Item description for Comprehensive Mathematics for Computer Scientists 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Universitext) by Guerino B. Mazzola...
The two-volume textbook Comprehensive Mathematics for Computer Scientists, of which this is the first volume, is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. Despite the theoretical soundness, the material stresses a large number of core computer science subjects, such as, for example, a discussion of floating point arithmetic, Backus-Naur normal forms, L-systems, Chomsky hierarchies, algorithms for data encoding, e.g., the Reed-Solomon code. The numerous course examples are motivated by computer science and bear a generic scientific meaning.
For the second edition the entire text has been carefully reread, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too shorthand style. This makes the book more comfortable to handle for instructors as well as for students.
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Est. Packaging Dimensions: Length: 9.21" Width: 6.14" Height: 0.94" Weight: 1.37 lbs.
Release Date Nov 13, 2006
ISBN 3540368736 ISBN13 9783540368731
Availability 82 units. Availability accurate as of May 23, 2017 08:23.
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Reviews - What do customers think about Comprehensive Mathematics for Computer Scientists 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Universitext)?
for computer scientists, not programmers Jan 22, 2007
If you are a computer professional and wondering how much maths you need, this book might be a good answer. Much of its content is discrete maths. Like factorising primes. A background in this leads into the theory of public key encryption. Something well worth knowing. Note that the book's discussion of factorising primes is brief. You'd need another text for the public key material.
Also potentially useful is a foray into graph theory. Rings and modules also make their appearance. Predicate logic is another topic explained.
The text also discusses matrices from a viewpoint more formal than that of a typical first course in linear algebra. It generalises to an exposition of vector spaces. This portion of the text is continuum maths.
Do note that the average computer programmer actually uses very little of the material. Emphasis on programmer. But as the title says, the book is directed towards the computer scientist, who needs a more formal grounding.
Set high standards Aug 17, 2004
This book is very exciting and motivating, as it sets high standards both with respect to the contents and the style.
It contains the main topics of modern math from the beginning, with applications to Computer Science: Sets, Relations, Logic, Numbers, Groups, Rings, Modules, Linear Algebra, Geometry, Quaternions.
The style is extremely compact, precise and readable, with a professional notation. The book is optimal designed (modularized) which results in a moderate size (360 p.)
The objective of his approach is to provide a better formal competence for computer scientists by a sound mathematical education:
"Improved formal competence is urged by the object-oriented paradigm which progressively requires a programming style and a design strategy of high abstraction level in conceptual engineering."
The accompanying online course contains illustrations and animations, which at the moment don't go far beyond the book's contents. Nevertheless, the online part has a great potential for further applications, e.g. programming projects (Moebius-Strip, Raytracing, 3D Stereo, ...)
We hope, this book will establish itself as a standard for ambitious schools and students.