Cryptography: Integers and Modular Arithmetic Cryptography and Modular Arithmetic Integers and Division Combinatorics: Sets, Counting, and Probability Sets Counting Probability Algorithmic Analysis: Searching and Sorting Algorithms for Searching and Sorting:...
Cambridge University Press, 2017. — 472 p. — ISBN: 978-1-107-06237-5. Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting...
Hoboken: Wiley, 2017. — 680 p. Written exclusively with computer science students in mind, Discrete Mathematics for Computer Science provides a comprehensive treatment of standard course topics for the introductory discrete mathematics course with a strong emphasis on the relationship between the concepts and their application to computer science. The book has been crafted to...
Springer Nature Singapore Pte Ltd., 2017. — 126 p. — ISBN: 978-981-10-6146-2. Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan...
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...
Hoboken: Wiley, 2015. — 241 p. A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set...
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...
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: 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...
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...
Springer International Publishing AG, 2018. — 70 p. — (SpringerBriefs in Electrical and Computer Engineering) — ISBN: 3319604678. This brief focuses on introducing a novel mathematical framework, referred as hypergraph theory, to model and solve the multiple interferer scenarios for future wireless communication networks. First, in Chap. 1, the authors introduce the basic...
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...
Berlin: Springer, 1975. — 113 p. Matroid theory has its origin in a paper by H. Whitney entitled "On the abstract properties of linear dependence" , which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear dependence and independence in vector spaces, and to use these for the axiomatic definition of a...
Strasbourg: European Mathematical Society, 2015. — 468 p. Since the seminal works of Gian-Carlo Rota and his school in the 1960s, combinatorics has become a respected branch of modern mathematics. Today it appears at the intersection of a wide variety of mathematical sciences. In fact, techniques and methods from combinatorics have become indispensable in such diverse areas as,...
Springer International Publishing AG, 2017. — 59 p. — (SpringerBriefs in Computer Science) — ISBN: 3319571826. This book is a pedagogical presentation aimed at advanced undergraduate students, beginning graduate students and professionals who are looking for an introductory text to the field of Distance Geometry, and some of its applications. This versions profits from feedback...
New York: Springer, 2017. — 388 p. — (Foundations in Signal Processing, Communications and Networking; 13). — ISBN: 978-3-319-53137-3. The fourth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Combinatorics. Rudolf Ahlswede's original motivation to study combinatorial aspects of Information Theory problems were zero-error codes: in this case the...
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...
London: Bentham Science Publishers, 2015. — 260 p. This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and attractive way. Readers will easily identify problems/techniques/solutions without the frustration of long searches through...
M.I.T., 2017. — 999 p. This book covers elementary discrete mathematics for Computer Science and Engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Proofs. What is a Proof? The Well Ordering Principle. Logical Formulas. Mathematical Data Types. Induction. State Machines. Recursive Data Types. Infinite Sets. Structures. Number Theory....
Bonn: Bernhard Korte, 2016. — 45 p. Fundamental Counting Rules Elementary Counting Coefficients Assignments Generalized Counting Coefficients Permutations Further Combinatorial Techniques Computation of Sums Sums: Direct Methods Difference and Sum Operators Inversions Linear Recursions of Depth Generating Functions Using Generating Functions to Solve Recursions Exponential...
Minneapolis: University of Minnesota, 2014. - 100 p. A partially ordered set, or poset, is a set of elements and a binary relation which determines an order within elements. Various combinatorial properties of finite and ordered posets have been extensively studied during the last 4 decades. The Sperner property states that the size of the largest subset of pairwise...
New York: Springer, 2003. — 229 p. Introduction and Motivation Definition and Formulation of the DOMP Several Linearisations of the Quadratic Formulation ( DOMP ) A Specific Branch-and-Bound Method Heuristic Procedures Particular Cases and Related Problems Extension to the Capacitated Case Conclusions and Further Research
Springer Science+Business Media LLC, 2017. — 620 p. — (The IMA Volumes in Mathematics and its Applications 161) — ISBN: 9781493970049. This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric...
Springer Science+Business Media, New York, 2013. — 427 p. — ISBN: 1461451272. This volume is a collection of research surveys on the Distance Geometry Problem (DGP) and its applications. It will be divided into three parts: Theory, Methods and Applications. Each part will contain at least one survey and several research papers. The first part, Theory, will deal with theoretical...
Springer, 2013. — 57 p. This monograph discusses some of the most well-known string selection problems (SSP), offering a compendium of the current state-of-the-art methods presented in the literature. In particular, this work is intended as a general and comprehensive guide to understanding the very basic notions of mathematical optimization for sequence selection in biology,...
New York: Leibniz Company, 2015. — 406 p. Graduate students and researchers in combinatorics and matroid theory as well as computer scientists, graph theorists and scientific libraries may find this book useful. Matroids were introduced in 1935 as an abstract generalization of graphs and matrices. Since the mid-1950s, much progress has been made, and there now exists a large...
Pearson, 2007. — 789 p. For a one- or two-term introductory course in discrete mathematics. Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh’s algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects...
Boston: The MIT Press, 2017. — 987 p. Proofs What is a Proof? Propositions Predicates The Axiomatic Method Our Axioms Proving an Implication Proving an “If and Only If” Proof by Cases Proof by Contradiction Good Proofs in Practice The Well Ordering Principle Well Ordering Proofs Template for Well Ordering Proofs Factoring into Primes Well Ordered Sets Logical Formulas...
2nd edition in progress. — Springer, 2017. — 660 p. This is a book about discrete mathematics which also discusses mathematical reasoning and logic. Since the publication of the first edition of this book a few years ago, I came to realize that for a significant number of readers, it is their first exposure to the rules of mathematical reasoning and to logic. As a consequence, the...
Chapman & Hall/CRC, 2006. — 243 p. This book contains original contributions of the author in the field of authentication schemes. Most of which are already published by international conferences and in journals, but they are presented with improvement in this book together with references and reviews of related work by other authors in the field. Gus Simmons first introduced...
4th Edition. — Jones & Bartlett Learning, 2017. — 1023 p. — ISBN: 978-1-284-07040-8. Includes access to student companion website. Updated to align to the latest 2013 ACM/IEEE Computer Science curricula, This Book is designed for the one- to two-term Discrete Mathematics course. The structure of the book supports the spiral method of learning, by first introducing basic...
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...
Springer Science+Business Media, New York, 2013. — 206 p. — ISBN10: 1461470978 It is a well-known fact that the concept of overconvergence in approximation theory may have several meanings. The most common, developed for the first time by Ostrovski and Walsh, is that given a sequence of functions approximating a given (analytic) function in a set (region), the convergence may...
Geneseo: SUNY, 2015. — 299 p. This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed...
University of Massachusetts, 2016. — 377 p. As a general description one could say that discrete mathematics is the mathematics that deals with “separated” or discrete sets of objects rather than with continuous sets such as the real line. For example, the graphs that we learn to draw in high school are of continuous functions. Even though we might have begun by plotting...
Springer, 1995. — 316 p. — (Tutorial Guides in Computing and Information Systems). — ISBN: 0412562804, 9780412562808 The purpose of this text is to teach the novice the foundations of discrete mathematics as applied to computing. Illustrative examples are given throughout the book, followed by exercises which should provide an understanding and an appreciation of the...
Glendale: Kapa & Omega, 2010. — 501 p. Maps as a mathematical topic arose probably from the four color problem and the more general map coloring problem in the mid of nineteenth century although maps as polyhedra which go back to the Platonic age. I could not list references in detail on them because it is well known for a large range of readers and beyond the scope of this...
L.: Springer, 2001. - 253 p. This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001. The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover...
Springer, 2013. — 214 p. Imagine walking along a beach, looking for seashells. Each seashell you unearth is precious and exquisite, with its own unique beauty. Discovering the connections between different areas of mathematics is much the same. There are treasures to be found in applying one field to another in unexpected ways. This text is intended for graduate and upper level...
New York: Springer, 2016. - 674 p. This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a...
Springer, 1974. — 389 p. The digital computer is a machine which is inherently finite in all of its aspects which are of importance to a programmer or user. Whether the problem posed to the computer relates to numerical computation, symbol manipulation, information retrieval, or picture generation, the procedures and results are restricted by the finiteness of word length and...
Edward A. Bender & S. Gill Williamson, 2005. — 256 p. —– ISBN: 0486442500 Discrete mathematics is fundamental to computer science, and interesting, challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, artificial intelligence, theoretical computer science, and elsewhere. This...
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...
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...
World Scientific Publishing Europe Ltd., 2016. — 182 p. — (LTCC Advanced Mathematics Series. Volume 3) — ISBN: 9781786340290 The London Taught Course Centre (LTCC) for Ph.D. students in the Mathematical Sciences has the objective of introducing research students to a broad range of advanced topics. For some students, these topics might include one or two in areas directly...
Cambridge University Press, UK, 2013. — 396 p. — (Cambridge Studies in Advanced Mathematics 140) — ISBN: 1107031575 This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are...
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...
Portland State University, 2005. — 160 p. This book contains programming experiments that are designed to reinforce the learning of discrete mathematics, logic, and computability. It is the outgrowth of the experimental portion of a one-year course in discrete structures, logic, and computability for sophomores at Portland State University. The course has evolved over the last...
The Great Courses, 2009. — 262 p. Discrete mathematics can be described as an advanced look at the mathematics that we learned as children. In elementary school, we learned to count, did basic arithmetic, and amused ourselves with solving puzzles, ranging from connecting the dots, to coloring, to more sophisticated creative pursuits. So what exactly is discrete mathematics?...
Johannes Kepler University, Linz, 2010. — 145 p. The objective of the course is to provide an overview of the main topics and techniques of Discrete Mathematics. The emphasis will be on the investigation of the most fundamental combinatorial structures. Words and Sets Graphs and Digraphs Eulerian and Hamiltonian graphs Introduction to Clones Minimal clones and CSP
Johannes Kepler University, Linz, 2006. — 164 p. The objective of the course is to provide an overview of the main topics and techniques of Discrete Mathematics. The emphasis will be on the investigation of the most fundamental combinatorial structures. In this course we address some of the most importand topics in Discrete Mathematics: elementary combinatorial configurations...
3rd edition. — Burlington: John&Barlett Learning, 2015. — 524 p. Written for the one-term course, Essentials of Discrete Mathematics, Third Edition is designed to serve computer science and mathematics majors, as well as students from a wide range of other disciplines. The mathematical material is organized around five types of thinking: logical, relational, recursive,...
Springer, 2016. – 167 p. – ISBN: 978-3-319-39557-9. Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes,...
New York: Springer, 2016. - 629 p. This book constitutes the refereed proceedings of the 22nd International Conference on Computing and Combinatorics, COCOON 2016, held in Ho Chi Minh City, Vietnam, in August 2016. The 50 revised full papers papers presented in this book were carefully reviewed and selected from various submissions. The papers cover various topics including:...
Arkansas Tech University, 2016. — 344. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, Business, and the sciences. Besides reading the book, students are strongly encouraged to do all...
2nd Ed. — CreateSpace Independent Publishing Platform, 2016. — 335 p. — ISBN: 1534970746, 9781534970748 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves...
Kluwer, 1984. — 207. The roots of the project which culminates with the writing this book can be traced to the work on logic synthesis started in 1979 the IBM Watson Research Center and at University of California, Berkeley. During the preliminary phases of these projects, the importance of logic minjmization for the synthesis of area and performance effective circuits clearly...
Singapore: World Scientific, 2001. — 286 p. This book describes and summarizes past work in important areas of combinatorics and computation, as well as gives directions for researchers working in these areas in the 21st century. It contains primarily survey papers and presents original research by Peter Fishburn, Jim Ho Kwak, Jaeun Lee, K.H. Kim, F.W. Roush and Susan Williams....
Cambridge: Cambridge University Press, 2016. - 497 p. Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include...
Singapore: World Scientific, 2016. - 260 p. The present volume covers the general area of algebra, logic and combinatorics. The main readers are likely to be graduate students and more experienced researchers in the mathematical sciences, looking for introductions to areas with which they are unfamiliar. The mathematics presented is intended to be accessible to first year Ph.D....
Springer, 2002. — 200 p. — (Springer Undergraduate Mathematics Series). — ISBN10: 1852332360; ISBN13: 978-1852332365. Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he...
Los Angeles: USCD, 2015. - 331 p. The material in this unit of study was, over several years, presented by the authors to lower division undergraduates in the Department of Mathematics and the Department of Computer Science and Engineering at the University of California, San Diego (UCSD). All material has been classroom tested by the authors and other faculty members at UCSD.
Los Angeles: USCD, 2012. - 348 p. The material in this unit of study was, over several years, presented by the authors to lower division undergraduates in the Department of Mathematics and the Department of Computer Science and Engineering at the University of California, San Diego (UCSD). All material has been classroom tested by the authors and other faculty members at UCSD.
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...
Cambridge: Cambridge University Press, 2009. - 376 p. This volume, the third in a sequence that began with The Theory of Matroids (1986) and Combinatorial Geometries (1987), concentrates on the applications of matroid theory to a variety of topics from geometry (rigidity and lattices), combinatorics (graphs, codes, and designs) and operations research (the greedy algorithm)....
Cambridge: Cambridge University Press, 1987. - 228 p. A continuation of The Theory of Matroids, (edited by N. White), this volume consists of a series of related surveys by top authorities on coordinatizations, matching theory, transversal and simplicial matroids, and studies of important matroid variants. An entire chapter is devoted to matroids in combinatorial optimization,...
Cambridge: Cambridge University Press, 2008 - 337 p. The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory, and field theory. Furthermore, matroid theory is alone among mathematical...
Bellin: Springer, 2011. - 424 p. Un'Introduzione Alla Teoria Delle Funzioni Di Möbius Some Remarks on the Critical Problem The Tutte Polynomial Part I: General Theory On 3-Connected Matroids and Graphs The Poset of Subpartitions and Cayley's Formula for the Complexity of a Complete Graph Engineering Applications of Matroids - A Survey Matroids and Combinatorial Optimisation...
New York: Springer, 2014. - 127 p. Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial...
Amsterdam: North Holland, 2015. - 438 p. Latin Squares and Their Applications Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the...
Academic Press, 1970. — 252. The development of the electronic computer has profoundly and irrevocably changed the scientific world. In so doing it has simultaneously created numerous opportunities for the application of mathematical ideas and methods to the solution of traditional scientific problems and made possible the exploration of research areas in mathematics and the...
Springer, 2014. — 154 p. — (Universitext). — ISBN: 3319079646. The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of...
4th edition. — Hoboken: Wiley, 2016. — 384 p. — (Wiley Series in Discrete Mathematics and Optimization) — ISBN: 978-1119061953. Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating...
Springer, 1993. — 382. In July 1992, the International Symposium on Logic Synthesis and Microprocessor Architecture was held in Iizuka, Japan. The papers presented at the symposium were quite significant and we decided to publish the most outstanding of those concerned with Logic Synthesis and Optimization in textbook form for graduate students and young researchers. There seem...
New York: Chapman & Hall/CRC , 2015. - 1244 p. The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both...
7th edition. — W. H. Freeman and Company, 2014. — 784 p. — ISBN: 1429215100 Judith Gersting's Mathematical Structures for Computer Science has long been acclaimed for its clear presentation of essential concepts and its exceptional range of applications relevant to computer science majors. Now with this new edition, it is the first discrete mathematics textbook revised to meet...
Cambridge: Cambridge University Press, 2012. - 352 p. Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of...
Thesis, Technische Universiteit Eindhoven, 1997, -156 p. With the increasing complexity and tight time-to-market schedules of today’s digital systems, it is becoming more and more difficult to design correct circuits for these systems. Therefore, throughout the design process it is necessary to check that no errors are made. This task is called verification. Traditionally, a...
Berlin: Springer, 2016. - 468 p. This book is a comprehensive explanation of graph and model transformation. It contains a detailed introduction, including basic results and applications of the algebraic theory of graph transformations, and references to the historical context. Then in the main part the book contains detailed chapters on M-adhesive categories, M-adhesive...
Kluwer, 1996. — 151 p. Symbolic Boolean manipulation using Binary Decision Diagrams (BDDs) has been applied successfully to a wide variety of tasks, particularly in very large scale integration (VLSI) computer-aided design (CAD). The concept of decision graphs as an abstract representation of Boolean functions dates back to early work by Lee and Akers. In the last ten years,...
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...
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...
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...
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, 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...
New York: Springer, 2015. - 735 p. This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs...
Springer, 1998. — 205 p. Within the last 10-13 years Binary Decision Diagrams (BDDs) have become the state-of-the-art data structure in VLSI CAD for representation and manipulation of Boolean functions. Today, BDDs are widely used and in the meantime have also been integrated in commercial tools, especially in the area of verification and synthesis. The interest in BDDs results...
3rd Edition. — CRC Press, 2009. — 843 p. — ISBN: 1439812802 Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet...
Hoboken: CRC Press, 2009. - 847 p. Logic Propositions and Truth Values Logical Connectives and Truth Tables Tautologies and Contradictions Logical Equivalence and Logical Implication The Algebra of Propositions Arguments Formal Proof of the Validity of Arguments Predicate Logic Arguments in Predicate Logic Mathematical Proof The Nature of Proof Axioms and Axiom Systems Methods...
Academic Press, 1983, -401 p. An international meeting devoted to the theme of Combinatorics on Words was held at the University of Waterloo, Canada during the week of August 16-22, 1982. There were 10 invited speakers and 23 contributed papers. Robert McNaughton has written that "the phenomenon underlying the call to this conference is the emergence of a theory of words as...
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...
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...
Cambridge University Press, 2004, -576 p. A series of important applications of combinatorics on words has emerged with the development of computerized text and string processing. The aim of this volume, the third in a trilogy, is to present a unified treatment of some of the major fields of applications. After an introduction that sets the scene and gathers together the basic...
Taylor & Francis, 2003. - 180 p. This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.
Cambridge University Press, 2010. — 703 p. This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda...
New York: Chapman & Hall/CRC, 2007. — 1354 p. Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook...
Cambridge University Press, 2012. — 412 p. — ISBN: 9780521767248 Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the...
N.-Y.: Taylor&Francis, 1988. - 304 p. This book makes the mathematical basis of formal methods accessible both to the student and to the professional. It is motivated in the later chapters by examples and exercises. Throughout, the premise is that mathematics is as essential to design and construction in software engineering as it is to other engineering disciplines. The...
Springer, 2015. — 471 p. — (Foundations in Signal Processing, Communications and Networking; 11). — ISBN: 978-3-319-12522-0. Classical information processing consists of the main tasks of gaining knowledge, storage, transmission, and hiding data. The first named task is the prime goal of Statistics and for the next two Shannon presented an impressive mathematical theory, called...
L.: Springer, 2013.- 500 p. This engaging text presents the fundamental mathematics and modeling techniques for computing systems in a novel and light-hearted way, which can be easily followed by students at the very beginning of their university education. Key concepts are taught through a large collection of challenging yet fun mathematical games and logical puzzles that...
Basel: Birkhäuser, 2002. - 543 p. The International Colloquium on Mathematics and Computer Science is a biennial event that first took place at the University of Versailles-St-Quentin in 2000 and was acknowledged a success. The second colloquium was held in September 16-19, 2002, again in Versailles; its proceedings are gathered in this book. The importance of these regular...
Basel: Birkhäuser, 2000. - 341 p. This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches. It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on...
Cambridge University Press, 2 ed., Vol. 2, 1999 – 1100 p. - This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science...
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...
L.: Dover Publications, 2010. - 251 p. 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 to combinatorial mathematics and to algebraic and logical structures focusing on the...
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...
5th edition. — Prentice Hall, 2002. — 612 p. Informal but thorough in its coverage, this introduction to discrete mathematics offers a carefully graded treatment of the basics essential to computer science. This book presents a sound mathematical treatment that increases smoothly in sophistication. Key Topics: The book presents utility-grade discrete math tools so that any...
N.-Y.: Springer, 2015. - 129 p. This monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and...
The MIT Press, 2010. — 153 p. - Overview. In problem solving, as in street fighting, rules are for fools: do whatever works-don’t just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing...
Third Edition. — A K Peters, 2005. — 803 p. — ISBN: 1568811667 Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. Written in a...
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...
Springer, 2011. — 248 p. — ISBN: 0857295993, 9780857296009 Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. Introduction to...
4th edition. — New Age International, 2009. — 315 p. — ISBN: 8122425747 , 8122425062 The fourth edition retains all chapters of third edition and chapter 4: Ordered Sets and Lattices and chapter 10: Combinatorics as well as several sections on Set Theory, Boolean Algebra, Geometric Linear Transformation and Linear Equation are added. We have tried to emphasize that concept and...
Wiley-Interscience, 1994. — 360 p. — ISBN: 0471571806, 9780471571803 Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are...
IOP Publishing, 2002, -766 p. 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 the frequent use of pertinent examples and...
MIT OpenCourse, 2008. — 91 p. An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works — don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is...
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,...
New York: Springer. – 2003. – 239 p. Recent history saw an unprecedented rise in amateur juggling. Today, there are hundreds of juggling clubs around the world, there are a number of specialized juggling magazines, and every year thousands of jugglers gather at juggling conventions to practice, exchange ideas, take part in competitions, and have fun together. Juggling is...
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...
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...
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, 2014. — 304 p. — (Foundations in Signal Processing, Communications and Networking; 10). — ISBN: 978-3-319-05479-7. Classical information processing consists of the main tasks gaining knowledge, storage, transmission, and hiding data. The first named task is the prime goal of Statistics and for the two next Shannon presented an impressive mathematical theory, called...
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.
Nova Science Publishers, 2009, -303 p. Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of computerized society for which traditional areas of mathematics such as...
Birkhäuser, 2003, -401 p. Order theory can be seen formally as a subject between lattice theory and graph theory. Indeed, one can say with good reason that lattices are special types of ordered sets, which are in tum special types of directed graphs. Yet this would be much too simplistic an approach. In each theory the distinct strengths and weaknesses of the given structure...
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. — 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...
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....
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...
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;...
CRC Press, 2012. — 538 p. — ISBN: 1466504994 Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting. Facilitating effective...
Chapman & Hall, London, 1992, 306 p., ISBN: 0-412-45650-8. This text aims to cover all the needed materials for a first course in its subject, yet it assumes no prior knowledge of computing. The book is written to show how discrete mathematics relates to program design. This computer science orientation stresses the importance of logic and proof, recursion, trees, algorithm...
Springer, 2000. — 344 p. — ISBN: 1852330899 This volume offers a new, "hands-on" approach to teaching Discrete Mathematics. A simple functional language is used to allow students to experiment with mathematical notations, which are traditionally difficult to pick up. This practical approach provides students with instant feedback and also allows lecturers to monitor progress...
Springer Basel, 2014. — 120 p. ISBN: 3034805535 Galileo Galilei said he was reading the book of nature as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers....
Springer, 2013. — 304 p. — ISBN: 144714533X, 1447145356 From the earliest examples of computation to the digital devices that are ubiquitous in modern society, the application of mathematics to computing has underpinned the technology that has built our world. This clearly written and enlightening textbook/reference provides a concise, introductory guide to the key mathematical...
Springer, 2013. — 118 p. — ISBN10: 3319017500 Adapted from a modular undergraduate course on computational mathematics, Concise Computer Mathematics delivers an easily accessible, self-contained introduction to the basic notions of mathematics necessary for a computer science degree. The text reflects the need to quickly introduce students from a variety of educational...
Dover, 2010. — 256 p. ISBN: 0486691152 This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer science majors, it emphasizes applications, offering more than 200 exercises to help students test their grasp of the material and providing...
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...
ISTE Ltd and John Wiley & Sons, 2010. — 915 p. — ISBN: 1848211961. How many ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network ? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts...
Springer, 2013. - 300 p. ISBN: 8132210522 This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general...
Dublin, Cambridge: 1853. — 736 p. Lectures on quaternions : containing a systematic statement of a new mathematical method, of which the principles were communicated in 1843 to the Royal Irish academy, and which has since formed the subject of successive courses of lectures, delivered in 1848 and subsequent years, in the halls of Trinity college, Dublin
Springer, 2013, -134 p. Hypergraphs are systems of finite sets and form, probably, the most general concept in discrete mathematics. This branch of mathematics has developed very rapidly during the latter part of the twentieth century, influenced by the advent of computer science. Many theorems on set systems were already known at the beginning of the twentieth century, but...
Chapman and Hall/CRC, 2011. – 921 p. – ISBN: 1420093649, 9781420093643 Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the...
3rd ed. — Wiley, 2008. — 373 p. — (Wiley-Interscience Series in Discrete Mathematics and Optimization). — ISBN: 978-0470170205. 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...
AK Peters, 2007. - 240 p. ISBN: 1568813236 (CMS Treatises in Mathematics) Every mathematician, and user of mathematics, needs to manipulate sums or to find and handle combinatorial identities. In this book, the author provides a coherent tour of many known finite algebraic sums and offers a guide for devising simple ways of changing a given sum to a standard form that can be...
3rd Edition. — Brooks Cole, 2012. — 504 p. — ISBN13: 978-0-8400-4942-1, 0-8400-4942-0. Master the fundamentals of discrete mathematics and proof-writing with mathematics: a discrete introduction. With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is...
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...
New Age International (P) Ltd., 2009. – 459 p. – 2nd ed. – ISBN: 8122426697, 9788122426694 This edition is a revision of 2002 edition of the book. Considerable attention has been given to improve the first edition. As far as possible efforts were made to keep the book free from typographic and other errors. Most of the changes were made at the suggestions of the individuals who...
Springer – 2012, 300 p. ISBN: 3642298397, 9783642298400 Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design - its...
CRC Press, 2005. - 379 p. ISBN: 0849331560 Advances in Discrete Mathematics and Applications Volume 4 Sharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little...
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...
Springer, 2003, -332 p. Spӓtestens seit der Entwicklung der NP-Vollstandigkeitstheorie ist die Komplexitatstheorie ein zentrales Lehr- und Forschungsgebiet der Informatik. Mit dem NP≠P-Problem beinhaltet sie eine der groβen intellektuellen Herausforderungen der Gegenwart . Im Gegensatz zu anderen Gebieten der Informatik, in denen oft suggeriert wird, dass mit Rechnerhilfe...
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....
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....
W.H. Freeman and Company, 2006. — 784 p. — ISBN: 071676864X. Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of Mathematical Structures...
New Age International, 2005. - 264 p. ISBN: 8122416926 Salient Features Mathematical logic, fundamental concepts, proofs and mathematical induction (Chapter 1) Set theory, fundamental concepts, theorems, proofs, Venn diagrams, product of sets, application of set theory and fundamental products (Chapter 2) An introduction to binary relations and concepts, graphs, arrow diagrams,...
McGraw-Hill, 2005. - 349 p. ISBN: 0071388974 This real-world, application-oriented outline introduces non-math majors to: linear equations and linear growth; exponential functions and geometric growth; sets; and counting. Following this material are applications using the formulas derived in topics such as: descriptive statistics; basic probability theory; graphs and networks;...
Springer, 2012. - 97 p. ISBN: 1461441897 Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements...
Leibniz, 1998, -491 p. The engineering advances of the second half of the 20th century have created an avalanche of new technology. Control and use of that technology require, among many things, effective computational methods for logic. This book proposes one such method. It is based on a new theory of logic computation. Main features of the theory are an extension of...
Society for Industrial Mathematics, 2000. 84 p. ISBN10: 0898714362 Here is an in-depth, up-to-date analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis is useful for the study of various physical...
Pearson Education, Inc. – 2011, 526 p. ISBN: 0132122715, 9780132122719 Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using...
Massachusets Institute of Technology, 2010. — 519 p. Objectives of this book are to explain and apply the basic methods of mathematics in Computer Science, to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems. After reading this book you will be able to: reason mathematically about...
Princeton University Computer Science Department, 2004. — 339 p. This book offers an introduction to Mathematics oriented toward Computer Science and Engineering. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline Fundamental concepts of mathematics: definitions, proofs, sets, functions, relations. Discrete...
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...
Revised Edition. — MIT, 2012. — 829 p. This text explains how to use mathematical models and methods to analyze problems that arise in computer science. The subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering, adnd covers: Fundamental concepts of Mathematics: definitions, proofs, sets, functions, relations; Discrete...
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...
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...
Oxford University Press, 2008, -461 p., Second Edition, Misprints corrected, Contents added This is the second edition of Invitation to Discrete Mathematics. Compared to the first edition we have added Chapter 2 on partially ordered sets, Section 4.7 on Turan’s theorem, several proofs of the Cauchy–Schwarz inequality in Section 7.3, a new proof of Cayley’s formula in Section...
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...
Cornell University, 2011, -153 p. Discrete mathematics deals with objects that come in discrete bundles, e.g., 1 or 2 babies. In contrast, continuous mathematics deals with objects that vary continuously, e.g., 3.42 inches from a wall. Think of digital watches versus analog watches (ones where the second hand loops around continuously without stopping). Why study discrete...
Johns Hopkins University Press, 2009, -272 p. The adventures in this book are launched by easily understood questions from the realm of discrete mathematics, a wide-ranging subject that studies fundamental properties of the counting numbers 1, 2, 3, . and arrangements of finite sets. The book grew from talks for mathematically inclined secondary school students and college...
Cambridge University Press, 2010, -249 p. This book is issued from a previous book of the authors, entitled Rational Series and their Languages. The present text is an entirely rewritten, and enriched version of this book. An important part of the material presented here appears for the first time in book form. The text served for advanced courses held several times by the...
Dover Publications, 2004. — 245 p. Discrete mathematics is an essential tool in almost all subareas of computer science. In- teresting and challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, AI, theoretical computer science, and other areas. The course. The University 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...
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, 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...
From the Foundations and Trends in Networking series by NOWPress, 2007, -149 p. Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new...
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...
IOS Press, 2007, -348 p. As a part of the NATO Security Through Science Programme, the goal of the Advanced Study Institute Physics and Computer Science was to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. No one can dispute the current importance of applied as well as theoretical Computer Science in the development...
Springer, 1998, -327 p. In the summer semester of 1993 at Universität Ulm, I tried out a new type of course, which I called Theory lab, as part of the computer science major program. As in an experimental laboratory with written preparatory materials (including exercises), as well as materials for the actual meeting, in which an isolated research result is represented with its...
World Scientific, 2004, -1317 p. This book continues the tradition of two previous books Current Trends in Theoretical Computer Science, published by World Scientific Publishing Company in 1993 and 2001. We have been very impressed and encouraged by the exceptionally good reception of the two previous books. The positive comments received show that books of this nature are...
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...
Springer, 1995, -287 p. This introductory textbook presents an algorithmic and computability based approach to circuit complexity. Intertwined with the consideration of practical examples and the design of efficient circuits for these, a lot of care is spent on the formal development of the computation model of uniform circuit families and the motivation of the complexity...
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...
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,...
University of Pennsylvania, 2000. - 35 p. Overview. Basic Generating Functions. Identities and Asymptotics. Pentagonal Numbers and Prefabs. The Involution Principle. Remmel’s bijection machine. Sieve equivalence. Gordon’s algorithm. The accelerated algorithm of Kathy O’Hara. Equidistributed partition statistics. Counting the rational numbers.
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...
N. Y. ; L. : Academic Press, 1967.— xvi, 260 p. Puzzling problems permeate mathematics, and this is probably the strongest reason for the burgeoning growth of this queen of the sciences. The object of this book is to discuss the methods in graph theory that have been developed in the last century for attacking the four-color problem. It may be said without exaggeration...
Springer, 2008, -326 p. In October 2006, the editors of this volume organized a Dagstuhl Seminar on Complexity of Constraints at the Schloss Dagstuhl Leibniz Center for Informatics inWadern, Germany. This event consisted of both invited and contributed talks by some of the approximately 40 participants, as well as problem sessions and informal discussions. After the conclusion...
SIAM, 2011. - 389 p. Graphs are among the most important abstract data types in computer science, and the algorithms that operate on them are critical to modern life. Graphs have been shown to be powerful tools for modeling complex problems because of their simplicity and generality. Graph algorithms are one of the pillars of mathematics, informing research in such diverse...
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...
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...
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...
McGraw-Hill, 2007. - 489 p. 3rd edition. 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 all the essential course information in an easy-to-follow, topic-by-topic format. You also...
Springer, 2006, -413 p. The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classification results. Almost a century...
Springer, 2006, -447 p. This book has two goals. On the one hand it develops a completely new unifying theory of self-dual codes that enables us to prove a far-reaching generalization of Gleason’s theorem on weight enumerators of self-dual codes. On the other hand it is an encyclopedia that gives a very extensive list of Types of self-dual codes and their properties — the...
World Scientific Publishing, 2011. — 465 p. — (World Scientific Series on Nonlinear Science, Series А). — ISBN: 978-9814343633. Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It...
Springer, 2011, -114 p. The monograph is devoted to theoretical and experimental study of decision trees with a focus on minimizing the average time complexity. The study resulted in upper and lower bounds on the minimum average time complexity of decision trees for identification problems. Previously known bounds from information theory are extended to the case of...
Trent University, 2006, -181 p. The word `democracy’ has been used to describe many different political systems, which often yield wildly different outcomes. The simple rule of `decision by majority’ can be made complicated in several ways: Granting veto power to some participants (e.g. the permanent members of the UN Security Council or the President of the United States),...
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...
InTech, 2011, -352 p. Invented by Marco Dorigo in 1992, Ant Colony Optimization (ACO) is a meta-heuristic stochastic combinatorial computational discipline inspired by the behavior of ant colonies which belong to a family of meta-heuristic stochastic methodologies such as simulated annealing, Tabu search and genetic algorithms. It is an iterative method in which populations of...
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...
Addison-Wesley, 1998, -699 p. Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore...
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...
Springer, 2006, -445 p. Computer science abounds with applications of discrete mathematics, yet students of computer science often study discrete mathematics in the context of purely mathematical applications. They have to figure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad...
Cambridge: Cambridge University Press, 2009. — 586 p. — (Mathematical Sciences Research Institute Publications). — ISBN: 0-521-86134-9. Highlights include some of Aaron N. Siegel’s groundbreaking work on loopy games, the unveiling by Eric J. Friedman and Adam S. Landsberg of the use of renormalization to give very intriguing results about Chomp, and Teigo Nakamura’s Counting...
Cambridge University Press, 2002, -547 p. This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It contains articles by some of the foremost researchers and pioneers of combinatorial game theory, such as Elwyn Berlekamp and John Conway, by other researchers in mathematics and computer science, and by top game...
MRSI, 1996, -482 p. Combinatorial Game Theory, as an academic discipline, is still in its infancy. Many analyses of individual games have appeared in print, starting in 1902 with C.L. Bouton's analysis of the game of Nim. (For exact references to the works mentioned here, please see A. Fraenkel's bibliography on page 493 . It is was not until the 1930's that a consistent theory...
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...
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...
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...
Springer, 2010, -579 p. Cuts and metrics are well-known and central objects in graph theory, combinatorial optimization and, more generally, discrete mathematics. They also occur in other areas of mathematics and its applications such as distance geometry, the geometry of numbers, combinatorial matrix theory, the theory of designs, quantum mechanics, statistical physics,...
Macquarie University, Sydney, 1982, -190 p. This set of notes has been compiled over a period of more than 25 years. Chapters 1-4 were used in various forms and on many occasions between 1981 and 1990 by the author at Imperial College, University of London. An extra 14 chapters were written in Sydney in 1991 and 1992. Chapters 7 and 12 were added in 1997. The material has been...
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...
John Wiley, 1988. — 552 p. — ISBN: 0-471-84902-2. Here is a first-year course in discrete mathematics, requiring no calculus or computer programming experience, for students on computer science and mathematics courses. The approach stresses finding efficient algorithms, rather than existential results. It provides an introduction to constructing proofs (especially by...
Springer, 2008, -535 p. János Bolyai Mathematical Society. Laszlo Lovasz, briefly called Laci by his friends, turned sixty on March 9, 2008. To celebrate this special birthday two conferences have been held in Hungary, one in Budapest (August 5–9, 2008) with invited speakers only and one in Keszthely (August 11–15, 2008). Several top mathematicians and computer scientists have...
Springer, 2007, -261 p. János Bolyai Mathematical Society. The present volume is a collection of survey papers in the fields given in the title. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics,...
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...
Springer, 2005, -246 p. Proceedings of the Third International Symposium, SAGA 2005 This volume constitutes the proceedings of the 3rd Symposium on Stochastic Algorithms, Foundations and Applications (SAGA 2005), held in Moscow, Russia, at Moscow State University on October 20–22, 2005. The symposium was organized by the Department of Discrete Mathematics, Faculty of Mechanics...
World Scientific Publishing Company, 2010. — 272 p. In the past 50 years, discrete mathematics has developed as a far-reaching and popular language for modeling fundamental problems in computer science, biology, sociology, operations research, economics, engineering, etc. The same model may appear in different guises, or a variety of models may have enough similarities such...
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...
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...
Springer, 2010, -366 p. This book is the second volume of mathematical papers to commemorate the 60th birthday of Laszlo ('Laci') Lovasz on March 9, 2008. Prominent mathematicians that were inspired by Laci were invited to contribute to the celebrations of this milestone in the Summer of 2008. The response was overwhelming, and therefore two conferences were organized , the...
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...
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...
Palgrave Macmillan, 2002. - 320 p. Written with a clear and informal style "Discrete Mathematics for Computing" is aimed at first-year undergraduate computing students with very little mathematical background. It is a low-level introductory text which takes the topics at a gentle pace, covering all the essential material that forms the background for studies in computing and...
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...
Chapman & Hall/CRC, 2011. - 221 p. To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique...
Brooks Cole, 2010. — 920 p. Get the background you need for future courses and discover the usefulness of mathematical concepts in analyzing and solving problems with FINITE MATHEMATICS, 7th Edition. The author clearly explains concepts, and the computations demonstrate enough detail to allow you to follow-and learn-steps in the problem-solving process. Hundreds of examples,...
Brooks Cole, 2005. — 592 p. This book has two primary objectives: It teaches students fundamental concepts in discrete mathematics (from counting to basic cryptography to graph theory), and it teaches students proof-writing skills. With a wealth of learning aids and a clear presentation, the book teaches students not only how to write proofs, but how to think clearly and...
McGraw-Hill, 1996. - 339 p. The first edition of this popular text and reference has been translated into five languages! Students and practitioners will understand why when they use this powerful study tool and see how it makes learning and doing finite mathematics so much easier. They'll also appreciate, in this edition, the all new sections on graph theory, descriptive and...
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.
A K Peters, 2006. - 245 p. Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in. * Combinatorics. * Probability Theory. * Statistics. * Theory of Markov Chains. * Number Theory. One of the most important...
Brooks Cole, 2010. - 984 p. 4 edition Susanna Epp's "Discrete Mathematics with Applications" provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical...
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....
McGraw-Hill, 2008. - 364 p. If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains...
McGraw-Hill Companies, 2009. — 489 p. Schaum’s Outline Series Third Edition ISBN: 0071615865 Confusing Textbooks? 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...
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...
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...
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...
Brooks Cole, 2003. — 928 p. Susanna Epp's Discrete Mathematics, Third edition provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought....
Springer, 2011. — xiv, 465 p. — (Universitext). — ISBN: 978-1-4419-8047-2. This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in...
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,...
CRC, 2009. - 280 p. Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical...
Oxford University Press, 1998. — 426 p. Invitation to Discrete Mathematics is at once an introduction and a thoroughly comprehensive textbook for courses in combinatorics and graph theory. It also contains introductory chapters for more specialized courses such as probabilistic methods, applied linear algebra, combinatorial enumeration, and operations research. A lively and...
New Age International, 2009. — 408 p. — ISBN: 978-81-224-2607-6. The salient features of this book include: strong coverage of key topics involving recurrence relation, combinatorics, Boolean algebra, graph theory and fuzzy set theory. Algorithms and examples integrated throughout the book to bring clarity to the fundamental concepts. Each concept and definition is followed by...
Springer, 2006. - 405 p. Bolyai Society Mathematical Studies 15. Discrete mathematics, including (combinatorial) number theory and set theory has always been a stronghold of Hungarian mathematics. The present volume honouring Vera Sos and Andras Hajnal contains survey articles (with classical theorems and state-of-the-art results) and cutting edge expository research papers...
Springer, 2010. - 377 p. The field of discrete calculus, also known as discrete exterior calculus, focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate...
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.
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...
Prentice Hall, 2002. - 808 p. For one-semester undergraduate Discrete Mathematics courses for math and computer science majors. This exceedingly well-written text equips students to apply discrete mathematics and provides opportunities for practice of the concepts presented. A semester of Calculus is useful for reasons of sophistication.
Prentice Hall, 2003. — 216 p. — ISBN: 0-13-018661-9. This book introduces readers to the mathematics of computer science and prepares them for the math they will encounter in other college courses. It includes applications that are specific to computer science, helps learners to develop reasoning skills, and provides the fundamental mathematics necessary for computer...
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,...
Kapa & Omega, Glendale, AZ, USA, 2010. - 503 p. Abstract: A Smarandache system (G;R) is such a mathematical system with at least one Smarandachely denied rule r in R such that it behaves in at least two different ways within the same set G, i.e. , validated and invalided, or only invalided but in multiple distinct ways. A map is a 2-cell decomposition of surface, which can be...
McGraw-Hill, 1997. - 528 p. The first edition of this book sold more than 100,000 copies - and this new edition will show you why! Schaum's Outline of Discrete Mathematics shows you step by step how to solve the kind of problems you're going to find on your exams. And this new edition features all the latest applications of discrete mathematics to computer science! This guide...
Addison Wesley, 2001. - 600 p. For one or two term introductory courses in discrete mathematics. This book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem-solving techniques with woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to...
Brooks Cole, 2005. — 718 p. Master the fundamentals of discrete mathematics with "Discrete Mathematics for Computer Science"! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth...
2nd ed. — Jones & Bartlett Publishers, 2002. — 731 p. This introduction to discrete mathematics prepares future computer scientists, engineers, and mathematicians for success by providing extensive and concentrated coverage of logic, functions, algorithmic analysis, and algebraic structures. Discrete Mathematics, Second Edition illustrates the relationships between key concepts...
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 the...
Springer New York, 2010. - 400 p. This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many...
New Age Publications (Academic), 2007. - 577 p. All definitions and theorems in this text are stated extremely carefully so that students will appreciate the precision of language and rigor needed in mathematical sciences. Proofs are motivated and developed slowly, their steps are all carefully justified. Recursive definitions are explained and used extensively.
Academic Press, 2003. - 1045 p. This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science...
Addison-Wesley Professional, 1994. - 672 p. ISBN-10: 0201558025. ISBN-13: 978-0201558029. This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous...
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