Sets, Numbers, and Graphs / I: |
Fundamentals-Concepts and Logic / 1: |
Propositional Logic / 1.1: |
Architecture of Concepts / 1.2: |
Axiomatic Set Theory / 2: |
The Axioms / 2.1: |
Basic Concepts and Results / 2.2: |
Boolean Set Algebra / 3: |
The Boolean Algebra of Subsets / 3.1: |
Functions and Relations / 4: |
Graphs and Functions / 4.1: |
Relations / 4.2: |
Ordinal and Natural Numbers / 5: |
Ordinal Numbers / 5.1: |
Natural Numbers / 5.2: |
Recursion Theorem and Universal Properties / 6: |
Recursion Theorem / 6.1: |
Universal Properties / 6.2: |
Universal Properties in Relational Database Theory / 6.3: |
Natural Arithmetic / 7: |
Natural Operations / 7.1: |
Euclid and the Normal Forms / 7.2: |
Infinities / 8: |
The Diagonalization Procedure / 8.1: |
The Classical Number Domains ${\op Z}, {\op Q}, {\op R}$ and ${\op C}$ / 9: |
Integers ${\op Z}[$ / 9.1: |
Rationals ${\op Q}$ / 9.2: |
Real Numbers ${\op R}$ / 9.3: |
Complex Numbers ${\op C}$ / 9.4: |
Categories of Graphs / 10: |
Directed and Undirected Graphs / 10.1: |
Morphisms of Digraphs and Graphs / 10.2: |
Cycles / 10.3: |
Construction of Graphs / 11: |
Some Special Graphs / 12: |
n-ary Trees / 12.1: |
Moore Graphs / 12.2: |
Planarity / 13: |
Euler's Formula for Polyhedra / 13.1: |
Kuratowski's Planarity Theorem / 13.2: |
First Advanced Topic / 14: |
Floating Point Arithmetic / 14.1: |
Example for an Addition / 14.2: |
Algebra, Formal Logic, and Linear Geometry / II: |
Monoids, Groups, Rings, and Fields / 15: |
Monoids / 15.1: |
Groups / 15.2: |
Rings / 15.3: |
Fields / 15.4: |
Primes / 16: |
Prime Factorization / 16.1: |
Roots of Polynomials and Interpolation / 16.2: |
Formal Propositional Logic / 17: |
Syntactics: The Language of Formal Propositional Logic / 17.1: |
Semantics: Logical Algebras / 17.2: |
Signification: Valuations / 17.3: |
Axiomatics / 17.4: |
Formal Predicate Logic / 18: |
Syntactics: First-order Language / 18.1: |
Semantics: S-Structures / 18.2: |
Signification: Models / 18.3: |
Languages, Grammars, and Automata / 19: |
Languages / 19.1: |
Grammars / 19.2: |
Automata and Acceptors / 19.3: |
Categories of Matrixes / 20: |
What Matrixes Are / 20.1: |
Standard Operations on Matrixes / 20.2: |
Square Matrixes and their Determinant / 20.3: |
Modules and Vector Spaces / 21: |
Linear Dependence, Bases, and Dimension / 22: |
Bases in Vector Spaces / 22.1: |
Equations / 22.2: |
Affine Homomorphisms / 22.3: |
Algorithms in Linear Algebra / 23: |
Gauss Elimination / 23.1: |
The LUP Decomposition / 23.2: |
Linear Geometry / 24: |
Euclidean Vector Spaces / 24.1: |
Trigonometric Functions from Two-Dimensional Rotations / 24.2: |
Gram's Determinant and the Schwarz Inequality / 24.3: |
Eigenvalues, the Vector Product, and Quaternions / 25: |
Eigenvalues and Rotations / 25.1: |
The Vector Product / 25.2: |
Quaternions / 25.3: |
Second Advanced Topic / 26: |
Galois Fields / 26.1: |
The Reed-Solomon (RS) Error Correction Code / 26.2: |
The Rivest-Shamir-Adelman (RSA) Encryption Algorithm / 26.3: |
Further Reading / A: |
Index |
Sets, Numbers, and Graphs / I: |
Fundamentals-Concepts and Logic / 1: |
Propositional Logic / 1.1: |
Architecture of Concepts / 1.2: |
Axiomatic Set Theory / 2: |
The Axioms / 2.1: |