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| discrete structures for computer science: Mathematics of Discrete Structures for Computer Science Gordon J. Pace, 2012-07-09 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 correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering. |
| discrete structures for computer science: 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. |
| discrete structures for computer science: Discrete Mathematics for Computer Science Jon Pierre Fortney, 2020-12-23 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 algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook. |
| discrete structures for computer science: Discrete Mathematics for Computer Scientists Clifford Stein, Robert L. Drysdale, Kenneth P. Bogart, 2011 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 motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises. |
| discrete structures for computer science: 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. |
| discrete structures for computer science: 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).''-- |
| discrete structures for computer science: Discrete Structures Of Computer Science Leon S Levy, 2003-01-01 Each Chapter Of The Book Deals With Mathematical Modelling Through One Or More Specified Techniques. These Include Mathematical Modelling Through Algebra, Geometry, Calculus, Ordinary And Partial Differential Equations, Integral Equations Etc. Each Chapter Contains Mathematical Models From Physical, Biological, Social, Management Sciences And Engineering And Technology And Illustrate Unit In Diversity Of Mathematical Sciences. The Book Contains Plenty Of Exercises In Mathematical Modelling And Is Aimed To Give A Panoramic View Of Applications Of Modelling In All Fields Of Knowledge. The Book Presumes Only The Knowledge Of Undergraduate Mathematics And Can Be Used As A Textbook At Senior Undergraduate Or Post-Graduate Level For A One Or Two Semester Course For Students Of Mathematics, Statistics, Physical, Social And Biological Sciences And Engineering. It Can Also Be Useful For All Users Of Mathematics And For All Mathematical Modellers.Stochastic Processes In Demography And Applications Suddhendu Biswas Department Of Mathematical Statistics University Of Delhi.The Book Attempts To Fulfill A Long Felt Gap In The Research And Pedagogy Of Mathematical Demography And Other Related Topics As Survival Analysis By Focussing Intensively On A Wide Range Of Traditional As Well As New Inputs Using A Modern Stochastic Process And Renewal Theory Oriented Approach. Special Topics As Martingales Theory. Cox'S Regression Model. Parametric And Nonparametric Techniques In Survival Theory Together With A Full Chapter On The Adjustment Techniques For The Deficiencies Of Vital Statistics In India Have Been Appended For The First Time In A Book Of This Kind. The Book Is Useful To Postgraduate Students Taking One Or Two Semester Course With Mathematical Demography Or Applied Stochastic Processes With Orientation In Population Studies, Biostatistics Or Biometry. |
| discrete structures for computer science: Essential Discrete Mathematics for Computer Science Harry Lewis, Rachel Zax, 2019-03-19 Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. |
| discrete structures for computer science: Mathematics of Discrete Structures for Computer Science Gordon J. Pace, 2012-09-13 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 correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering. |
| discrete structures for computer science: Connecting Discrete Mathematics and Computer Science David Liben-Nowell, 2022-08-04 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 technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures – like logic, proofs, number theory, counting, probability, graphs – are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures. |
| discrete structures for computer science: Discrete Structures, Logic, and Computability James L. Hein, 2001 Discrete Structure, Logic, and Computability introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic, and computability. The emphasis is on the computational aspects, so that the reader can see how the concepts are actually used. Because of logic's fundamental importance to computer science, the topic is examined extensively in three phases that cover informal logic, the technique of inductive proof; and formal logic and its applications to computer science. |
| discrete structures for computer science: Discrete Structures Harriet Fell, Javed Aslam, 2016-12-21 Discrete Structures introduces readers to the mathematical structures and methods that form the foundation of computer science and features multiple techniques that readers will turn to regularly throughout their careers in computer and information sciences. Over the course of five modules, students learn specific skills including binary and modular arithmetic, set notation, methods of counting, evaluating sums, and solving recurrences. They study the basics of probability, proof by induction, growth of functions, and analysis techniques. The book also discusses general problem-solving techniques that are widely applicable to real problems. Each module includes motivation applications, technique, theory, and further opportunities for application. Informed by extensive experience teaching in computer science programs, Discrete Structures has been developed specifically for first-year students in those programs. The material is also suitable for courses in computer engineering, as well as those for students who are transferring from other disciplines and just beginning their computer science or engineering education. |
| discrete structures for computer science: Introductory Discrete Mathematics V. K . Balakrishnan, 2012-04-30 This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition. |
| discrete structures for computer science: Fundamentals of Discrete Math for Computer Science Tom Jenkyns, Ben Stephenson, 2018-05-03 This clearly written textbook presents an accessible introduction to discrete mathematics for computer science students, offering the reader an enjoyable and stimulating path to improve their programming competence. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Its motivational and interactive style provokes a conversation with the reader through a questioning commentary, and supplies detailed walkthroughs of several algorithms. This updated and enhanced new edition also includes new material on directed graphs, and on drawing and coloring graphs, in addition to more than 100 new exercises (with solutions to selected exercises). Topics and features: assumes no prior mathematical knowledge, and discusses concepts in programming as and when they are needed; designed for both classroom use and self-study, presenting modular and self-contained chapters that follow ACM curriculum recommendations; describes mathematical processes in an algorithmic manner, often supported by a walkthrough demonstrating how the algorithm performs the desired task; includes an extensive set of exercises throughout the text, together with numerous examples, and shaded boxes highlighting key concepts; selects examples that demonstrate a practical use for the concept in question. Students embarking on the start of their studies of computer science will find this book to be an easy-to-understand and fun-to-read primer, ideal for use in a mathematics course taken concurrently with their first programming course. |
| discrete structures for computer science: 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. |
| discrete structures for computer science: 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. |
| discrete structures for computer science: Discrete Mathematical Structures B. V. Senthil Kumar, Hemen Dutta, 2019-07-08 This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension. Features Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra Provides end of chapter solved examples and practice problems Delivers materials on valid arguments and rules of inference with illustrations Focuses on algebraic structures to enable the reader to work with discrete structures |
| discrete structures for computer science: Discrete Math for Computer Science Students Stahl Zsolt, 2016-08-28 Discrete Mathematics for Computer Science Students emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. |
| discrete structures for computer science: Essential Discrete Mathematics for Computer Science Todd Feil, Joan Krone, 2003 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 scientists. Chapter topics include sets, functions and relations, Boolean algebra, natural numbers and induction, number theory, recursion, solving recurrences, counting, matrices, and graphs. For computer scientists and the enhancement of programming skills. |
| discrete structures for computer science: Discrete Structure and Automata Theory for Learners Dr. Umesh Gill Sehgal, Ms. Sukhpreet Kaur, 2020-09-05 Learn to identify the implementation of Discrete Structure and Theory of Automata in a myriad of applications used in day to day lifeKey Featuresa- Learn how to write an argument using logical notation and decide if the argument is valid or not valid.a- Learn how to use the concept of different data structures (stacks, queues, sorting concept, etc.) in the computer science field.a- Learn how to use Automata Machines like FSM, Pushdown automata, Turing machine, etc. in various applications related to computer science through suitable practical illustration.a- Learn how to implement the finite state machine using JFLAP (Java Formal Languages and Automata Package).DescriptionThis book's purpose is to provide a modern and comprehensive introduction to the subject of Discrete Structures and Automata Theory. Discrete structures, also called Discrete Mathematics, are an exciting and active subject, particularly due to its extreme relevance to both Mathematics and Computer Science and Algorithms. This subject forms a common foundation for rigorous Mathematical, Logical Reasoning and Proofs, as well as a formal introduction to abstract objects that are essential tools in an assortment of applications and effective computer implementations. Computing skills are now an integral part of almost all the Scientific fields, and students are very enthusiastic about being able to harness the full computing power of these tools. Further, this book also deep dives into the Automata Theory with various examples that illustrate the basic concepts and is substantiated with multiple diagrams. The book's vital feature is that it contains the practical implementation of the Automata Machine example through the JFLAP Tool. Courses on Discrete Structures and Automata theory are offered at most universities and colleges.What will you learna- Understand the basic concepts of Sets and operations in Sets.a- Demonstrate different traversal techniques for Trees and Graphs.a- Deep dive into the concept of Mathematical Induction, Sets, Relations, Functions, Recursion, Graphs, Trees, Boolean Algebra, and Proof techniques.a- Understand the concept of Automata Machines in day to day life like the Elevator, Turnstile, Genetic Algorithms, Traffic lights, etc.a- Use the JFLAP tool to solve the various exercise problems related to automata theory.Who this book is forThis book is a must-read to everyone interested in improving their concepts regarding Discrete Structure and Automata Theory.Table of Contents1. Set Theory2. Relations and Functions3. Graph Theory4. Trees5. Algebraic Structure6. Recursion and Recurrence Relations7. Sorting8. Queues9. Introduction10. Finite Automata Theory11. Theory of Machines12. Regular Language13. Grammar14. Pushdown Automata15. Cellular Automata16. Turning Machine17. Problems Solving Using JFLAP Tool18. Revision QuestionsAbout the AuthorsDr. UMESH SEHGAL completed his Ph.D.,M.Phil. Computer Science and MCA. He held academic positions at the GNA University as an A.P in FCS Department. He has achieved the Best Educationist Award in 2017.He has achieved the Indira Gandhi Education Excellence Award in 2017.He has achieved the Best Researcher Award in 2018-19.He has published several articles in leading International and National Computer science journals and has been an invited speaker at Wireless networks based lectures and conferences in the many universities and Institutes in India, Malaysia, China, and UAE.SUKHPREET KAUR GILL received the M.Tech. degree in Computer Science and Engineering from Guru Nanak Dev Engineering College, Ludhiana. She is currently working as Assistant Professor at GNA University Phagwara. She has achieved the Bright Educator Award 2019. She has published several articles in leading International and National Computer science journals. |
| discrete structures for computer science: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-03-08 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. |
| discrete structures for computer science: Discrete Mathematics For Computer Scientist Ali Selamat, Md Hafiz Selamat, 2012 This book serves as an introduction to computer sciences students in the undergraduate levels. It will be used as the foundation to understand the discrete mathematic in developing the logic of computer programs. Since there are also similar undergraduate computer science programmes in other local and overseas institutions, this book is expected to find wider local and international readership. Topics covered in this book include set theory and relations, functions sequence and string, propositional logic, predicate logic, matrices, graph theory and trees. As the book serves as an introductory level to computer science students, it is expected that once the students are already familiar with the presented contents, it will enable them to understand the advanced topics in computer science such as advanced theory of computer science and computational complexity theories. The chapters in this book have been organized for the students to learn and understand the main concepts of discrete mathematics for developing computer applications during the period of their studies. In information technology (IT) and computer science fields, most of information is represented in digital electronics based on the basic knowledge of discrete mathematics. Therefore, discrete mathematics is one of the relevant courses to support students for better learning and understanding the nature of computer science and IT. It is expected that by using the materials presented in this book students should be able to write statements using mathematical language, develop mathematical arguments using logic, apply the concept of integers and its role in modeling and solving problems in IT, and apply the concept of graph and tree for modeling and solving problems related to real situations. |
| discrete structures for computer science: Mathematical Structures for Computer Science Judith Gersting, 2014-01-01 Mathematical Structures for Computer Science, written by Judith L. Gersting, is a vital textbook for computer science undergraduate students, which helps to introduce readers to the maths behind computing. This textbook has long been much loved and acclaimed for its clear, concise presentation of essential concepts and its exceptional range of applications relevant to computer science majors. This new edition made the textbook the first discrete mathematics textbook to be revised in order to meet the proposed new ACM/IEEE standards of the course. It features new material, including new sections on probability, coding theory, matrices and order of magnitude. It also includes roughly 30% more exercises and examples, further aiding students’ learning of this complex subject underpinning the field of computing. |
| discrete structures for computer science: Discrete Mathematical Structures for Computer Science Ronald E. Prather, 1976 |
| discrete structures for computer science: Fundamentals of Discrete Math for Computer Science Tom Jenkyns, Ben Stephenson, 2012-10-16 This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Features: no university-level background in mathematics required; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question. |
| discrete structures for computer science: Applied Discrete Structures for Computer Science Alan Doerr, Kenneth Levasseur, 1991 |
| discrete structures for computer science: Discrete Mathematics Jean Gallier, 2011-02-01 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 place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs. |
| discrete structures for computer science: Discrete Mathematics László Lovász, József Pelikán, Katalin Vesztergombi, 2006-05-10 Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book. |
| discrete structures for computer science: Discrete Mathematical Structures with Applications to Computer Science Jean-Paul Tremblay, R. Manohar, 1987 |
| discrete structures for computer science: Discrete Computational Structures Robert R. Korfhage, 1974 Basic forms and operations; Undirected graphs; Gorn trees; Directed graphs; Formal and natural languages; Finite groups and computing; Partial orders and lattices; Boolean algebras; The propositional calculus; Combinatorics; Systems of distinct representatives; Discrete probability. |
| discrete structures for computer science: Discrete Mathematics for Computer Science David Liben-Nowell, 2017-09-05 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 enhance teaching and learning ease and includes a wide selection of exercises, detailed exploration problems, examples and problems inspired by wide-ranging applications of computer science and handy quick reference guides for key technical topics throughout. Discrete Mathematics for Computer Science provides a lucidly written introduction to discrete mathematics with abundant support for learning, including over 450 examples, thorough chapter summaries, simple quizzes, and approximately 1600 homework exercises of widely varying difficulty. Each chapter begins with motivational content that relates the chapter topic to computer science practice and the book also includes over fifty Computer Science Connections which discuss applications to computer science such as Rotation Matrices; Game Trees, Logic, and Winning Tic-Tac(-Toe); Moore's Law; Secret Sharing; The Enigma Machine and the First Computer; Bayesian Modeling and Spam Filtering; and Quantum Computing. |
| discrete structures for computer science: Discrete Mathematical Algorithm, and Data Structures Sanjib Sinha, 2020-05-28 Readers will learn discrete mathematical abstracts as well as its implementation in algorithm and data structures shown in various programming languages, such as C, C++, PHP, Java, C#, Python and Dart. This book combines two major components of Mathematics and Computer Science under one roof. Without the core conceptions and tools derived from discrete mathematics, one cannot understand the abstract or the general idea involving algorithm and data structures in Computer Science. The objects of data structures are basically objects of discrete mathematics. This book tries to bridge the gap between two major components of Mathematics and Computer Science.In any computer science course, studying discrete mathematics is essential, although they are taught separately, except in a few cases. Yet, a comprehensive book, combining these two major components, is hard to find out; not only that, it is almost impossible to understand one without the help of other.Hope, this book will fill the gap. Readers will learn discrete mathematical abstracts as well as its implementation in algorithm and data structures shown in various programming language, such as C++, Java, C#, Python and Dart.1. Introduction to the Discourse Is Discrete Mathematics enough to study Computer Science? A short Introduction to Discrete Mathematics What is Discrete Mathematics What is the relationship between Discrete Mathematics and Computer Science Introducing necessary conceptions 2. Introduction to Programming Language and Boolean Algebra Logic, Mathematics, and Programming Language Introduction to Boolean Algebra 3. De Morgan's Laws on Boolean Algebra, Logical Expression, and Algorithm Logical Expression Short Circuit Evaluation Syntax, Semantics and Conditional Execution Why we need Control Constructs Discrete Mathematical Notations and Algorithm 4. Data Structures in different Programming languages Mean, Median and Mode Array, the First Step to Data Structure Let us understand some Array features Set Theory, Probability and Array Skewed Mean, Maximized Median Complex Array Algorithm 5. Data Structures: Abstractions and Implementation How objects work with each other More Algorithm and Time Complexity Introducing Data Structures How Calculus and Linear Algebra are Related to this Discourse 6. Data Structures in Detail Frequently Asked Questions about Data Structures Abstract Data Type (ADT) Linear Data Structures Modeling of a Structure ArrayList to overcome limitations of Array ArrayList or LinkedList, which is faster? Collection Framework in programming languages Stack and Queue in Java Deque, a high-performance Abstract Data Type 7. Algorithm, Data Structure, Collection Framework and Standard Template Library (STL) Introducing Algorithm Library Different types of Algorithms Binary Tree and Data Structure Collection Framework in Java Discrete Mathematical Abstractions and Implementation through Java Collection Comparator, Comparable and Iterator Standard Template Library in C++ 8. Time Complexity Order of n, or O(n) Big O Notation 9. Set, Symmetric Difference and Propositional Logic Why Set is important in Data Structures How Symmetric Difference and Propositional Logic combine 10. Combinatorics and Counting, Permutation and Combinations Permutation and Combination What Next |
| discrete structures for computer science: Discrete Mathematics with Computer Science Applications Romualdas Skvarcius, William B. Robinson, 1986 |
| discrete structures for computer science: A Beginner's Guide to Discrete Mathematics W.D. Wallis, 2011-10-07 Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a 'beginner's guide', this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. —Zentralblatt Math (Review of the First Edition) This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter * Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and computer science, however, featured special topics and applications may also interest graduate students. |
| discrete structures for computer science: Lectures On Discrete Mathematics For Computer Science Bakhadyr M Khoussainov, Nodira Khoussainova, 2012-03-21 This textbook presents fundamental topics in discrete mathematics introduced from the perspectives of a pure mathematician and an applied computer scientist. The synergy between the two complementary perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples, and yet are still formalized with mathematical rigor. The book is an excellent introduction to discrete mathematics for computer science, software engineering, and mathematics students.The first author is a leading mathematician in the area of logic, computability, and theoretical computer science, with more than 25 years of teaching and research experience. The second author is a computer science PhD student at the University of Washington specializing in database systems. The father-and-daughter team merges two different views to create a unified book for students interested in learning discrete mathematics, the connections between discrete mathematics and computer science, and the mathematical foundations of computer science.Readers will learn how to formally define abstract concepts, reason about objects (such as programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook studies several well-known algorithmic problems including the path problem for graphs and finding the greatest common divisor, inductive definitions, proofs of correctness of algorithms via loop invariants and induction, the basics of formal methods such as propositional logic, finite state machines, counting, probability, as well as the foundations of databases such as relational calculus. |
| discrete structures for computer science: Elements Of Discrete Mathematics 2/E C L Liu, 2000-10-01 |
| discrete structures for computer science: Mathematical Structures for Computer Science Judith L. Gersting, 2007 This edition offers a pedagogically rich and intuitive introduction to discrete mathematics structures. It meets the needs of computer science majors by being both comprehensive and accessible. |
| discrete structures for computer science: Concrete Mathematics Ronald L. Graham, Donald E. Knuth, Oren Patashnik, 1994-02-28 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 sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. |
| discrete structures for computer science: Street-Fighting Mathematics Sanjoy Mahajan, 2010-03-05 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 largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license. |
| discrete structures for computer science: A Short Course in Discrete Mathematics Edward A. Bender, S. Gill Williamson, 2005-01-01 What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index. |
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