Author : Lars Garding
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 24,70 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461387973
The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students.
Author : Leo Dorst
Publisher : Elsevier
Page : 664 pages
File Size : 34,61 MB
Release : 2010-07-26
Category : Juvenile Nonfiction
ISBN : 0080553109
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
Author : Wolfgang Wechler
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 31,50 MB
Release : 2012-12-06
Category : Computers
ISBN : 3642767710
A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.
Author : Philip N. Klein
Publisher :
Page : 530 pages
File Size : 46,1 MB
Release : 2013-07
Category : Algebras, Linear
ISBN : 9780615856735
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.
Author : Eric Lehman
Publisher :
Page : 988 pages
File Size : 18,48 MB
Release : 2017-03-08
Category : Business & Economics
ISBN : 9789888407064
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 : Ernest Davis
Publisher : CRC Press
Page : 431 pages
File Size : 26,86 MB
Release : 2012-05-02
Category : Mathematics
ISBN : 1466501596
Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB functi
Author : Leo Dorst
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 18,69 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146120089X
Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
Author : Richard Bird
Publisher :
Page : 322 pages
File Size : 41,22 MB
Release : 1997
Category : Computers
ISBN :
Describing an algebraic approach to programming, based on a categorical calculus of relations, this book is suitable for the derivation of individual programs and for the study of programming principles in general.
Author : Joachim von zur Gathen
Publisher : Cambridge University Press
Page : 811 pages
File Size : 33,62 MB
Release : 2013-04-25
Category : Computers
ISBN : 1107039037
Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.
Author : George S. Boolos
Publisher : Cambridge University Press
Page : 365 pages
File Size : 46,79 MB
Release : 2007-09-17
Category : Computers
ISBN : 0521877520
This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.
