Author: Eric Lehman

Publisher:

ISBN:

Category:

Page: 1010

View: 549

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.

A Visual Approach

Author: John Vince

Publisher: Springer

ISBN:

Category: Computers

Page: 407

View: 708

In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, 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 to 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 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. This second 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: Max A. Viergever

Publisher: Springer

ISBN:

Category: Computers

Page: 546

View: 260

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.

A Problem-Solving Primer

Author: Tom Jenkyns

Publisher: Springer Science & Business Media

ISBN:

Category: Computers

Page: 416

View: 249

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.

Algorithms, Trees, Combinatorics and Probabilities

Author: Brigitte Chauvin

Publisher: Birkhäuser

ISBN:

Category: Mathematics

Page: 543

View: 375

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.

A Foundation for Computer Science

Author: Ronald L. Graham

Publisher: Addison-Wesley Professional

ISBN:

Category: Computers

Page: 657

View: 233

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.

Mathematics for Computer Science

Author: Faron Moller

Publisher: Springer

ISBN:

Category: Computers

Page: 500

View: 582

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: John Vince

Publisher: Springer

ISBN:

Category: Computers

Page: 301

View: 469

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.

Author: Donald F. Stanat

Publisher: Prentice Hall

ISBN:

Category: Mathematics

Page: 401

View: 548

Essays in Memory of Thomas Beth

Author: Jacques Calmet

Publisher: Springer Science & Business Media

ISBN:

Category: Computers

Page: 191

View: 312

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.

Discrete Mathematics for Computer Scientists

Author: Gunther Schmidt

Publisher: Springer

ISBN:

Category: Computers

Page: 301

View: 258

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.

Author: Harry Lewis

Publisher: Princeton University Press

ISBN:

Category: Mathematics

Page:

View: 580

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

Author: John Vince

Publisher: Springer

ISBN:

Category: Computers

Page: 505

View: 154

John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded fifth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, matrix algebra, transforms, interpolation, curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples. Mathematics for Computer Graphics covers all of the key areas of the subject, including: · Number sets · Algebra · Trigonometry · Coordinate systems · Determinants · Vectors · Quaternions · Matrix algebra · Geometric transforms · Interpolation · Curves and surfaces · Analytic geometry · Barycentric coordinates · Geometric algebra · Differential calculus · Integral calculus This fifth edition contains over 120 worked examples and over 320 colour illustrations, which are central to the author's descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics, giving a fascinating insight into the design of computer graphics software and setting the scene for further reading of more advanced books and technical research papers.

Author: Khoussainov Bakhadyr M

Publisher: World Scientific Publishing Company

ISBN:

Category: Mathematics

Page: 364

View: 784

This textbook presents fundamental topics in discrete mathematics introduced from the perspectives of a pure mathematician and an applied computer scientist. The synergy between the two complementary perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples, and yet are still formalized with mathematical rigor. The book is an excellent introduction to discrete mathematics for computer science, software engineering, and mathematics students.The first author is a leading mathematician in the area of logic, computability, and theoretical computer science, with more than 25 years of teaching and research experience. The second author is a computer science PhD student at the University of Washington specializing in database systems. The father-and-daughter team merges two different views to create a unified book for students interested in learning discrete mathematics, the connections between discrete mathematics and computer science, and the mathematical foundations of computer science.Readers will learn how to formally define abstract concepts, reason about objects (such as programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook studies several well-known algorithmic problems including the path problem for graphs and finding the greatest common divisor, inductive definitions, proofs of correctness of algorithms via loop invariants and induction, the basics of formal methods such as propositional logic, finite state machines, counting, probability, as well as the foundations of databases such as relational calculus.

Author: Rajeshwari S. Setty

Publisher: New Age International

ISBN:

Category: Biochemistry

Page: 323

View: 380

Written As Per Bangalore University Syllabus. Covers Biochemistry, Mathematics, Statistics And Introduction To Computer Science. Large Number Of Worked Examples And Illustrations. Summary At The End Of Each Chapter. A Large Number Of Theory Questions That Help Make Concepts Clear And Exercise Problems For Practice. An Exhaustive List Of Formulae That Will Serve As Ready Reckoner For Last Minute References.

Author: Eric Lehman

Publisher:

ISBN:

Category: Business & Economics

Page: 988

View: 349

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.

Theory and Practice for Science, Mathematics, and Engineering

Author: Roman Maeder

Publisher: Cambridge University Press

ISBN:

Category: Computers

Page: 389

View: 587

This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.

An Example-Based Introduction

Author: Jon Pierre Fortney

Publisher: CRC Press

ISBN:

Category: Computer science

Page: 260

View: 815

"Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features designed to be especially useful for courses at the community college level Ideal as a first or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers. Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode. An appendix on basic circuit design provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers"--

Author: Gary Haggard

Publisher: Brooks/Cole Publishing Company

ISBN:

Category: Mathematics

Page: 600

View: 211

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.

Algorithms, Trees, Combinatorics and Probabilities

Author: Brigitte Chauvin

Publisher: Birkhäuser

ISBN:

Category: Mathematics

Page: 543

View: 715

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.