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Algebra for Computer Science

Algebra for Computer Science
Author: Lars Garding
Publisher: Springer Science & Business Media
Total Pages: 206
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461387973
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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.

Geometric Algebra for Computer Science

Geometric Algebra for Computer Science
Author: Leo Dorst
Publisher: Elsevier
Total Pages: 664
Release: 2010-07-26
Genre: Juvenile Nonfiction
ISBN: 0080553109
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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

Mathematics for Computer Science

Mathematics for Computer Science
Author: Eric Lehman
Publisher:
Total Pages: 988
Release: 2017-03-08
Genre: Business & Economics
ISBN: 9789888407064
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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.

Universal Algebra for Computer Scientists

Universal Algebra for Computer Scientists
Author: Wolfgang Wechler
Publisher: Springer Science & Business Media
Total Pages: 345
Release: 2012-12-06
Genre: Computers
ISBN: 3642767710
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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.

Coding the Matrix

Coding the Matrix
Author: Philip N. Klein
Publisher:
Total Pages: 530
Release: 2013-07
Genre: Algebras, Linear
ISBN: 9780615856735
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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.

Algorithmic Algebra

Algorithmic Algebra
Author: Bhubaneswar Mishra
Publisher: Springer Science & Business Media
Total Pages: 427
Release: 2012-12-06
Genre: Computers
ISBN: 1461243440
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Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

Linear Algebra and Probability for Computer Science Applications

Linear Algebra and Probability for Computer Science Applications
Author: Ernest Davis
Publisher: CRC Press
Total Pages: 431
Release: 2012-05-02
Genre: Mathematics
ISBN: 1466501596
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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

Algebra of Programming

Algebra of Programming
Author: Richard Bird
Publisher:
Total Pages: 322
Release: 1997
Genre: Computers
ISBN:
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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.

The Unreal Universe

The Unreal Universe
Author: Manoj Thulasidas
Publisher: Thulasidas
Total Pages: 284
Release: 2007
Genre: Physics
ISBN: 9810575947
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"In this immensely thought-provoking book, Thulasidas explores our notions of space and time and shows how our sense of reality rests on uncertain supports. Space is unreal the same way sound and smell are unreal, and time is no more real than mathematics. In a space created by the brain out of the light falling on our retinas (for the Hubble telescope), is it a surprise that nothing can travel faster than light? Generated by our sensory perception and fabricated by our cognitive process, the space-time continuum is the arena of physics. Looking at reality as a cognitive model of perception, Thulasidas sheds new light on spiritual philosophies, both Western and Eastern. Exploring the overlaps among the sciences and philosophies with impressive surety and clarity, The Unreal Universe looks set to revolutionize the way we think of reality and understand both modern physics and ancient spiritual writings"--Back cover

Principles of Quantitative Development

Principles of Quantitative Development
Author: Manoj Thulasidas
Publisher: John Wiley & Sons
Total Pages: 253
Release: 2012-03-13
Genre: Business & Economics
ISBN: 0470971525
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Principles of Quantitative Development is a practical guide to designing, building and deploying a trading platform. It is also a lucid and succinct exposé on the trade life cycle and the business groups involved in managing it, bringing together the big picture of how a trade flows through the systems, and the role of a quantitative professional in the organization. The book begins by looking at the need and demand for in-house trading platforms, addressing the current trends in the industry. It then looks at the trade life cycle and its participants, from beginning to end, and then the functions within the front, middle and back office, giving the reader a full understanding and appreciation of the perspectives and needs of each function. The book then moves on to platform design, addressing all the fundamentals of platform design, system architecture, programming languages and choices. Finally, the book focuses on some of the more technical aspects of platform design and looks at traditional and new languages and approaches used in modern quantitative development. The book is accompanied by a CD-ROM, featuring a fully working option pricing tool with source code and project building instructions, illustrating the design principles discussed, and enabling the reader to develop a mini-trading platform. The book is also accompanied by a website http://pqd.thulasidas.com that contains updates and companion materials.