Comprehensive Mathematics for Computer Scientists 1

Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

Guerino Mazzola, Gérard Milmeister, Jody Weissmann - Collection Universitext

358 pages, parution le 20/04/2004

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Résumé

This two-volume textbook Comprehensive Mathematics for Computer Scientists 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. This text is complemented by an online university course which covers the same theoretical content, however, in a totally different presentation. The student or working scientist who once gets involved in this text may at any time consult the online interface which comprises applets and other interactive tools.

Written for:

Students in Computer Science

L'auteur - Guerino Mazzola

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Sommaire

I Sets, Numbers, and Graphs
- Fundamentals-Concepts and Logic
- Axiomatic Set Theory
- Boolean Set Algebra
- Functions and Relations
- Ordinal and Natural Numbers
- Recursion Theorem and Universal Properties
- Natural Arithmetic
- Infinities
- The Classical Number Domains Z, Q, R, and C
- Categories of Graphs
- Construction of Graphs
- Some Special Graphs
- Planarity
- First Advanced Topic
II Algebra, Formal Logic, and Linear Geometry
- Monoids, Groups, Rings, and Fields
- Primes
- Formal Propositional Logic
- Formal Predicate Logic
- Languages, Grammars, and Automata
- Categories of Matrixes
- Modules and Vector Spaces
- Linear Dependence, Bases, and Dimension
- Algorithms in Linear Algebra
- Linear Geometry
- Eigenvalues, the Vector Product, and Quaternions
- Second Advanced Topic
- Further Reading
III Topology and Calculus
IV Selected Higher Subjects

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Guerino Mazzola, Gérard Milmeister, Jody Weissmann
Collection	Universitext
Parution	20/04/2004
Nb. de pages	358
Format	15,5 x 23,5
Couverture	Broché
Poids	555g
Intérieur	Noir et Blanc
EAN13	9783540208358