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During the twentieth century mathematics has expanded at an unprecedented rate. This expansion has been accompanied by the increased application of mathematics to science. At a time when pure mathematics has been placing more and more emphasis on abstraction and the analysis of broad concepts there has been a corresponding proliferation of practical applications. This seems to have resulted from the fact that the sciences, too, have become more concerned with the discernment of general patterns in the study of nature. This search for simplifying ideas has increased the demand for ever more abstract tools of analysis.

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