E-Book Overview
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.
E-Book Content
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Guerino Mazzola • Gérard Milmeister • Jody Weissmann
Comprehensive Mathematics for Computer Scientists 1 Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Second Edition) With 118 Figures
Guerino Mazzola Gérard Milmeister Jody Weissmann Department of Informatics University Zurich Winterthurerstr. 190 8057 Zurich, Switzerland
The text has been created using LATEX 2ε . The graphics were drawn using Dia, an open-source diagramming software. The main text has been set in the Y&Y