By Nicolas Bourbaki (auth.)
This paintings gathers jointly, with no large amendment, the most important ity of the old Notes that have looked as if it would date in my components de M atMmatique. in basic terms the stream has been made self sufficient of the weather to which those Notes have been connected; they're for this reason, in precept, obtainable to each reader who possesses a legitimate classical mathematical history, of undergraduate general. after all, the separate reports which make up this quantity couldn't whatsoever fake to caricature, even in a precis demeanour, an entire and con nected heritage of the advance of arithmetic as much as our day. whole elements of classical arithmetic similar to differential Geometry, algebraic Geometry, the Calculus of adaptations, are just pointed out in passing; others, resembling the idea of analytic capabilities, that of differential equations or partial vary ential equations, are rarely touched on; all of the extra do those gaps develop into extra quite a few and extra very important because the glossy period is reached. It is going with out asserting that this isn't a case of intentional omission; it truly is easily in view that the corresponding chapters of the weather haven't but been released. ultimately the reader will locate in those Notes essentially no bibliographic or anecdotal information regarding the mathematicians in query; what has been tried especially, for every concept, is to deliver out as essentially as attainable what have been the guiding principles, and the way those principles constructed and reacted those at the others.