Elements of the History of Mathematics

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Springer Science & Business Media, 1998 M11 18 - 301 páginas
This work gathers together, without substantial modification, the major ity of the historical Notes which have appeared to date in my Elements de M atMmatique. Only the flow has been made independent of the Elements to which these Notes were attached; they are therefore, in principle, accessible to every reader who possesses a sound classical mathematical background, of undergraduate standard. Of course, the separate studies which make up this volume could not in any way pretend to sketch, even in a summary manner, a complete and con nected history of the development of Mathematics up to our day. Entire parts of classical mathematics such as differential Geometry, algebraic Geometry, the Calculus of variations, are only mentioned in passing; others, such as the theory of analytic functions, that of differential equations or partial differ ential equations, are hardly touched on; all the more do these gaps become more numerous and more important as the modern era is reached. It goes without saying that this is not a case of intentional omission; it is simply due to the fact that the corresponding chapters of the Elements have not yet been published. Finally the reader will find in these Notes practically no bibliographic or anecdotal information about the mathematicians in question; what has been attempted above all, for each theory, is to bring out as clearly as possible what were the guiding ideas, and how these ideas developed and reacted the ones on the others.
 

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Contenido

I
1
II
45
III
47
IV
57
V
69
VI
85
VII
93
VIII
117
XV
165
XVI
167
XVII
199
XVIII
203
XIX
205
XX
207
XXI
219
XXII
231

IX
125
X
139
XI
145
XII
147
XIII
157
XIV
161
XXIII
237
XXIV
247
XXV
269
XXVI
275
XXVII
297
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Acerca del autor (1998)

Nicolas Bourbaki is the pseudonym for a group of mathematicians that included Henri Cartan, Claude Chevalley, Jean Dieudonne, and Andres Weil. Mostly French, they emphasized an axiomatic and abstract treatment on all aspects of modern mathematics in Elements de mathematique. The first volume of Elements appeared in 1939. Subsequently, a wide variety of topics have been covered, including works on set theory, algebra, general topology, functions of a real variable, topological vector spaces, and integration. One of the goals of the Bourbaki series is to make the logical structure of mathematical concepts as transparent and intelligible as possible. The books listed below are typical of volumes written in the Bourbaki spirit and now available in English.

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