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電子ブック

EB
Ernesto; D'Antona, Ottavio; Marra, Vincenzo Damiani, Ottavio D'Antona, Ernesto Damiani
出版情報: Springer eBooks Computer Science , Springer US, 2009
所蔵情報: loading…
目次情報: 続きを見る
Gian-Carlo Rota, the Man / Part I:
Gianco, my Brother / Ester Gasperoni Rota1:
References
Remembering Gian-Carlo Rota / Joseph J. Kohn2:
Gian-Carlo Rota, the Mathematician / Part II:
A Glimpse of Vector Invariant Theory. The Points of View of Weyl, Rota, De Concini and Procesi, and Grosshans / Andrea Brini3:
Introduction / 3.1:
The Characteristic Zero Approach / 3.2:
Preliminaries / 3.2.1:
Weyl's Theorem (The Reduction Principle) / 3.2.2:
Absolute Invariants for the Special Linear Group S L(d) / 3.2.3:
Absolute Invariants for the Symplectic Group S p2m / 3.2.4:
Absolute Invariants for the Special Orthogonal Group S O(d) / 3.2.5:
Absolute Invariants for the Orthogonal Group O(d) / 3.2.6:
The Straightening Formulae / 3.3:
Standard Young Tableaux / 3.3.1:
Bideterminants / 3.3.2:
Pfaffians / 3.3.3:
Gramians / 3.3.4:
The E. Pascal Theorems and the Cancellation Laws / 3.4:
The E. Pascal Theorem and the Cancellation Law for Scalar Products / 3.4.1:
The E. Pascal Theorem and the Cancellation Law for Symplectic Products / 3.4.2:
The E. Pascal Theorem and the Cancellation Law for Inner Products / 3.4.3:
The First and the Second Fundamental Theorems / 3.5:
The First Fundamental Theorems / 3.5.1:
The Second Fundamental Theorems / 3.5.2:
Grosshans's Theorem / 3.6:
Partitions of a Finite Partially Ordered Set / Pietro Codara4:
Background, and Preliminary Results / 4.1:
Partitions as Sets of Fibres / 4.3:
Partitions as Partially Ordered Sets of Blocks / 4.4:
Partitions Induced by Quasiorders / 4.5:
Further Work / 4.6:
An Algebra of Pieces of Space - Hermann Grassmann to Gian Carlo Rota / Henry Crapo5:
Almost Ten Years Later / 5.1:
Synthetic Projective Geometry / 5.2:
Hermann Grassmann's Algebra / 5.3:
Extensors and Vectors / 5.4:
Reduced Forms / 5.5:
Grassmann-Cayley Algebra, Peano Spaces / 5.6:
Whitney Algebra / 5.7:
Geometric Product / 5.8:
Regressive Product / 5.9:
Higher Order Syzygies / 5.10:
Balls in Boxes / 5.11:
The Eleventh and Twelveth Problems of Rota's Fubini Lectures: from Cumulants to Free Probability Theory / Elvira Di Nardo ; Domenico Senato6:
Prologue / 6.1:
The Classical Umbral Calculus / 6.2:
Generating Functions / 6.2.1:
Sequences of Binomial Type, Bell Umbrae and Poisson Processes / 6.3:
Cumulants / 6.4:
Singleton Umbra / 6.4.1:
Cumulant Umbra / 6.4.2:
Applications in Statistics / 6.5:
U-Statistics / 6.5.1:
Moments of Sampling Distributions / 6.5.2:
Products of Statistics / 6.5.3:
k-statistics / 6.5.4:
Fast Symbolic Computation of k-statistics / 6.5.5:
Sheppard's Corrections / 6.5.6:
Sheffer Sequences / 6.6:
Abel Polynomials / 6.6.1:
Quasi-free Cumulant Umbra / 6.6.2:
Boolean Cumulants / 6.6.3:
Free Cumulant Theory / 6.7:
Two Examples of Applied Universal Algebra / Joseph P. S. Kung7:
The Bohnenblust-Spitzer Identity / 7.1:
Baxter Algebras / 7.3:
The Standard Baxter Algebra / 7.4:
A Precursor Identity / 7.5:
Abstract Random Variables / 7.6:
On the Euler Characteristic of Finite Distributive Lattices / Emanuele Munarini8:
Posets and Distributive Lattices / 8.1:
Euler Characteristic / 8.3:
Uniform Distributions of the Characteristic / 8.4:
X-uniform Lattices / 8.4.1:
Order-preserving Euler Characteristic / 8.4.2:
Rank X-uniform Lattices / 8.4.3:
Pseudo-planar Distributive Lattices / 8.5:
Graphs and Hypergraphs / 8.6:
Dual Gödel Lattices / 8.7:
Tree maps / 8.8:
Rota, Probability, Algebra and Logic / Daniele Mundici9:
MV-algebraic States and De Finetti Coherence Criterion / 9.1:
MV-algebraic and C*-algebraic States After Elliott Classification / 9.2:
MV-algebraic ?-states and Carathéodory Probability Theory / 9.3:
A Symbolic Treatment of Abel Polynomials / Pasquale Petrullo10:
Abel polynomials, Lagrange inversion formula and sequences of binomial type / 10.1:
Generalized Abel polynomials / 10.3:
Cumulants and convolutions / 10.4:
Gian-Carlo Rota, the Philosopher / Part III:
Ethics in Thought. Gian-Carlo Rota and Philosophy / Francesca Bonicalzi11:
Telling/Inventing the Truth / 11.1:
The Winding Streets, and the Straight and Wide Avenue of Precision / 11.2:
The Food of Philosophical Thought and the Medicine of Axiomatics / 11.3:
The Ethics of Knowledge and the Genesis of its Disciplines / 11.4:
Indiscrete Variations on Gian-Carlo Rota's Themes / Carlo Cellucci12:
The Existence of Mathematical Objects / 12.1:
Irrelevance of the Existence of Mathematical Objects / 12.2.1:
Mathematical Objects as Hypotheses / 12.2.2:
Hypotheses vs. Fictions / 12.2.3:
Existence and Identity / 12.2.4:
The Inexhaustibility of Mathematical Objects / 12.2.5:
Definition in Mathematics / 12.3:
Definition, Description and Analysis of Concepts / 12.3.1:
Definition in Mathematics and in Philosophy / 12.3.2:
The Alleged Circularity of Definitions and Theorems / 12.3.3:
The Notion of Proof / 12.4:
Proof as the Opening up of Possibilities / 12.4.1:
Axiomatic Presentation and Gödel's Incompleteness Theorems / 12.4.2:
Are there Definitive Proofs? / 12.4.3:
Proof and Evidence / 12.4.4:
The Relation of Philosophy of Mathematics to Mathematics / 12.5:
The Descriptive Character of the Philosophy of Mathematics / 12.5.1:
The Need for a Drastic Overhaul of Logic / 12.5.2:
Rota's Place in the Philosophy of Mathematics / 12.6:
On the Courage Needed to Do Phenomenology. Rota and Analytic Philosophy / Albino Lanciani ; Claudio Majolino13:
Twilight of an Idol / 13.1:
Three Senses of Phenomenology / 13.2:
Coda / 13.3:
Rota's Philosophical Insights / Massimo Mugnai14:
What Kind of Reductionism? / 14.1:
Rota's Objectivism and Husserl's Naturalism / 14.3:
Beyond Classical Logic / 14.4:
Concluding Remarks / 14.5:
"A Minority View". Gian-Carlo Rota's Phenomenological Realism / Fabrizio Palombi15:
Considerations on the Problem of Realism / 15.1:
Phenomenological Realism / 15.2:
Fringe Phenomena and State-of-Mind / 15.3:
Psychologistic Misunderstandings / 15.4:
Descriptions, Not Prescriptions / 15.5:
Gian-Carlo Rota, the Man / Part I:
Gianco, my Brother / Ester Gasperoni Rota1:
References
2.

電子ブック

EB
Ernesto; D'Antona, Ottavio; Marra, Vincenzo Damiani, Ottavio D'Antona, Ernesto Damiani, Vincenzo Marra, Fabrizio Palombi
出版情報: SpringerLink Books - AutoHoldings , Springer US, 2009
所蔵情報: loading…
目次情報: 続きを見る
Gian-Carlo Rota, the Man / Part I:
Gianco, my Brother / Ester Gasperoni Rota1:
References
Remembering Gian-Carlo Rota / Joseph J. Kohn2:
Gian-Carlo Rota, the Mathematician / Part II:
A Glimpse of Vector Invariant Theory. The Points of View of Weyl, Rota, De Concini and Procesi, and Grosshans / Andrea Brini3:
Introduction / 3.1:
The Characteristic Zero Approach / 3.2:
Preliminaries / 3.2.1:
Weyl's Theorem (The Reduction Principle) / 3.2.2:
Absolute Invariants for the Special Linear Group S L(d) / 3.2.3:
Absolute Invariants for the Symplectic Group S p2m / 3.2.4:
Absolute Invariants for the Special Orthogonal Group S O(d) / 3.2.5:
Absolute Invariants for the Orthogonal Group O(d) / 3.2.6:
The Straightening Formulae / 3.3:
Standard Young Tableaux / 3.3.1:
Bideterminants / 3.3.2:
Pfaffians / 3.3.3:
Gramians / 3.3.4:
The E. Pascal Theorems and the Cancellation Laws / 3.4:
The E. Pascal Theorem and the Cancellation Law for Scalar Products / 3.4.1:
The E. Pascal Theorem and the Cancellation Law for Symplectic Products / 3.4.2:
The E. Pascal Theorem and the Cancellation Law for Inner Products / 3.4.3:
The First and the Second Fundamental Theorems / 3.5:
The First Fundamental Theorems / 3.5.1:
The Second Fundamental Theorems / 3.5.2:
Grosshans's Theorem / 3.6:
Partitions of a Finite Partially Ordered Set / Pietro Codara4:
Background, and Preliminary Results / 4.1:
Partitions as Sets of Fibres / 4.3:
Partitions as Partially Ordered Sets of Blocks / 4.4:
Partitions Induced by Quasiorders / 4.5:
Further Work / 4.6:
An Algebra of Pieces of Space - Hermann Grassmann to Gian Carlo Rota / Henry Crapo5:
Almost Ten Years Later / 5.1:
Synthetic Projective Geometry / 5.2:
Hermann Grassmann's Algebra / 5.3:
Extensors and Vectors / 5.4:
Reduced Forms / 5.5:
Grassmann-Cayley Algebra, Peano Spaces / 5.6:
Whitney Algebra / 5.7:
Geometric Product / 5.8:
Regressive Product / 5.9:
Higher Order Syzygies / 5.10:
Balls in Boxes / 5.11:
The Eleventh and Twelveth Problems of Rota's Fubini Lectures: from Cumulants to Free Probability Theory / Elvira Di Nardo ; Domenico Senato6:
Prologue / 6.1:
The Classical Umbral Calculus / 6.2:
Generating Functions / 6.2.1:
Sequences of Binomial Type, Bell Umbrae and Poisson Processes / 6.3:
Cumulants / 6.4:
Singleton Umbra / 6.4.1:
Cumulant Umbra / 6.4.2:
Applications in Statistics / 6.5:
U-Statistics / 6.5.1:
Moments of Sampling Distributions / 6.5.2:
Products of Statistics / 6.5.3:
k-statistics / 6.5.4:
Fast Symbolic Computation of k-statistics / 6.5.5:
Sheppard's Corrections / 6.5.6:
Sheffer Sequences / 6.6:
Abel Polynomials / 6.6.1:
Quasi-free Cumulant Umbra / 6.6.2:
Boolean Cumulants / 6.6.3:
Free Cumulant Theory / 6.7:
Two Examples of Applied Universal Algebra / Joseph P. S. Kung7:
The Bohnenblust-Spitzer Identity / 7.1:
Baxter Algebras / 7.3:
The Standard Baxter Algebra / 7.4:
A Precursor Identity / 7.5:
Abstract Random Variables / 7.6:
On the Euler Characteristic of Finite Distributive Lattices / Emanuele Munarini8:
Posets and Distributive Lattices / 8.1:
Euler Characteristic / 8.3:
Uniform Distributions of the Characteristic / 8.4:
X-uniform Lattices / 8.4.1:
Order-preserving Euler Characteristic / 8.4.2:
Rank X-uniform Lattices / 8.4.3:
Pseudo-planar Distributive Lattices / 8.5:
Graphs and Hypergraphs / 8.6:
Dual Gödel Lattices / 8.7:
Tree maps / 8.8:
Rota, Probability, Algebra and Logic / Daniele Mundici9:
MV-algebraic States and De Finetti Coherence Criterion / 9.1:
MV-algebraic and C*-algebraic States After Elliott Classification / 9.2:
MV-algebraic ?-states and Carathéodory Probability Theory / 9.3:
A Symbolic Treatment of Abel Polynomials / Pasquale Petrullo10:
Abel polynomials, Lagrange inversion formula and sequences of binomial type / 10.1:
Generalized Abel polynomials / 10.3:
Cumulants and convolutions / 10.4:
Gian-Carlo Rota, the Philosopher / Part III:
Ethics in Thought. Gian-Carlo Rota and Philosophy / Francesca Bonicalzi11:
Telling/Inventing the Truth / 11.1:
The Winding Streets, and the Straight and Wide Avenue of Precision / 11.2:
The Food of Philosophical Thought and the Medicine of Axiomatics / 11.3:
The Ethics of Knowledge and the Genesis of its Disciplines / 11.4:
Indiscrete Variations on Gian-Carlo Rota's Themes / Carlo Cellucci12:
The Existence of Mathematical Objects / 12.1:
Irrelevance of the Existence of Mathematical Objects / 12.2.1:
Mathematical Objects as Hypotheses / 12.2.2:
Hypotheses vs. Fictions / 12.2.3:
Existence and Identity / 12.2.4:
The Inexhaustibility of Mathematical Objects / 12.2.5:
Definition in Mathematics / 12.3:
Definition, Description and Analysis of Concepts / 12.3.1:
Definition in Mathematics and in Philosophy / 12.3.2:
The Alleged Circularity of Definitions and Theorems / 12.3.3:
The Notion of Proof / 12.4:
Proof as the Opening up of Possibilities / 12.4.1:
Axiomatic Presentation and Gödel's Incompleteness Theorems / 12.4.2:
Are there Definitive Proofs? / 12.4.3:
Proof and Evidence / 12.4.4:
The Relation of Philosophy of Mathematics to Mathematics / 12.5:
The Descriptive Character of the Philosophy of Mathematics / 12.5.1:
The Need for a Drastic Overhaul of Logic / 12.5.2:
Rota's Place in the Philosophy of Mathematics / 12.6:
On the Courage Needed to Do Phenomenology. Rota and Analytic Philosophy / Albino Lanciani ; Claudio Majolino13:
Twilight of an Idol / 13.1:
Three Senses of Phenomenology / 13.2:
Coda / 13.3:
Rota's Philosophical Insights / Massimo Mugnai14:
What Kind of Reductionism? / 14.1:
Rota's Objectivism and Husserl's Naturalism / 14.3:
Beyond Classical Logic / 14.4:
Concluding Remarks / 14.5:
"A Minority View". Gian-Carlo Rota's Phenomenological Realism / Fabrizio Palombi15:
Considerations on the Problem of Realism / 15.1:
Phenomenological Realism / 15.2:
Fringe Phenomena and State-of-Mind / 15.3:
Psychologistic Misunderstandings / 15.4:
Descriptions, Not Prescriptions / 15.5:
Gian-Carlo Rota, the Man / Part I:
Gianco, my Brother / Ester Gasperoni Rota1:
References
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