Mathematicians in Bologna 1861–1960 [electronic resource] /
Coen, Salvatore.editor.
The scientific personalities of Luigi Cremona, Eugenio Beltrami, Salvatore Pincherle, Federigo Enriques, Beppo Levi, Giuseppe Vitali, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861–1960 are examined by different authors, in some cases providing different view points. Most contributions in the volume are historical; they are reproductions of original documents or studies on an original work and its impact on later research. The achievements of other mathematicians are investigated for their present-day importance.
Description based upon print version of record.
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
ReferencesGiuseppe 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 Responsabilities4 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
ReferencesEnrico 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 Period9 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
Includes bibliographical references and index.
The scientific personalities of Luigi Cremona, Eugenio Beltrami, Salvatore Pincherle, Federigo Enriques, Beppo Levi, Giuseppe Vitali, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861–1960 are examined by different authors, in some cases providing different view points. Most contributions in the volume are historical; they are reproductions of original documents or studies on an original work and its impact on later research. The achievements of other mathematicians are investigated for their present-day importance.
Università di Bologna
Mathematics.
History.
Mathematics.
History of Mathematical Sciences.