Mathematicians in Bologna 1861-1960

Name: Mathematicians in Bologna 1861-1960
Brand: Birkhäuser
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Salvatore COEN(Herausgeber*in)

Birkhäuser (Verlag)

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Erschienen am 11. Mai 2012

X, 554 Seiten

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Intro
Mathematicians in Bologna 1861-1960
A Short Overview on Mathematicians in Bologna in the First Century after the Establishment of Italy
References
Contents
Beltrami's Models of Non-Euclidean Geometry
1 Introduction
2 Non-Euclidean Geometry Before Beltrami
3 The Models of Beltrami
3.1 The ``Projective'' Model
3.1.1 Anisotropy
3.2 The ``Conformal'' Models
3.2.1 Imbedding the Pseudosphere in Euclidean Space
3.2.2 Anachronism (for the Complex Reader)
3.3 What was Beltrami's Interpretation of His Own Work?
4 From the Boundary to the Interior: An Example from Signal Processing
References
Giuseppe Vitali: Real and Complex Analysisand Differential Geometry
1 Formation and Career
2 First Research Works in Complex Analysis
3 Research on Real Analysis
4 The Years of Secondary School Teaching
5 Between the Two Wars: Differential Geometry
6 Conclusions
References
Pincherle's Early Contributions to Complex Analysis
1 Introduction
2 Attending Weierstrass's Lectures
3 Expansions in Series
4 Functional Operations
5 A Glance Ahead
References
Luigi Cremona's Years in Bologna: From Research to Social Commitment
1 The Beginnings
2 The Academic Environment
3 Teaching and Institutional Responsabilities
4 Cremona's Studies and Research
References
Federigo Enriques: The First Years in Bologna
1 Introduction
2 The Route to Bologna
3 First Lectures in Bologna
4 The Lectures on Higher Geometry
4.1 Segre's Influence
4.2 Philosophical Reflections on Foundations of Geometry
4.3 A Closer Look at the Contents of the Lecture Notes
4.4 From the Lectures to the Enzyklopädie
4.5 Towards the Questions About Elementary Mathematics
5 The Program of the Course of Higher Geometry
5.1 The Contents of the Course
5.2 A Few Comments
6 Conclusions
References
Enrico Bompiani: The Years in Bologna
1 Introduction
2 The End of Our Story
3 First Years in Rome
4 First Digression: Corrado Segre
5 Rome, Pavia and Milan
5.1 Assistant in Rome and Pavia
5.2 Professor in Milan
6 The Chair in Bologna
6.1 Reaching Bologna
6.2 Visits Abroad
6.3 Becoming an Ordinary Professor
7 Second Digression: Guido Fubini
7.1 Fubini's Idea: Differential Forms
7.1.1 Fubini's First Two Fundamental Forms and the First Rigidity Theorem
7.1.2 Fubini's Third Fundamental Form and the Main Rigidity Theorem
8 Some Glimpses to Bompiani's Work in the Bologna Period
9 Back to Rome
10 Final Comments
10.1 Bompiani in the Following Years
10.2 Bompiani and the Fascist Regime
10.3 Final Comments on Projective Differential Geometry
11 Conclusion
References
Dario Graffi in a Complex Historical Period
Pietro Burgatti and His Studies on Mechanics
1 Vector Calculus in Mechanics Treatises in Italy in the Early Twentieth Century
2 The Vector Calculus of Burgattiand of Burali-Forti-Marcolongo
3 Burgatti's Treatise on Mechanics
4 Some Other Relevant Contributions of Burgatti to Mechanics and Analysis
5 Some Conclusions
References
Federigo Enriques (1871-1946) and the Training of Mathematics Teachers in Italy
1 Introduction
1.1 The Scuole di Magistero
2 The Emergence of Enriques' Cultural Project and the Project's Effects on Mathematics Education
2.1 The Teaching of Projective Geometry in Bologna
2.2 Klein's Influence
2.3 Epistemological Assumptions at the Basis of Enriques'Vision of Mathematics Teaching
2.3.1 A Genetic and Dynamic Vision of the Scientific Process and the Significance of Error
2.3.2 Inductive Aspects of Scientific Research and the Dialectic Between Intuition and Rigour
2.3.3 Science as a ``Conquest and Activity of the Spirit'' and Unified Vision of Culture
2.3.4 The History of Science
3 The Battle for a Scientific Humanitas: Strategies and Teacher Training
3.1 The Textbooks for Secondary Schools
3.2 The Initiatives of the First Decades of the Twentieth Century
3.3 Enriques' Mathesis Presidency and Direction of the Periodico di Matematiche
3.4 The Roman Initiatives and Teacher Training
References
Beppo Levi and Quantum Mechanics
1 Wave Mechanics and the Schrödinger Equation
1.1 ``Derivation'' of the Schrödinger Equation
1.2 What About Classical Mechanics?
2 The Contribution of Beppo Levi
References
Leonida Tonelli: A Biography
1 Introduction
2 From Bologna to Bologna
3 The Transfer to Pisa
4 Tonelli in Pisa
5 The Relations with Severi and Picone
6 Return to Pisa
References
Bruno Pini and the Parabolic Harnack Inequality: The Dawning of Parabolic Potential Theory
1 Bruno Pini: A Short Biography
2 The Parabolic Harnack Inequality
3 The Pini's Wiener-Type Solutions for the Heat Equation
3.1 The Mean Value Property for Caloric Functions
3.2 Subcaloric and Supercaloric Functions
3.3 The Caloric Wiener-Type Solutions
3.4 Caloric Capacity, Heat Equilibrium Potential,Wiener-Type Test
4 Final Remarks: The Abstract Parabolic Potential Theory
References
Federigo Enriques as a Philosopher of Science
1 Psychology and Geometry
2 The Problems of Science
3 The History of Logic
4 Logical Controversies
5 Conclusion
References
The Enciclopedia delle Matematiche elementari and the Contributions of Bolognese Mathematicians
1 The Complicated Circumstances of the Publication
2 Contents and Contributors
3 The Contribution of Bolognese Mathematicians
References
The Role of Salvatore Pincherle in the Development of Fractional Calculus
1 Some Biographical Notes of Salvatore Pincherle
2 Pincherle and the Mellin-Barnes Integrals
3 Pincherle's Foundation of Fractional Derivatives
4 Conclusions
References
Tullio Viola and his Maestri in Bologna: Giuseppe Vitali, Leonida Tonelli and Beppo Levi
References
Developement of the Theory of Lie Groupsin Bologna (1884-1900)
1 Introduction
2 Levi-Civita, Pincherle and Amaldi
3 Some Notes on Lie's Theory of Differential Equations
4 Levi-Civita and Enriques
5 Conclusions
References
Difference Equations in Spaces of Regular Functions: a tribute to Salvatore Pincherle
1 Introduction
2 Convolution Equations in Analytically Uniform Spaces
3 Regular Functions of a Quaternionic Variable
References
The Work of Beniamino Segre on Curves and Their Moduli
1 The Context
2 Severi's Vorlesungen
3 On Riemann's Existence Theorem
4 On Moduli of Plane Curves
5 On Plane Curves with Nodes and Cusps
6 Final Considerations
References
Lamberto Cattabriga and the Theory of Linear Constant Coefficients Partial Differential Equations
1 Introduction
2 Analytically Uniform Spaces and Surjectivity of Linear Constant Coefficients Operators
3 The Case of Real Analytic Functions
4 Cattabriga and De Giorgi: Surjectivity Results
References
New Perspectives on Beltrami's Life and Work - Considerations Based on his Correspondence
1 Introduction
2 The Risorgimento Generation
3 New Perspectives
3.1 A Biographical Sketch
3.2 The New Physics
3.3 Beltrami's Reputation
4 Appendix
4.1 The correspondence Beltrami-Dedekind
4.2 Letters by Eugenio Beltrami to Pierre Duhem
4.3 A Letter by Beltrami to Wilhelm Killing
4.4 Letters by Eugenio Beltrami to Felix Klein
4.5 Letters by Beltrami to Rudolph Lipschitz
4.6 Letters by Beltrami to Gösta Mittag-Leffler
4.7 Some letters concerning Sonya Kowalewskaia's affair of 1886
4.8 Beltrami's Report on Sonya Kowalewskaia (1889)
References
On Cimmino Integrals as Residues of Zeta Functions
1 Introduction
2 Theta functions and their Mellin transform
3 Zeta functions machinery
4 Quadratic forms
5 Lattices
6 Integral representation
7 Linear systems
References
Index of Names and Locations

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