Understanding Mathematics And Computers

Author : Arnold L. Rosenberg,Denis Trystram
Publisher : Springer Nature
Page : 550 pages
File Size : 48,7 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 : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 48,8 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 : David Makinson
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 45,6 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 : K. V. Mital
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2007
Category : Electronic
ISBN : OCLC:1280716764

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Understanding Mathematics and Computers by K. V. Mital Pdf

Author : John Vince
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 53,6 Mb
Release : 2005-12-19
Category : Computers
ISBN : 9781846282836

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Mathematics for Computer Graphics by John Vince Pdf

This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.

Author : John Vince
Publisher : Springer
Page : 334 pages
File Size : 46,6 Mb
Release : 2015-07-27
Category : Computers
ISBN : 9783319214375

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Foundation Mathematics for Computer Science by John Vince Pdf

John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

Author : Gerard O’Regan
Publisher : Springer Nature
Page : 468 pages
File Size : 46,5 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 : Richard Noss,Celia Hoyles
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400916968

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Windows on Mathematical Meanings by Richard Noss,Celia Hoyles Pdf

This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

Author : John Vince
Publisher : Springer Nature
Page : 519 pages
File Size : 43,9 Mb
Release : 2023-01-24
Category : Computers
ISBN : 9783031174117

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Foundation Mathematics for Computer Science by John Vince Pdf

In this third edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the second edition, and added chapters on systems of counting, area and volume. These subjects complement the existing chapters on visual mathematics, numbers, algebra, logic, combinatorics, probability, modular arithmetic, trigonometry, coordinate systems, determinants, vectors, complex numbers, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics that provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with calculating area and volume using calculus. Readers will find that the author’s visual approach should greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. This third edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts. Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

Author : Cordelia Hall,John O'Donnell
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 48,8 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 : Faron Moller,Georg Struth
Publisher : Springer
Page : 0 pages
File Size : 45,6 Mb
Release : 2013-07-24
Category : Computers
ISBN : 1848003218

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Modelling Computing Systems by Faron Moller,Georg Struth Pdf

This engaging text presents the fundamental mathematics and modelling techniques for computing systems in a novel and light-hearted way, which can be easily followed by students at the very beginning of their university education. Key concepts are taught through a large collection of challenging yet fun mathematical games and logical puzzles that require no prior knowledge about computers. The text begins with intuition and examples as a basis from which precise concepts are then developed; demonstrating how, by working within the confines of a precise structured method, the occurrence of errors in the system can be drastically reduced. Features: demonstrates how game theory provides a paradigm for an intuitive understanding of the nature of computation; contains more than 400 exercises throughout the text, with detailed solutions to half of these presented at the end of the book, together with numerous theorems, definitions and examples; describes a modelling approach based on state transition systems.

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 40,8 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 : Jonathan M. Borwein,Matthew P. Skerritt
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 55,7 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9781461442530

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An Introduction to Modern Mathematical Computing by Jonathan M. Borwein,Matthew P. Skerritt Pdf

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

Author : MICHAEL JOHN. DE SMITH
Publisher : Unknown
Page : 236 pages
File Size : 50,7 Mb
Release : 2018-02-08
Category : Electronic
ISBN : 1912556006

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Understanding Mathematics in the Digital Age by MICHAEL JOHN. DE SMITH Pdf

This book provides a new and highly approachable introduction to mathematics in the digital age. Numerous practical case studies are provided, from CD data recording to population modeling, with clear explanations and worked examples using widely available personal computer tools. These tools include spreadsheets such as Excel and modern mathematical software packages such as MATLab and Maple. Part I of the book introduced the topic and its intended audience. Parts II to IV are the main sections of the book. Part II provides foundation materials explaining the origins of our system of numbers and the notation used in mathematics. It then explores a number of familiar topics including the determination of times and distances, the structure of sound waves, the speed of light and gravity measurement. Part III takes the exploration process further, using the computer as a tool to investigate credit card and email security, digital photography, arithmetic by computers and the modeling of population dynamics. Part IV concludes the exploration with details of a wide range of interesting numbers and number sequences, coupled with a little of the history for some of those that are regarded as being of greatest importance. Part V provides number of "mathematical extras" together with a selection of suggested books to read, web sites to explore and software to use. Collectively these five Parts offer a brief, but wide-ranging introduction to many areas of mathematics, physics and modern computing science. In the process and without recourse to "higher mathematics" it introduces readers to the history of mathematics, algebra, number theory, finite and infinite series, trigonometry, calculus, statistics and a fair sprinkling of computational mathematics

Author : Gary Haggard,John Schlipf,Sue Whitesides
Publisher : Cengage Learning
Page : 0 pages
File Size : 49,8 Mb
Release : 2006
Category : Computers
ISBN : 053449501X

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Discrete Mathematics for Computer Science by Gary Haggard,John Schlipf,Sue Whitesides Pdf

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.