Understand Mathematics Understand Computing

Author : Arnold L. Rosenberg,Denis Trystram
Publisher : Springer Nature
Page : 550 pages
File Size : 51,8 Mb
Release : 2020-12-05
Category : Computers
ISBN : 9783030583767

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Understand Mathematics, Understand Computing by Arnold L. Rosenberg,Denis Trystram Pdf

In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Author : Gerard O’Regan
Publisher : Springer Nature
Page : 468 pages
File Size : 49,5 Mb
Release : 2020-01-10
Category : Computers
ISBN : 9783030342098

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Mathematics in Computing by Gerard O’Regan Pdf

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Author : K.V. Mital
Publisher : Taylor & Francis
Page : 252 pages
File Size : 55,5 Mb
Release : 2003
Category : Electronic
ISBN : 8122403875

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Understanding Mathematics And Computers by K.V. Mital Pdf

Author : Clive Maxfield,Alvin Brown
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 47,5 Mb
Release : 2005-09-27
Category : Computers
ISBN : 9780471732785

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The Definitive Guide to How Computers Do Math by Clive Maxfield,Alvin Brown Pdf

The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning "The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer functions, you can easily extrapolate to more complex machines." -Fred Hudson, retired engineer/scientist "This book-along with the virtual DIY Calculator-is an incredibly useful teaching and learning tool. The interesting trivia nuggets keep you turning the pages to see what's next. Students will have so much fun reading the text and performing the labs that they won't even realize they are learning." -Michael Haghighi, Chairperson of the Business and Computer Information Systems Division, Calhoun Community College, Alabama "At last, a book that presents an innovative approach to the teaching of computer architecture. Written with authority and verve, witty, superbly illustrated, and enhanced with many laboratory exercises, this book is a must for students and teachers alike." -Dr. Albert Koelmans, Lecturer in Computer Engineering, University of Newcastle upon Tyne, UK, and the 2003 recipient of the EASIT-Eng. Gold Award for Innovative Teaching in Computer Engineering Packed with nuggets of information and tidbits of trivia, How Computers Do Math provides an incredibly fun and interesting introduction to the way in which computers perform their magic in general and math in particular. The accompanying CD-ROM contains a virtual computer/calculator called the DIY Calculator, and the book's step-by-step interactive laboratories guide you in the creation of a simple program to run on your DIY Calculator. How Computers Do Math can be enjoyed by non-technical individuals; students of computer science, electronics engineering, and mathematics; and even practicing engineers. All of the illustrations and interactive laboratories featured in the book are provided on the CD-ROM for use by high school, college, and university educators as lecture notes and handouts. For online resources and more information please visit the author's website at www.DIYCalculator.com.

Author : Clifford Stein,Robert L. Drysdale,Kenneth P. Bogart
Publisher : Unknown
Page : 525 pages
File Size : 45,6 Mb
Release : 2011
Category : Computer science
ISBN : 0131377108

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Discrete Mathematics for Computer Scientists by Clifford Stein,Robert L. Drysdale,Kenneth P. Bogart Pdf

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.

Author : David Makinson
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 53,8 Mb
Release : 2009-06-29
Category : Computers
ISBN : 9781846288456

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Sets, Logic and Maths for Computing by David Makinson Pdf

The first part of this preface is for the student; the second for the instructor. But whoever you are, welcome to both parts. For the Student You have finished secondary school, and are about to begin at a university or technical college. You want to study computing. The course includes some mathematics { and that was not necessarily your favourite subject. But there is no escape: some finite mathematics is a required part of the first year curriculum. That is where this book comes in. Its purpose is to provide the basics { the essentials that you need to know to understand the mathematical language that is used in computer and information science. It does not contain all the mathematics that you will need to look at through the several years of your undergraduate career. There are other very good, massive volumes that do that. At some stage you will probably find it useful to get one and keep it on your shelf for reference. But experience has convinced this author that no matter how good the compendia are, beginning students tend to feel intimidated, lost, and unclear about what parts to focus on. This short book, on the other hand, offers just the basics which you need to know from the beginning, and on which you can build further when needed.

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 40,9 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

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.

Author : Tom Jenkyns,Ben Stephenson
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 48,5 Mb
Release : 2012-10-16
Category : Computers
ISBN : 9781447140696

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Fundamentals of Discrete Math for Computer Science by Tom Jenkyns,Ben Stephenson Pdf

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.

Author : Willem Labuschagne
Publisher : Unisa Press
Page : 320 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : 0869818104

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A User-friendly Introduction to Discrete Mathematics for Computer Science by Willem Labuschagne Pdf

What mathematical skills do you need to understand computers and the problems they can solve? This book introduces the basic ideas of set theory, logic and combinatorics. Intended for those who work alone and whose experiences of mathematics have in the past perhaps been somewhat intimidating, the book adopts an informal tone and chats to the reader as a well-informed friend might. In addition to its treatment of mathematical topics, it draws the attention of the reader to general patterns of thought, some of which constitute useful problem-solving skills that may be used in other domains.

Author : Ali Selamat,Md Hafiz Selamat
Publisher : Penerbit UTM Press
Page : 7 pages
File Size : 40,6 Mb
Release : 2012
Category : Computer science
ISBN : 9789835208461

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Discrete Mathematics For Computer Scientist by Ali Selamat,Md Hafiz Selamat Pdf

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.

Author : Walter Gander,Martin J. Gander,Felix Kwok
Publisher : Springer Science & Business
Page : 905 pages
File Size : 55,7 Mb
Release : 2014-04-23
Category : Mathematics
ISBN : 9783319043258

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Scientific Computing - An Introduction using Maple and MATLAB by Walter Gander,Martin J. Gander,Felix Kwok Pdf

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Author : Cordelia Hall,John O'Donnell
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 42,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781447136576

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Discrete Mathematics Using a Computer by Cordelia Hall,John O'Donnell Pdf

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 45,7 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

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Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf

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.

Author : Nabil Nassif,Dolly Khuwayri Fayyad
Publisher : CRC Press
Page : 338 pages
File Size : 53,8 Mb
Release : 2013-08-05
Category : Mathematics
ISBN : 9781466589483

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Introduction to Numerical Analysis and Scientific Computing by Nabil Nassif,Dolly Khuwayri Fayyad Pdf

Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple and double-precision standards as used in scientific computer environments such as MATLAB® version 7. Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors discuss computer arithmetic as a source for generating round-off errors and how to avoid the use of algebraic expression that may lead to loss of significant figures. They cover nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB®. Each chapter ends with a large number of exercises, with answers to odd-numbered exercises provided at the end of the book. Throughout the seven chapters, several computer projects are proposed. These test the students' understanding of both the mathematics of numerical methods and the art of computer programming.

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 410 pages
File Size : 44,9 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118315354

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Theory of Computation by George Tourlakis Pdf

Learn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do—from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational phenomena and provides insights on what makes things tick and also what restrains the ability of computational processes. Recognizing the importance of acquired practical experience, the book begins with the metatheory of general purpose computer programs, using URMs as a straightforward, technology-independent model of modern high-level programming languages while also exploring the restrictions of the URM language. Once readers gain an understanding of computability theory—including the primitive recursive functions—the author presents automata and languages, covering the regular and context-free languages as well as the machines that recognize these languages. Several advanced topics such as reducibilities, the recursion theorem, complexity theory, and Cook's theorem are also discussed. Features of the book include: A review of basic discrete mathematics, covering logic and induction while omitting specialized combinatorial topics A thorough development of the modeling and mathematical analysis of computational phenomena, providing a solid foundation of un-computability The connection between un-computability and un-provability: Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well as other programming languages including Loop Programs, FA (Deterministic Finite Automata), NFA (Nondeterministic Finite Automata), and PDA (Pushdown Automata). Exercises at the end of each chapter allow readers to test their comprehension of the presented material, and an extensive bibliography suggests resources for further study. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory of computation at the upper-undergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.