Rowe / McCleary Institutions and Applications

Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989
1. Auflage 2014
ISBN: 978-0-08-092546-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 325 Seiten, Web PDF

The History of Modern Mathematics, Volume II: Institutions and Applications focuses on the history and progress of methodologies, techniques, principles, and approaches involved in modern mathematics. The selection first elaborates on crystallographic symmetry concepts and group theory, case of potential theory and electrodynamics, and geometrization of analytical mechanics. Discussions focus on differential geometry and least action, intrinsic differential geometry, physically-motivated research in potential theory, introduction of potentials in electrodynamics, and group theory and crystallography in the mid-19th century. The text then elaborates on Schouten, Levi-Civita, and emergence of tensor calculus, modes and manners of applied mathematics, and pure and applied mathematics in divergent institutional settings in Germany. Topics include function of mathematics within technical colleges, evolvement of the notion of applied mathematics, rise of technical colleges, and an engineering approach to mechanics. The publication examines the transformation of numerical analysis by the computer; mathematics at the Berlin Technische Hochschule/Technische Universität; and contribution of mathematical societies to promoting applications of mathematics in Germany. The selection is a valuable reference for mathematicians and researchers interested in the history of modern mathematics. - Mathematical institutions in France and Germany and their role in promoting applications - Relationship between mathematics and physics - Foundations of mathematics - Complex variable theory, geometry and topology - Geometry in the spirit of Klein's Erlangen program - Algebra and number theory - Formative influences on mathematics in the United States

Autoren/Hrsg.

Rowe, David E.

Mccleary, John

Inhaltsverzeichnis

1;Front Cover;1
2;Institutions and Applications;4
3;Copyright Page;5
4;Table of Contents;6
5;Table of Contents for Volume I;8
6;Contributors List;10
7;Preface;12
8;Part I: The Crossroads of Mathematics and Physics;18
8.1;Chapter 1. Crystallographic Symmetry Concepts and Group Theory (1850-1880);20
8.1.1;INTRODUCTION;20
8.1.2;1. GROUP THEORY AND CRYSTALLOGRAPHYIN THE MID-19TH CENTURY;21
8.1.3;2. BRAVAIS' THEORY OF CRYSTAL STRUCTURE;24
8.1.4;3. JORDAN'S FIRST EXPLICIT USEOF THE GROUP CONCEPT IN GEOMETRY;29
8.1.5;4 . THE INFLUENCE OF JORDAN'S MÉMOIRE ( 1 8 6 9 )ON THE DEVELOPMENT OF LIE'S AND KLEIN'S IDEAS REGARDING TRANSFORMATION GROUPS;32
8.1.6;NOTES;37
8.1.7;LITERATURE AND SOURCES;38
8.2;Chapter 2. Physics as a Constraint on Mathematical Research:The Case of Potential Theory and Electrodynamics;46
8.2.1;1. INTRODUCTION;46
8.2.2;2. GAUSS AND THE FOUNDING OF POTENTIAL THEORY AS A RESEARCH SPECIALTY;48
8.2.3;3. The introduction of potentials in electrodynamics:Franz Neumann;52
8.2.4;4. DlRICHLET AND THE EXTENSION OF THE GAUSSIAN PROGRAM;61
8.2.5;5. PHYSICALLY-MOTIVATED RESEARCH IN POTENTIAL THEORY:KIRCHOFF, HELMHOLTZ AND CLAUSIUS;63
8.2.6;6. PHYSICALLY-MOTIVATED RESEARCH IN POTENTIAL THEORY:THE CASE OF PROPAGATED POTENTIALS;71
8.2.7;7. A RETURN TO MATHEMATICAL FOUNDATIONS:Holder and Neumann;81
8.2.8;8. CONCLUDING REMARKS;83
8.2.9;NOTES;84
8.2.10;BIBLIOGRAPHY;89
8.3;Chapter 3. The Geometrization of Analytical Mechanics: A Pioneering Contribution by josseph liouville;94
8.3.1;INTRODUCTION;94
8.3.2;HAMILTON-JACOBI MECHANICS;95
8.3.3;LIOUVILLE'S CONTRIBUTIONS;97
8.3.4;INTRINSIC DIFFERENTIAL GEOMETRY;100
8.3.5;DIFFERENTIAL GEOMETRY AND LEAST ACTION;107
8.3.6;LIOUVILLE'S SUCCESSORS;110
8.3.7;CONCLUDING REMARKS;111
8.3.8;NOTES;111
8.3.9;REFERENCES;111
8.4;Chapter 4. Schouten, Levi-Civita, and the Emergence of Tensor Calculus;116
8.4.1;NOTES;122
9;Part II: Applied Mathematics in the Early 19th-century France;124
9.1;Chapter 5. Modes and Manners of Applied Mathematics:The Case of Mechanics;126
9.1.1;1. THE MODES OF APPLICATION;126
9.1.2;2. THE FRENCH COMMUNITIES, 1800-1840;127
9.1.3;3. AN ENGINEERING APPROACH TO MECHANICS;131
9.1.4;4. FOUR CASE-STUDIES FROM MECHANICS;133
9.1.5;5. CONCLUDING REMARKS: COMPLEMENT OR COMPETITION;138
9.1.6;BIBLIOGRAPHY;139
9.2;Chapter 6. La Propagation des Ondes en Eau Profonde Et ses Developpements Mathématiques: (Poisson, Cauchy 1815-1825);146
9.2.1;Abstract;146
9.2.2;I. INTRODUCTION;148
9.2.3;II. LE MEMOIRE DE CAUCHY DE 1815;151
9.2.4;III. LES RÉSULTATS DE POISSON(1815);157
9.2.5;IV. CAUCHY, L'ELUCIDATION DES DIVERGENCES;163
9.2.6;BIBLIOGRAPHIE;178
9.2.7;NOTES;180
10;Part III: Pure versus Applied Mathematics in Late 19th-century Germany;186
10.1;Chapter 7. Pure and Applied Mathematics in Divergent Institutional Settings in Germany: The Role and Impact of Felix Klein;188
10.1.1;II. PROFESSIONAL CAREERS AND DISCIPLINARY ORIENTATIONS;190
10.1.2;III. MATHEMATICS: AUTONOMY VIA TEACHER EDUCATION;192
10.1.3;IV. THE RISE OF THE TECHNICAL COLLEGES;196
10.1.4;V. THE FUNCTION OF MATHEMATICS WITHIN THE TECHNICAL COLLEGES;197
10.1.5;VI. THE DEVELOPMENT OF KLEIN'S POLICY REGARDING APPLICATIONS AND HIS Gutachten OF MAY 1900;198
10.1.6;VII. THE EVOLVEMENT OF THE NOTION OF APPLIED MATHEMATICS;209
10.1.7;NOTES;214
10.1.8;BIBLIOGRAPHY;220
10.1.9;APPENDIX I;225
10.1.10;APPENDIX II;228
10.2;Chapter 8. On the Contribution of Mathematical Societies to Promoting Applications of Mathematics in Germany;240
10.2.1;NOTES;258
10.2.2;APPENDIX;261
10.3;Chapter 9. Mathematics at the Berlin Technische Hochschule/Technische Universität: Social, Institutional, and Scientific Aspects;268
10.3.1;SUMMARY;268
10.3.2;1. ACADEMIC RIGHTS AND DUTIES;268
10.3.3;2. THE ERA OF THE INDEPENDENT ACADEMIES(1770-1879 AND 1770-1916);272
10.3.4;3. MATHEMATICS AT THE TECHNISCHE HOCHSCHULE 1879-1945;275
10.3.5;4. MATHEMATICS AT THE TECHNISCHE UNIVERSITÄT AFTER THE SECOND WORLD WAR;281
10.3.6;5. THE MATHEMATICIANS OF THE BERLIN TECHNISCHE HOCHSCHULE/BERLIN TECHNISCHE UNIVERSITÄT AND THE MATHEMATICAL SOCIETY OF BERLIN;283
10.3.7;REFERENCES;294
11;Part IV: Applied Mathematics in the United States During World War II;302
11.1;Chapter 10. Mathematicians at War: Warren Weaver and the Applied Mathematics Panel, 1942-1945;304
11.1.1;NOTES;317
11.2;Chapter 11. The Transformation of Numerical Analysis by the Computer:an Example from the Work of John von Neumann;324
11.2.1;PARTIAL DIFFERENTIAL EQUATIONSAND THE QUESTION OF NUMERICAL STABILITY;325
11.2.2;RANDOM NUMBERS AND MONTE CARLO METHODS;329
11.2.3;GENERALIZATIONS;332
11.2.4;NOTES;333
11.2.5;BIBLIOGRAPHY;338
11.3;Notes on the Contributors;340