Studies in Modern Analysis - Vol. 1

Studies in Modern Analysis - Vol. 1

Studies in Modern Analysis - Vol. 1

Studies in Modern Analysis - Vol. 1

Excerpt

The four papers that are presented in this volume do not pretend to cover all of modern analysis. They are, however, representative; each discusses topics that are fundamental, both for pure and for applied analysis, and which indeed should be part of the experience of every practicing mathematician, regardless of his field. These papers also achieve something which seems more important to me, for they succeed in the more difficult task of conveying some of the attitudes that are characteristic of modern mathematicians.

It would be difficult to devise a concise definition of analysis that is broad enough to cover all that now carries this label. It would seem no longer appropriate to confine analysis to "the theory of functions" since algebra and topology have equal rights to claim this as their domain; indeed, algebra has been called the study of homomorphisms, and topology the study of continuous mappings. The dissolution of traditional boundaries between branches of mathematics is probably the most striking aspect of the modern period of development. In the field of analysis, this has shown itself in a growing concern for matters of . . .

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