Nicolas Bourbaki: Encyclopedia II - Nicolas Bourbaki - Books by Bourbaki

Nicolas Bourbaki - Books by Bourbaki

Aiming at a completely self-contained treatment of most of modern mathematics based on set theory, the group produced the following volumes (with the original French titles in brackets):

and later

The book Variétés différentielles et analytiques was a fascicule de résultats, that is, a summary of results, on the theory of manifolds, rather than a worked-out exposition. A final volume IX on spectral theory (Théories spectrales) from 1983 marked the presumed end of the publishing project; but a further commutative algebra fascicle was produced at the end of the twentieth century.

While several of Bourbaki's books have become standard references in their fields, the austere presentation makes them unsuitable as textbooks. The books' influence may have been at its strongest when few other graduate-level texts in current pure mathematics were available, between 1950 and 1960.

Notations introduced by Bourbaki include: the symbol for the empty set, and the terms injective, surjective, and bijective.

It is frequently claimed that the use of the blackboard bold letters for the various sets of numbers was first introduced by the group. There are several reasons to doubt this claim: (1) the symbols do not appear in Bourbaki publications (rather, ordinary bold is used) at or near the era when they began to be used elsewhere, for instance, in typewritten lecture notes from Princeton University (achieved in some cases by overstriking R or C with I), and (an apparent first) typeset in Gunning and Rossi's textbook on several complex variables; (2) Jean-Pierre Serre, a member of the Bourbaki group, has publicly inveighed against the use of "blackboard bold" anywhere other than on a blackboard.

Adapted from the Wikipedia article "Books by Bourbaki", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki