Discrete Mathematics With Algorithms
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Discrete Mathematics With Algorithms
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Author : Michael O. Albertson
language : en
Publisher:
Release Date : 1988-08-05
Discrete Mathematics With Algorithms written by Michael O. Albertson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08-05 with Mathematics categories.
This first-year course in discrete mathematics requires no calculus or computer programming experience. The approach stresses finding efficient algorithms, rather than existential results. Provides an introduction to constructing proofs (especially by induction), and an introduction to algorithmic problem-solving. All algorithms are presented in English, in a format compatible with the Pascal programming language. Contains many exercises, with answers at the back of the book (detailed solutions being supplied for difficult problems).
Discrete Mathematical Algorithm And Data Structures
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Author : Sanjib Sinha
language : en
Publisher:
Release Date : 2020-05-28
Discrete Mathematical Algorithm And Data Structures written by Sanjib Sinha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-28 with categories.
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
Foundations Of Discrete Mathematics With Algorithms And Programming
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Author : R. Balakrishnan
language : en
Publisher: CRC Press
Release Date : 2018-10-26
Foundations Of Discrete Mathematics With Algorithms And Programming written by R. Balakrishnan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-26 with Mathematics categories.
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 Engineering. A number of examples have been given to enhance the understanding of concepts. The programming languages used are Pascal and C.
Fundamentals Of Discrete Math For Computer Science
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Author : Tom Jenkyns
language : en
Publisher: Springer
Release Date : 2018-05-03
Fundamentals Of Discrete Math For Computer Science written by Tom Jenkyns and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Computers categories.
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.
Foundations Of Discrete Mathematics With Algorithms And Programming
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Author : R. Balakrishnan
language : en
Publisher: CRC Press
Release Date : 2018-10-26
Foundations Of Discrete Mathematics With Algorithms And Programming written by R. Balakrishnan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-26 with Mathematics categories.
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 Engineering. A number of examples have been given to enhance the understanding of concepts. The programming languages used are Pascal and C.
Probabilistic Methods For Algorithmic Discrete Mathematics
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Author : Michel Habib
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Probabilistic Methods For Algorithmic Discrete Mathematics written by Michel Habib and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.
Practical Discrete Mathematics
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Author : Ryan T. White
language : en
Publisher: Packt Publishing Ltd
Release Date : 2021-02-22
Practical Discrete Mathematics written by Ryan T. White and has been published by Packt Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
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 Mathematics For Computer Science
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Author : Jon Pierre Fortney
language : en
Publisher: CRC Press
Release Date : 2020-12-23
Discrete Mathematics For Computer Science written by Jon Pierre Fortney and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-23 with Mathematics categories.
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 Mathematics
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Author : Sriraman Sridharan
language : en
Publisher: CRC Press
Release Date : 2019-07-30
Discrete Mathematics written by Sriraman Sridharan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-30 with Mathematics categories.
Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a given positive integer is prime or not in polynomial time is presented- the first time in a textbook. Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given.
The Discrete Math Workbook
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Author : Sergei Kurgalin
language : en
Publisher: Springer
Release Date : 2018-07-31
The Discrete Math Workbook written by Sergei Kurgalin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-31 with Computers categories.
This practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments. Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language.