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Author: Arnold L. Rosenberg Publisher: Springer Nature ISBN: 3030583767 Category : Computers Languages : en Pages : 550
Book Description
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: Arnold L. Rosenberg Publisher: Springer Nature ISBN: 3030583767 Category : Computers Languages : en Pages : 550
Book Description
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 ISBN: 3030342093 Category : Computers Languages : en Pages : 468
Book Description
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: Clive Maxfield Publisher: John Wiley & Sons ISBN: 0471732788 Category : Computers Languages : en Pages : 480
Book Description
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: David Makinson Publisher: Springer Science & Business Media ISBN: 1846288452 Category : Computers Languages : en Pages : 302
Book Description
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: Walter Gander Publisher: Springer Science & Business ISBN: 3319043250 Category : Mathematics Languages : en Pages : 905
Book Description
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: Ali Selamat Publisher: Penerbit UTM Press ISBN: 9835208468 Category : Computer science Languages : en Pages : 7
Book Description
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: George Tourlakis Publisher: John Wiley & Sons ISBN: 1118315359 Category : Mathematics Languages : en Pages : 410
Book Description
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.
Author: Willem Labuschagne Publisher: Unisa Press ISBN: 9780869818107 Category : Mathematics Languages : en Pages : 320
Book Description
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: Leonard S. Woody III Publisher: Packt Publishing Ltd ISBN: 1801070180 Category : Mathematics Languages : en Pages : 252
Book Description
Demystify quantum computing by learning the math it is built on Key Features Build a solid mathematical foundation to get started with developing powerful quantum solutions Understand linear algebra, calculus, matrices, complex numbers, vector spaces, and other concepts essential for quantum computing Learn the math needed to understand how quantum algorithms function Book Description Quantum computing is an exciting subject that offers hope to solve the world's most complex problems at a quicker pace. It is being used quite widely in different spheres of technology, including cybersecurity, finance, and many more, but its concepts, such as superposition, are often misunderstood because engineers may not know the math to understand them. This book will teach the requisite math concepts in an intuitive way and connect them to principles in quantum computing. Starting with the most basic of concepts, 2D vectors that are just line segments in space, you'll move on to tackle matrix multiplication using an instinctive method. Linearity is the major theme throughout the book and since quantum mechanics is a linear theory, you'll see how they go hand in hand. As you advance, you'll understand intrinsically what a vector is and how to transform vectors with matrices and operators. You'll also see how complex numbers make their voices heard and understand the probability behind it all. It's all here, in writing you can understand. This is not a stuffy math book with definitions, axioms, theorems, and so on. This book meets you where you're at and guides you to where you need to be for quantum computing. Already know some of this stuff? No problem! The book is componentized, so you can learn just the parts you want. And with tons of exercises and their answers, you'll get all the practice you need. What you will learn Operate on vectors (qubits) with matrices (gates) Define linear combinations and linear independence Understand vector spaces and their basis sets Rotate, reflect, and project vectors with matrices Realize the connection between complex numbers and the Bloch sphere Determine whether a matrix is invertible and find its eigenvalues Probabilistically determine the measurement of a qubit Tie it all together with bra-ket notation Who this book is for If you want to learn quantum computing but are unsure of the math involved, this book is for you. If you've taken high school math, you'll easily understand the topics covered. And even if you haven't, the book will give you a refresher on topics such as trigonometry, matrices, and vectors. This book will help you gain the confidence to fully understand quantum computation without losing you in the process!
Author: Arnold L. Rosenberg
Author: Arnold L. Rosenberg
Author: Gerard O’Regan
Author: K.V. Mital
Author: Clive Maxfield
Author: David Makinson
Author: Walter Gander
Author: Ali Selamat
Author: George Tourlakis
Author: Willem Labuschagne
Author: Leonard S. Woody III