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The twovolume textbook Comprehensive Mathematics for Computer Scientists, of which this is the first volume, is a selfcontained 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 toposoriented 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, BackusNaur normal forms, Lsystems, Chomsky hierarchies, algorithms for data encoding, e.g., the ReedSolomon 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.
 Table of Contents

Table of Contents
 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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