Download PDF Comprehensive Mathematics for Computer Scientists 1 Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry With 118 Figures Second Edition by Guerino Mazzola

Sinopsis

Propositional logic helps us to navigate in a world painted in black and white, a world in which there is only truth or falsehood, but nothing in between. It is a boiled down version of common sense reasoning. It is the essence of Sherlock Holmes' way of deducing that Professor Moriarty was the mastermind behind a criminal organization (“Elementary, my dear Watson”). Propositional logic builds on the following two propositions, which are declared to be true as basic principles (and they seem to make sense. . . ):

Content

1. Fundamentals—Concepts and Logic
2. Axiomatic Set Theory
3. Boolean Set Algebra
4. Functions and Relations
5. Ordinal and Natural Numbers
6. Recursion Theorem and Universal Properties
7. Natural Arithmetic
8. In nities
9. The Classical Number Domains Z, Q, R, and C
10. Categories of Graphs
11. Construction of Graphs
12. Some Special Graphs
13. Planarity
14. First Advanced Topic
15. Monoids, Groups, Rings, and Fields
16. Primes
17. Formal Propositional Logic
18. Formal Predicate Logic
19. Languages, Grammars, and Automata
20. Categories of Matrixes
21. Modules and Vector Spaces
22. Linear Dependence, Bases, and Dimension
23. Algorithms in Linear Algebra
24. Linear Geometry
25. Eigenvalues, the Vector Product, and Quaternions
26. Second Advanced Topic

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