Institutions and Applications (eBook)

Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989

John McCleary, David E. Rowe (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
325 Seiten
Elsevier Science (Verlag)
978-0-08-092546-2 (ISBN)

Infos

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

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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 Universitat; 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

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Technik
• ISBN-10: 0-08-092546-4 / 0080925464
• ISBN-13: 978-0-08-092546-2 / 9780080925462