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| cartesian product discrete math: A Spiral Workbook for Discrete Mathematics Harris Kwong, 2015-11-06 A Spiral Workbook for Discrete Mathematics 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. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills. |
| cartesian product discrete math: Topics in Graph Theory Wilfried Imrich, Sandi Klavzar, Douglas F Rall, 2008-10-27 From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, |
| cartesian product discrete math: Discrete Mathematics James L. Hein, 2003 Winner at the 46th Annual New England Book Show (2003) in the College Covers & Jackets category 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 through its thematic organization and provides a seamless transition between subjects. Distinct for the depth with which it covers logic, this text emphasizes problem solving and the application of theory as it carefully guides the reader from basic to more complex topics. Discrete Mathematics is an ideal resource for discovering the fundamentals of discrete math. Discrete Mathematics, Second Edition is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who wants to learn how the ideas apply to computer sciences.The choice of topics-and the breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses at the upper division level in undergraduate computer science courses. This book differs in several ways from current books about discrete mathematics.It presents an elementary and unified introduction to a collection of topics that has not been available in a single source.A major feature of the book is the unification of the material so that it does not fragment into a collection of seemingly unrelated ideas. |
| cartesian product discrete math: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
| cartesian product discrete math: Discrete Mathematics Oscar Levin, 2016-08-16 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 in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| cartesian product discrete math: Handbook of Product Graphs Richard Hammack, Wilfried Imrich, Sandi Klavžar, 2011-06-06 This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website. |
| cartesian product discrete math: Theoretical Computer Science and Discrete Mathematics S. Arumugam, Jay Bagga, Lowell W. Beineke, B.S. Panda, 2017-08-14 This volume constitutes the refereed post-conference proceedings of the International Conference on Theoretical Computer Science and Discrete Mathematics, held in Krishnankoil, India, in December 2016. The 57 revised full papers were carefully reviewed and selected from 210 submissions. The papers cover a broad range of topics such as line graphs and its generalizations, large graphs of given degree and diameter, graphoidal covers, adjacency spectrum, distance spectrum, b-coloring, separation dimension of graphs and hypergraphs, domination in graphs, graph labeling problems, subsequences of words and Parike matrices, lambda-design conjecture, graph algorithms and interference model for wireless sensor networks. |
| cartesian product discrete math: Discrete and Combinatorial Mathematics: An applied Introduction ( For VTU) Grimaldi Ralph P., 2013 |
| cartesian product discrete math: Discrete Mathematics for Computer Science Gary Haggard, John Schlipf, Sue Whitesides, 2006 Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! 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 of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career. |
| cartesian product discrete math: Discrete Mathematics B. S. Vatssa, 1993 |
| cartesian product discrete math: Practical Discrete Mathematics Ryan T. White, Archana Tikayat Ray, 2021-02-22 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 FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book. |
| cartesian product discrete math: Discrete Mathematical Structures for Computer Science Bernard Kolman, Robert C. Busby, 1987 This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow. |
| cartesian product discrete math: Product Graphs Wilfried Imrich, Sandi Klavžar, 2000-04-11 A comprehensive introduction to the four standard products of graphs and related topics Addressing the growing usefulness of current methods for recognizing product graphs, this new work presents a much-needed, systematic treatment of the Cartesian, strong, direct, and lexicographic products of graphs as well as graphs isometrically embedded into them. Written by two leading experts in this rapidly evolving area of combinatorics, Product Graphs: Structure and Recognition compiles and consolidates a wealth of information previously scattered throughout the literature, providing researchers in the field with ready access to numerous recent results as well as several new recognition algorithms and proofs. The authors explain all topics from the ground up and make the requisite theory and data structures easily accessible for mathematicians and computer scientists alike. Coverage includes * The basic algebraic and combinatorial properties ofproduct graph * Hypercubes, median graphs, Hamming graphs, triangle-free graphs, and vertex-transitive graphs * Colorings, automorphisms, homorphisms, domination, and the capacity of products of graphs Sample applications, including novel applications to chemical graph theory Clear connections to other areas of graph theory Figures, exercises, and hundreds of references |
| cartesian product discrete math: Combinatorial Optimization and Applications Zhao Zhang, Lidong Wu, Wen Xu, Ding-Zhu Du, 2014-11-13 This book constitutes the refereed proceedings of the 8th International Conference on Combinatorial Optimization and Applications, COCOA 2014, held on the island of Maui, Hawaii, USA, in December 2014. The 56 full papers included in the book were carefully reviewed and selected from 133 submissions. Topics covered include classic combinatorial optimization; geometric optimization; network optimization; optimization in graphs; applied optimization; CSoNet; and complexity, cryptography, and games. |
| cartesian product discrete math: Smart Computing Mohammad Ayoub Khan, Sanjay Gairola, Bhola Jha, Pushkar Praveen, 2021-05-12 The field of SMART technologies is an interdependent discipline. It involves the latest burning issues ranging from machine learning, cloud computing, optimisations, modelling techniques, Internet of Things, data analytics, and Smart Grids among others, that are all new fields. It is an applied and multi-disciplinary subject with a focus on Specific, Measurable, Achievable, Realistic & Timely system operations combined with Machine intelligence & Real-Time computing. It is not possible for any one person to comprehensively cover all aspects relevant to SMART Computing in a limited-extent work. Therefore, these conference proceedings address various issues through the deliberations by distinguished Professors and researchers. The SMARTCOM 2020 proceedings contain tracks dedicated to different areas of smart technologies such as Smart System and Future Internet, Machine Intelligence and Data Science, Real-Time and VLSI Systems, Communication and Automation Systems. The proceedings can be used as an advanced reference for research and for courses in smart technologies taught at graduate level. |
| cartesian product discrete math: Foundations of Discrete Mathematics K. D. Joshi, 1989 This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book. |
| cartesian product discrete math: Frontiers in Algorithmics Jianer Chen, Pinyan Lu, 2018-05-01 This book constitutes the refereed proceedings of the 12th International Workshop on Frontiers in Algorithmics, FAW 2018, held in Guangzhou, China, in May 2018.The 23 full papers presented in this volume were carefully reviewed and selected from 38 submissions. The papers of this workshop provide a focused forum on current trends of research on algorithms, discrete structures, and their applications. |
| cartesian product discrete math: Domination Games Played on Graphs Boštjan Brešar, Michael A. Henning, Sandi Klavžar, Douglas F. Rall, 2021-04-15 This concise monograph present the complete history of the domination game and its variants up to the most recent developments and will stimulate research on closely related topics, establishing a key reference for future developments. The crux of the discussion surrounds new methods and ideas that were developed within the theory, led by the imagination strategy, the Continuation Principle, and the discharging method of Bujtás, to prove results about domination game invariants. A toolbox of proof techniques is provided for the reader to obtain results on the domination game and its variants. Powerful proof methods such as the imagination strategy are presented. The Continuation Principle is developed, which provides a much-used monotonicity property of the game domination number. In addition, the reader is exposed to the discharging method of Bujtás. The power of this method was shown by improving the known upper bound, in terms of a graph's order, on the (ordinary) domination number of graphs with minimum degree between 5 and 50. The book is intended primarily for students in graph theory as well as established graph theorists and it can be enjoyed by anyone with a modicum of mathematical maturity. The authors include exact results for several families of graphs, present what is known about the domination game played on subgraphs and trees, and provide the reader with the computational complexity aspects of domination games. Versions of the games which involve only the “slow” player yield the Grundy domination numbers, which connect the topic of the book with some concepts from linear algebra such as zero-forcing sets and minimum rank. More than a dozen other related games on graphs and hypergraphs are presented in the book. In all these games there are problems waiting to be solved, so the area is rich for further research. The domination game belongs to the growing family of competitive optimization graph games. The game is played by two competitors who take turns adding a vertex to a set of chosen vertices. They collaboratively produce a special structure in the underlying host graph, namely a dominating set. The two players have complementary goals: one seeks to minimize the size of the chosen set while the other player tries to make it as large as possible. The game is not one that is either won or lost. Instead, if both players employ an optimal strategy that is consistent with their goals, the cardinality of the chosen set is a graphical invariant, called the game domination number of the graph. To demonstrate that this is indeed a graphical invariant, the game tree of a domination game played on a graph is presented for the first time in the literature. |
| cartesian product discrete math: Recent Trends in Signal and Image Processing Siddhartha Bhattacharyya, Leo Mršić, Maja Brkljačić, Joseph Varghese Kureethara, Mario Koeppen, 2021-04-01 This book gathers selected papers presented at the Third International Symposium on Signal and Image Processing (ISSIP 2020), organized by the Department of Information Technology, RCC Institute of Information Technology, Kolkata, during March 18–19, 2020. It presents fascinating, state-of-the-art research findings in the field of signal and image processing. It includes conference papers covering a wide range of signal processing applications involving filtering, encoding, classification, segmentation, clustering, feature extraction, denoising, watermarking, object recognition, reconstruction and fractal analysis. It addresses various types of signals, such as image, video, speech, non-speech audio, handwritten text, geometric diagram, ECG and EMG signals; MRI, PET and CT scan images; THz signals; solar wind speed signals (SWS); and photoplethysmogram (PPG) signals, and demonstrates how new paradigms of intelligent computing, like quantum computing, can be applied to process and analyze signals precisely and effectively. |
| cartesian product discrete math: Algorithms and Discrete Applied Mathematics Manoj Changat, Sandip Das, 2020-01-25 This book constitutes the proceedings of the 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020, held in Hyderabad, India, in February 2020. The 38 papers presented together with 2 invited talks in this volume were carefully reviewed and selected from 102 submissions. The papers are organized in topical sections on graph algorithms, graph theory, combinatorial optimization, distributed algorithms, combinatorial algorithms, and computational complexity. |
| cartesian product discrete math: Schaum's Outline of Discrete Mathematics Seymor Lipschutz, Marc Lipson, 1997-06-22 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 can be used as a supplement, to reinforce and strengthen the work you do with your class text. (It works well with virtually any discrete mathematics textbook.) But it is so comprehensive that it can even be used alone as a text in discrete mathematics or as independent study tool! |
| cartesian product discrete math: Cycles in Graphs B.R. Alspach, C.D. Godsil, 1985-08-01 This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems. |
| cartesian product discrete math: Artificial Intelligence for Communications and Networks Xianbin Wang, Kai-Kit Wong, Shanji Chen, Mingqian Liu, 2021-11-02 This two-volume set LNICST 396 and 397 constitutes the post-conference proceedings of the Third EAI International Conference on Artificial Intelligence for Communications and Networks, AICON 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 79 full papers were carefully reviewed and selected from 159 submissions. The papers are organized in topical sections on Artificial Intelligence in Wireless Communications and Satellite Communications; Artificial Intelligence in Electromagnetic Signal Processing; Artificial Intelligence Application in Wireless Caching and Computing; Artificial Intelligence Application in Computer Network. |
| cartesian product discrete math: Discrete Mathematics and Functional Programming Thomas VanDrunen, 2013 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 mathematics with ...... |
| cartesian product discrete math: Combinatorial Optimization and Applications Xiaofeng Gao, Hongwei Du, Meng Han, 2017-12-06 The two-volume set LNCS 10627 and 10628 constitutes the refereed proceedings of the 11th International Conference on Combinatorial Optimization and Applications, COCOA 2017, held in Shanghai, China, in December 2017. The 59 full papers and 19 short papers presented were carefully reviewed and selected from 145 submissions. The papers cover most aspects of theoretical computer science and combinatorics related to computing, including classic combinatorial optimization, geometric optimization, complexity and data structures, and graph theory. They are organized in topical sections on network, approximation algorithm and graph theory, combinatorial optimization, game theory, and applications. |
| cartesian product discrete math: Fundamentals of Computation Theory Gabriel Ciobanu, Gheorghe Paun, 2003-07-31 This book constitutes the refereed proceedings of the 12th International Symposium on Fundamentals of Computation Theory, FCT '99, held in Iasi, Romania in August/September 1999. The 42 revised full papers presented together with four invited papers were carefully selected from a total of 102 submissions. Among the topics addressed are abstract data types, algorithms and data structures, automata and formal languages, categorical and topological approaches, complexity, computational geometry, concurrency, cryptology, distributed computing, logics in computer science, process algebras, symbolic computation, molecular computing, quantum computing, etc. |
| cartesian product discrete math: CRC Concise Encyclopedia of Mathematics Eric W. Weisstein, 2002-12-12 Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
| cartesian product discrete math: Topics in Discrete Mathematics Martin Klazar, Jan Kratochvil, Martin Loebl, Robin Thomas, Pavel Valtr, 2007-05-28 This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings. |
| cartesian product discrete math: An Introduction to Measure Theory Terence Tao, 2021-09-03 This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book. |
| cartesian product discrete math: Topics in Domination in Graphs Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning, 2020-10-19 This volume comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The focus is on primary dominating sets such as paired domination, connected domination, restrained domination, dominating functions, Roman domination, and power domination. Additionally, surveys include known results with a sample of proof techniques for each parameter. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms; the second chapter provides an overview of models of domination from which the parameters are defined. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments in the field and proof techniques used. |
| cartesian product discrete math: Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy Manoj Sahni, José M. Merigó, Brajesh Kumar Jha, Rajkumar Verma, 2021-02-28 This book presents new knowledge and recent developments in all aspects of computational techniques, mathematical modeling, energy systems, applications of fuzzy sets and intelligent computing. The book is a collection of best selected research papers presented at the International Conference on “Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy,” organized by the Department of Mathematics, Pandit Deendayal Petroleum University, in association with Forum for Interdisciplinary Mathematics, Institution of Engineers (IEI) – Gujarat and Computer Society of India (CSI) – Ahmedabad. The book provides innovative works of researchers, academicians and students in the area of interdisciplinary mathematics, statistics, computational intelligence and renewable energy. |
| cartesian product discrete math: Discrete Mathematics with Applications, Metric Edition Susanna Epp, 2019 DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition 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 thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology. |
| cartesian product discrete math: Handbook of Graph Theory, Combinatorial Optimization, and Algorithms Krishnaiyan "KT" Thulasiraman, Subramanian Arumugam, Andreas Brandstädt, Takao Nishizeki, 2016-01-05 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 graph theory and c |
| cartesian product discrete math: Handbook of Graph Theory Jonathan L. Gross, Jay Yellen, Ping Zhang, 2013-12-17 In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede |
| cartesian product discrete math: Mathematical Combinatorics, Vol. 1/2010 Linfan Mao, Papers on Singed Total Domatic Number of a Graph, Euler-Savarys Formula for the Planar Curves in Two Dimensional Lightlike Cone, Dynamical Knot and Their Fundamental Group, Counting Rooted Eulerian Planar Maps, and other topics. Contributors: H.B. Walikar, Shailaja S. Shirkol, Kishori P. Narayankar, B. Sooryanarayana, Vishu Kumar M. Manjula K., P. Siva Kota Reddy, S. Vijay, V. Lokesha, Junliang Cai, Yanpei Liu, and others. |
| cartesian product discrete math: Mathematical Methods in Linguistics Barbara B.H. Partee, A.G. ter Meulen, R. Wall, 1990-04-30 Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language. |
| cartesian product discrete math: Discrete Mathematics and Graph Theory K. Erciyes, 2021-01-28 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 Science or Mathematics curricula. The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications. |
| cartesian product discrete math: MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES), Vol. 4, 2019 Linfan Mao, The mathematical combinatorics is a subject that applying combinatorial notions to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr. Linfan MAO on mathematical sciences. The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences. |
| cartesian product discrete math: Research Problems in Discrete Geometry Peter Brass, William O. J. Moser, János Pach, 2006-06-19 This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. |
| cartesian product discrete math: Discrete Mathematics Rowan Garnier, John Taylor, 2020-10-29 In a comprehensive yet easy-to-follow manner, Discrete Mathematics for New Technology follows the progression from the basic mathematical concepts covered by the GCSE in the UK and by high-school algebra in the USA to the more sophisticated mathematical concepts examined in the latter stages of the book. The book punctuates the rigorous treatment of theory with frequent uses of pertinent examples and exercises, enabling readers to achieve a feel for the subject at hand. The exercise hints and solutions are provided at the end of the book. Topics covered include logic and the nature of mathematical proof, set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras, and a thorough treatise on graph theory. Although aimed primarily at computer science students, the structured development of the mathematics enables this text to be used by undergraduate mathematicians, scientists, and others who require an understanding of discrete mathematics. |
Cartesian 为什么翻译成笛卡尔? - 知乎
May 25, 2014 · Cartesian means of or relating to the French philosopher and discoverer René Descartes —from his Latinized name Cartesius. — Cartesian Cartesian 表示与 Descartes 相 …
笛卡尔坐标系 - 知乎
笛卡尔坐标系（法语：système de coordonnées cartésiennes，英语：Cartesian coordinate system，也称直角坐标系）在数学中是一种正交坐标系，由法国数学家勒内·笛卡尔引入而得 …
笛卡尔其名Descartes形容词为何作Cartesian？ - 知乎
笛卡尔其名Descartes形容词为何作Cartesian？ 逻辑学与离散数学中常用Cartesian product，认识论相关哲学中也常见Cartesianism，无疑皆源自Descartes。 而问题在于De… 显示全部 关注 …
笛卡尔乘积 - 知乎
笛卡尔乘积是指在数学中，两个 集合 X和 Y的笛卡尓积（Cartesian product），又称 直积，表示为 X × Y，第一个对象是 X的成员而第二个对象是 Y的所有可能 有序对的其中一个成员。 假设集 …
trajectory plan中joint-space和Cartesian space的区别是什么？
May 7, 2021 · cartesian space指 笛卡尔空间，由三个正交向量x, y, z来描述。 对于串联机器人， 关节空间 和笛卡尔空间都可以用来描述最末端点的位置和姿态。 区别是前者更直观（给出关 …
怎么通俗地理解张量？ - 知乎
Dan Fleisch是《A Student’s Guide to Vectors and Tensors》的作者，他发现很大一部分读者都有一个疑问：到底张量是TMD什么东西? (What’s a tensor? ） 于是乎就做了这个视频，用12分 …
谁能解释一下密度泛函理论（DFT）的基本假设和原理么？ - 知乎
本文将简要介绍密度泛函理论（DFT）的导出和一些交换关联（XC）势，以期能给初学者一些基本的帮助。我是一个学渣，所以行文之中很可能有些错误，还望不吝指正。 按：似乎知乎的公 …
Cartesian 为什么翻译成笛卡尔? - 知乎
May 25, 2014 · Cartesian means of or relating to the French philosopher and discoverer René Descartes —from his Latinized name Cartesius. — Cartesian Cartesian 表示与 Descartes 相 …
笛卡尔坐标系 - 知乎
笛卡尔坐标系（法语：système de coordonnées cartésiennes，英语：Cartesian coordinate system，也称直角坐标系）在数学中是一种正交坐标系，由法国数学家勒内·笛卡尔引入而得 …
笛卡尔其名Descartes形容词为何作Cartesian？ - 知乎
笛卡尔其名Descartes形容词为何作Cartesian？ 逻辑学与离散数学中常用Cartesian product，认识论相关哲学中也常见Cartesianism，无疑皆源自Descartes。 而问题在于De… 显示全部 关注 …
笛卡尔乘积 - 知乎
笛卡尔乘积是指在数学中，两个 集合 X和 Y的笛卡尓积（Cartesian product），又称 直积，表示为 X × Y，第一个对象是 X的成员而第二个对象是 Y的所有可能 有序对的其中一个成员。 假设集 …
trajectory plan中joint-space和Cartesian space的区别是什么？
May 7, 2021 · cartesian space指 笛卡尔空间，由三个正交向量x, y, z来描述。 对于串联机器人， 关节空间 和笛卡尔空间都可以用来描述最末端点的位置和姿态。 区别是前者更直观（给出关 …
怎么通俗地理解张量？ - 知乎
Dan Fleisch是《A Student’s Guide to Vectors and Tensors》的作者，他发现很大一部分读者都有一个疑问：到底张量是TMD什么东西? (What’s a tensor? ） 于是乎就做了这个视频，用12分 …
谁能解释一下密度泛函理论（DFT）的基本假设和原理么？ - 知乎
本文将简要介绍密度泛函理论（DFT）的导出和一些交换关联（XC）势，以期能给初学者一些基本的帮助。我是一个学渣，所以行文之中很可能有些错误，还望不吝指正。 按：似乎知乎的公 …
