Foundation Mathematics for Computer Science

Foundation Mathematics for Computer Science

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 ...

Author: John Vince

Publisher: Springer

ISBN: 3319214365

Category: Computers

Page: 334

View: 753

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.
Categories: Computers

Mathematics for Computer Science

Mathematics for Computer Science

This book covers elementary discrete mathematics for computer science and engineering.

Author: Eric Lehman

Publisher:

ISBN: 1680921223

Category:

Page: 1010

View: 386

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. The color images and text in this book have been converted to grayscale.
Categories:

Mathematics for Computer Science

Mathematics for Computer Science

This book covers elementary discrete mathematics for computer science and engineering.

Author: Eric Lehman

Publisher:

ISBN: 9888407066

Category: Business & Economics

Page: 988

View: 847

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.
Categories: Business & Economics

Mathematics and Computer Science II

Mathematics and Computer Science II

This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science.

Author: Brigitte Chauvin

Publisher: Birkhäuser

ISBN: 3034894759

Category: Mathematics

Page: 543

View: 321

This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science.
Categories: Mathematics

Mathematics and Computer Science in Medical Imaging

Mathematics and Computer Science in Medical Imaging

It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986.

Author: Max A. Viergever

Publisher: Springer

ISBN: 364283308X

Category: Computers

Page: 546

View: 605

Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.
Categories: Computers

Mathematical Methods in Computer Science

Mathematical Methods in Computer Science

This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, which was held during December 17-19, 2008, in Karlsruhe, Germany, in memory of Thomas Beth.

Author: Jacques Calmet

Publisher: Springer Science & Business Media

ISBN: 9783540899938

Category: Computers

Page: 191

View: 765

This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, which was held during December 17-19, 2008, in Karlsruhe, Germany, in memory of Thomas Beth. The themes of the conference reflected the many interests of Thomas Beth. Although, these interests might seem diverse, mathematical methods and especially algebra as a language constituted the common denominator of all of his scientific achievements. The 12 contributed talks presented were carefully selected from 30 submissions and cover the topics cryptography, designs, quantum computing, algorithms, and coding theory. Furthermore, this volume contains two invited talks held at the conference. One focuses on the area of coding theory and symbolic computation, an area especially appreciated by Thomas Beth, because it combines algebra and algorithmics. The other one discusses quantum information, which again was a focus of Thomas Beth’s research.
Categories: Computers

Relations and Graphs

Relations and Graphs

In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods.

Author: Gunther Schmidt

Publisher: Springer

ISBN: 3642779700

Category: Computers

Page: 301

View: 886

Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.
Categories: Computers

Fundamentals of Discrete Math for Computer Science

Fundamentals of Discrete Math for Computer Science

The book assumes no prior mathematical knowledge, and discusses concepts in programming as needed, allowing it to be used in a mathematics course taken concurrently with a student’s first programming course.

Author: Tom Jenkyns

Publisher: Springer Science & Business Media

ISBN: 9781447140696

Category: Computers

Page: 416

View: 639

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.
Categories: Computers

Concrete Mathematics

Concrete Mathematics

This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills.

Author: Ronald L. Graham

Publisher: Addison-Wesley Professional

ISBN: UOM:49015002633049

Category: Computers

Page: 657

View: 990

This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline.
Categories: Computers

Imaginary Mathematics for Computer Science

Imaginary Mathematics for Computer Science

Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science.

Author: John Vince

Publisher: Springer

ISBN: 9783319946375

Category: Computers

Page: 301

View: 965

The imaginary unit i = √-1 has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately, René Descartes referred to it as “imaginary”, and the use of the term “complex number” compounded the unnecessary mystery associated with this amazing object. Today, i = √-1 has found its way into virtually every branch of mathematics, and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamilton’s quaternions, Cayley’s octonions, to Grassmann’s geometric algebra. In spite of the aura of mystery that surrounds the subject, John Vince makes the subject accessible and very readable. The first two chapters cover the imaginary unit and its integration with real numbers. Chapter 3 describes how complex numbers work with matrices, and shows how to compute complex eigenvalues and eigenvectors. Chapters 4 and 5 cover Hamilton’s invention of quaternions, and Cayley’s development of octonions, respectively. Chapter 6 provides a brief introduction to geometric algebra, which possesses many of the imaginary qualities of quaternions, but works in space of any dimension. The second half of the book is devoted to applications of complex numbers, quaternions and geometric algebra. John Vince explains how complex numbers simplify trigonometric identities, wave combinations and phase differences in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the Mandelbrot set, both of which use complex numbers. The last chapter references the role of complex numbers in quantum mechanics, and ends with Schrödinger’s famous wave equation. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science.
Categories: Computers

The Beauty of Mathematics in Computer Science

The Beauty of Mathematics in Computer Science

The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph ...

Author: Jun Wu

Publisher: CRC Press

ISBN: 9781351689113

Category: Business & Economics

Page: 268

View: 464

The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school. The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph theory and web crawler Pagerank for web search Matrix operation and document classification Mathematical background of big data Neural networks and Google’s deep learning Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.
Categories: Business & Economics

Modelling Computing Systems

Modelling Computing Systems

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.

Author: Faron Moller

Publisher: Springer

ISBN: 1848003218

Category: Computers

Page: 500

View: 772

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.
Categories: Computers

Essential Discrete Mathematics for Computer Science

Essential Discrete Mathematics for Computer Science

Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof.

Author: Harry Lewis

Publisher: Princeton University Press

ISBN: 9780691179292

Category: Computers

Page: 408

View: 573

A more intuitive approach to the mathematical foundation of computer science Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, this flexible book can be tailored to fit the syllabi for a variety of courses. Proven in the classroom, 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. The text requires only precalculus, and where calculus is needed, a quick summary of the basic facts is provided. Essential Discrete Mathematics for Computer Science is the ideal introductory textbook for standard undergraduate courses, and is also suitable for high school courses, distance education for adult learners, and self-study. The essential introduction to discrete mathematics Features thirty-one short chapters, each suitable for a single class lesson Includes more than 300 exercises Almost every formula and theorem proved in full Breadth of content makes the book adaptable to a variety of courses Each chapter includes a concise summary Solutions manual available to instructors
Categories: Computers

Problems With A Point Exploring Math And Computer Science

Problems With A Point  Exploring Math And Computer Science

'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume.

Author: Gasarch William

Publisher: World Scientific

ISBN: 9789813279742

Category: Computers

Page: 284

View: 932

Ever notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)?Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques.This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.
Categories: Computers

Structured Matrices in Mathematics Computer Science and Engineering

Structured Matrices in Mathematics  Computer Science  and Engineering

In the past few years, a number of practical algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in these volumes, which collect 38 papers devoted to the numerous aspects of the topic.

Author: Vadim Olshevsky

Publisher: American Mathematical Soc.

ISBN: 9780821820926

Category: Mathematics

Page: 344

View: 744

Many important problems in applied sciences, mathematics, and engineering can be reduced to matrix problems. Moreover, various applications often introduce a special structure into the corresponding matrices, so that their entries can be described by a certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices, Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and observability matrices, and others. Exploiting these and the more general structures often allows us to obtain elegant solutions to mathematical problems as well as to design more efficient practical algorithms for a variety of applied engineering problems. Structured matrices have been under close study for a long time and in quite diverse (and seemingly unrelated) areas, for example, mathematics, computer science, and engineering. Considerable progress has recently been made in all these areas, and especially in studying the relevant numerical and computational issues. In the past few years, a number of practical algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in these volumes, which collect 38 papers devoted to the numerous aspects of the topic. The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numerical issues. The presentation fully illustrates the fact that the techniques of engineers, mathematicians, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices. The book is published in two volumes. The first contains articles on interpolation, system theory, signal and image processing, control theory, and spectral theory. Articles in the second volume are devoted to fast algorithms, numerical and iterative methods, and various applications.
Categories: Mathematics

Mathematical Foundations of Computer Science 2014

Mathematical Foundations of Computer Science 2014

This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014.

Author: Ersébet Csuhaj-Varjú

Publisher: Springer

ISBN: 366244464X

Category: Computers

Page: 640

View: 806

This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.
Categories: Computers

A User friendly Introduction to Discrete Mathematics for Computer Science

A User friendly Introduction to Discrete Mathematics for Computer Science

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.

Author: Willem Labuschagne

Publisher: Unisa Press

ISBN: 0869818104

Category: Computer science

Page: 304

View: 780

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.
Categories: Computer science

Practice Test for the TestAS Mathematics Computer Science and Natural Sciences

Practice Test for the TestAS Mathematics  Computer Science and Natural Sciences

Included in The Practice Test for the TestAS Mathematics, Computer Science and Natural Sciences are:✔ One complete practice test for the subject module "Mathematics, Computer Science and Natural Sciences"✔ The Core Test with four ...

Author: edulink edulink GmbH

Publisher:

ISBN: 9798681793557

Category:

Page: 169

View: 504

Your preparation for the TestAS 2021 With our books, get everything you need to achieve a high test score. The TestAS (Test for Academic Studies) is a study aptitude test for applicants from non-EU countries who want to study in Germany. Start preparing for the TestAS now to improve your chances of being admitted to a German university. Our books completely cover the Core Test and the Subject Module "Mathematics, Computer Science and Natural Science" and prepare you efficiently for the test day. The key to success lies in having learned and practiced in the best possible way for the exam: Achieve an above-average test score based on our strategies and practice questions. Included in The Practice Test for the TestAS Mathematics, Computer Science and Natural Sciences are:✔ One complete practice test for the subject module "Mathematics, Computer Science and Natural Sciences"✔ The Core Test with four subtests and the Subject Module with two subtests✔ A total of 132 questions✔ Detailed answers and solutions Our series for the TestAS Subject Module Mathematics, Computer Science and Natural Sciences:► 1. Preparation Book for the TestAS Mathematics, Computer Science and Natural Sciences: Analyzing Scientific Interrelationships► 2. Preparation Book for the TestAS Mathematics, Computer Science and Natural Sciences: Understanding Formal Depictions► The Practice Test for the TestAS Mathematics, Computer Science and Natural Sciences Our series for the TestAS Core Test:► 1. Preparation Book for the TestAS Core Test: Guideline for the TestAS and Completing Patterns► 2. Preparation Book for the TestAS Core Test: Solving Quantitative Problems► 3. Preparation Book for the TestAS Core Test: Inferring Relationships and Continuing Numerical Series
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Mathematical Logic and Theoretical Computer Science

Mathematical Logic and Theoretical Computer Science

This book includes articles on denotational semanitcs, recursion theoretic aspects of computer science, model theory and algebra, automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic.

Author: Kueker

Publisher: CRC Press

ISBN: 0824777468

Category: Mathematics

Page: 408

View: 213

This book includes articles on denotational semanitcs, recursion theoretic aspects of computer science, model theory and algebra, automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. It is intended for mathematical logicians and computer scientists.
Categories: Mathematics