Sets and numbers, graphs and algebra, logic and machines, linear geometry
著者
書誌事項
Sets and numbers, graphs and algebra, logic and machines, linear geometry
（Universitext, . Comprehensive mathematics for computer scientists ; 1）
Springer, c2004
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注記
Includes bibliographical references (p. [333]-336) and index
内容説明・目次
内容説明
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.
目次
- I Sets, Numbers, and Graphs. Fundamentals - Concepts and Logic. 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. Modules and Vector Spaces. Linear Dependence, Bases and Dimension. Linear Maps and Matrixes. Algorithms in Linear Algebra. Geometric Algebra. Eigenvalues, Symmetry Groups, and Quaternions. Second Advanced Topic.
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