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図書

図書
Guerino Mazzola, Gérard Milmeister, Jody Weissmann
出版情報: Berlin : Springer, c2004  xii, 357 p. ; 24 cm
シリーズ名: Universitext ; . Comprehensive mathematics for computer scientists ; 1
所蔵情報: loading…
目次情報: 続きを見る
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:
2.

電子ブック

EB
Guerino Mazzola, Gérard Milmeister, Gérard Milmeister, Jody Weissmann
出版情報: Springer eBooks Computer Science , Springer Berlin Heidelberg, 2005
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目次情報: 続きを見る
Topology and Calculus: Limits and Topology / III:
Differentiability
Inverse and Implicit Fuctions
Integration
Fubini and Changing Variables
Vector Field
Fixpoints
Main Theorem of ODEs
Topology and Calculus: Limits and Topology / III:
Differentiability
Inverse and Implicit Fuctions
3.

電子ブック

EB
Guerino Mazzola, Gérard Milmeister, Gérard Milmeister, Jody Weissmann
出版情報: Springer eBooks Computer Science , Springer Berlin Heidelberg, 2006
所蔵情報: loading…
目次情報: 続きを見る
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:
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