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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
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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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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:
4.

電子ブック

EB
Gérard Milmeister, Gérard Milmeister
出版情報: Springer eBooks Computer Science , Springer Berlin Heidelberg, 2009
所蔵情報: loading…
目次情報: 続きを見る
Concepts and Theory / Part I:
Overview of Music Theories / 1:
The Representation of Music / 2:
Types of Representation / 2.1:
Symbolic Representation of Music / 2.2:
Electronic Scores / 2.2.1:
MIDI / 2.2.2:
Musical Representation Languages / 2.2.3:
Language of General Concepts / 2.2.4:
Architecture of Concepts I: Principles / 3:
Pure Architecture / 3.1:
Selection / 3.1.1:
Conjunction / 3.1.2:
Disjunction / 3.1.3:
Architecture with Primitives / 3.2:
Examples / 3.3:
Macro Notes / 3.3.1:
Frequency Modulation / 3.3.2:
Full Score / 3.3.3:
The Category of Modules / 4:
From Monoids to Modules / 4.1:
Monoids / 4.1.1:
Groups / 4.1.2:
Rings / 4.1.3:
Modules / 4.1.4:
Categories / 4.2:
Definition / 4.2.1:
Functors / 4.2.2:
Natural Transformations / 4.2.3:
Yoneda's Lemma / 4.2.4:
Limits and Colimits / 4.2.5:
Topoi / 4.2.6:
Architecture of Concepts II: Forms and Denotators / 5:
Forms / 5.1:
Denotators / 5.2:
Computational Category Theory / 5.3:
Data Types in Programming Languages / 5.3.1:
The Role of Diagrams / 5.3.2:
Software Components for Computational Theories / 6:
Types of User Interface / 6.1:
Rubato Composer: Computational Theories / 6.2:
Historical Overview / 7:
presto / 7.1:
"Classic" Rubato / 7.2:
Experiments in Java / 7.3:
Rubato Composer / 7.4:
The Implementation / Part II:
Overview / 8:
Architecture / 9:
Overall Structure / 9.1:
The Rubato Composer Universe / 9.2:
Java Packages / 9.3:
Modules and Morphisms / 10:
Modules and their Elements / 10.1:
The Module Interface / 10.1.1:
The ModuleElement Interface / 10.1.2:
Module Morphisms / 10.2:
The ModuleMorphism Interface / 10.2.1:
Forms and Denotators / 11:
Requirements / 11.1:
Form Class / 11.2:
SimpleForm Class / 11.2.2:
LimitForm and ColimitForm Classes / 11.2.3:
PowerForm and ListForm Classes / 11.2.4:
SimpleDenotator Class / 11.3:
LimitDenotator Class / 11.3.2:
ColimitDenotator Class / 11.3.3:
PowerDenotator and ListDenotator Classes / 11.3.4:
Tools and Operations / 11.4:
Construction of Forms and Denotators / 11.4.1:
Paths / 11.4.2:
Module Mapping and Structural Replacement / 11.4.3:
Reforming / 11.4.4:
Address Changing / 11.4.5:
List and Set Operations / 11.4.6:
Tools and Utilities / 12:
Low-Level Mathematical Tools / 12.1:
Numbers / 12.1.1:
Matrixes / 12.1.2:
Repository and Predefined Universe / 12.2:
MIDI Sequencer and Synthesizer / 12.3:
Scheme Interpreter / 12.4:
XML as File Format for Rubato Composer / 12.5:
Rubato Composer GUI / 13:
Terminology / 13.1:
The Implementation of Networks / 13.2:
Running a Network / 13.3:
Macro Rubettes / 13.4:
Tools / 13.5:
The Plug-In System / 13.6:
Rubato Composer in Practice / Part III:
A Tutorial / 14:
First Applications in Rubette Construction / 16:
Rubettes for Macro Objects / 16.1:
The Wallpaper Rubette / 16.2:
The Alteration Rubette / 16.3:
Counterpoint Theory / 16.4:
Music Composition / 16.5:
The BigBang Rubette / 17:
Spontaneous Algorithmic Composition / 17.1:
Facts about Geometric Composition Strategies / 17.1.1:
Gestural Interaction Concept / 17.2:
Gesture Theory / 17.2.1:
Application of Gesture Theory / 17.2.2:
Modular Views / 17.3:
View Concept / 17.3.1:
Note representation / 17.3.2:
Basic Functionality and Navigation / 17.3.3:
Layers / 17.3.4:
Implemented Gestures / 17.4:
Geometrical Transformations / 17.4.1:
Wallpapers / 17.4.2:
Alteration / 17.4.3:
The BigBang Rubette in Context / 17.5:
Creative Analysis of Boulez's Structures / 18:
Boulez's Creative Analysis Revisited / 18.1:
Ligeti's Analysis / 18.2:
A First Creative Analysis of Structure Ia / 18.3:
Address Change / 18.3.1:
Primary Parameter Address Changes / 18.3.2:
Secondary Parameter Address Changes / 18.3.3:
The First Creative Analysis / 18.3.4:
Implementing Creative Analysis in Rubato Composer / 18.4:
The System of Boulettes / 18.4.1:
A Second More Creative Analysis and Reconstruction / 18.5:
The Conceptual Extensions / 18.5.1:
A Composition / 18.5.2:
Conclusion and Outlook / 19:
Lessons Learned / 19.1:
Things To Do / 19.2:
Ideas for Future Work / 19.3:
Appendix / Part IV:
User's Manual / 20:
Introduction / 20.1:
Concepts / 20.2:
Rubato Composer's World of Objects / 20.2.1:
Rubettes / 20.2.2:
Networks / 20.2.3:
Using Rubato Composer / 20.2.4:
Starting up / 20.3.1:
General Usage / 20.3.2:
Main Window / 20.3.3:
Main Menu and Toolbar / 20.3.4:
Network / 20.3.5:
Scheme Tools / 20.3.6:
Preferences / 20.3.8:
Recurring User Interface Elements / 20.3.9:
Core Rubettes / 20.4:
Rubette Description Schema / 20.4.1:
List of Core Rubettes / 20.4.2:
Built-in Non-Core Rubettes / 20.5:
Writing Rubettes / 20.6:
Developing with the Rubato Framework / 20.6.1:
Rubette Interface / 20.6.2:
Rubette Example / 20.7:
Specification / 20.7.1:
The LatchRubette class / 20.7.2:
Packaging a Plug-In / 20.7.3:
Types of Module Morphisms / 20.8:
The Rubette Java Interface / 20.9:
Example LatchRubette class / 20.10:
Keyboard Shortcuts / 20.11:
Rubato Scheme / 20.12:
Concepts and Theory / Part I:
Overview of Music Theories / 1:
The Representation of Music / 2:
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