Reviews for Complex Analysis and Geometry: International Conference in Honor of Pierre Lelong

The average rating for Complex Analysis and Geometry: International Conference in Honor of Pierre Lelong based on 2 reviews is 5 stars.

Review # 1 was written on 2016-02-18 00:00:00 Robert Wolf (Video : Wolfgang Smith on René Guénon's Principles of Infinitesimal Calculus) A rather overlooked book by Guénon unfortunately because of it's special subject - it is in fact an excellent example of linking back an specific field (here, infinitesimal calculus) with it's principles. Thus, errors automatically disappear, and a much more coherent picture emerges. It can be compared, in a way, to what Ibn Ajiba did in his commentary on the Ajurrumia by demonstrating the link between Arabic grammar subtleties and higher spiritual meanings. Precise mathematical points are discussed and put in their rightful perspective here. The "infinite"/"indefinite" confusion, the continuous/discontinuous and others. Many of Leibnitz's assertions (also Jean Bernoulli and Pierre Varignon) are here supported or refuted, many ideas here are given a clean shave and are pushed to their limit (!) in order to show their (in)consistency. "[...] These observations will allow us to understand more precisely in what sense one can say, as we did at the beginning, that the limits of the indefinite can never be reached through any analytical procedure, or, in other words, that the indefinite, while not absolutely and in every way inexhaustible, is at least analytically inexhaustible. In this regard, we must naturally consider those procedures analytical which ,in order to reconstitute a whole, consist in taking its elements distinctly and successively; such is the procedure for the formation of an arithmetical sum, and it is precisely in this regard that it differs essentially from integration. This is particularly interesting from our point of view, for one can see in it, as a very clear example, the true relationship between analysis and synthesis: contrary to current opinion, according to which analysis is as it were a preparation for synthesis, or again something leading to it, so much so that one must always begin with analysis, even when one does not intend to stop there, the truth is that one can never actually arrive at synthesis through analysis. All synthesis, in the true sense of the word, is something immediate, so to speak, something that is not preceded by any analysis and is entirely independent of it, just as integration is an operation carried out in a single stroke, by no means presupposing the consideration of elements comparable to those of an arithmetical sum; and as this arithmetical sum can yield no means of attaining and exhausting the indefinite, this latter must, in every domain, be one of those things that by their very nature resist analysis and can be known only through synthesis.[3] [3]Here, and in what follows, it should be understood that we take the terms 'analysis' and 'synthesis' in their true and original sense, and one must indeed take care to distinguish this sense from the completely different and quite improper sense in which one currently speaks of 'mathematical analysis', according to which integration itself, despite its essentially synthetic character, is regarded as playing a part in what one calls 'infinitesimal analysis'; it is for this reason, moreorever, that we prefer to avoid using this last expression, availing ourselves only of those of 'the infinitesimal calculus' and 'the infinitesimal method', which lead to no such equivocation." No need to be good at math here, as this study refers specifically to the principles. To be noted that Guénon has written a thesis in 1916 called "Examen des idées de Leibnitz sur la signification du Calcul infinitésimal" and that Principles of Infinitesimal Calculus was released in 1946. Highly recommended. And a definite re-read sometime in the future.

Review # 2 was written on 2011-02-08 00:00:00 Carol Riseing Great for the student interested in learning more about calculus. Good first math book for college.