Comprehensive Mathematics for Computer Scientists 1 Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Second Edition) /

• Main Authors: Mazzola, Guerino (Author), Milmeister, Gérard (Author), Weissmann, Jody (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Subjects: Computer science.; Mathematical logic.; Computer science > Mathematics.; Applied mathematics.; Engineering mathematics.; Computer Science.; Discrete Mathematics in Computer Science.; Applications of Mathematics.; Mathematical Logic and Formal Languages.; Mathematics of Computing.

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, w...

Table of Contents:

• 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
• 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.