Edmund Landau, "Foundations of Analysis: The Arithmetic of Whole, Rational, Irrational, and Complex Numbers. A Supplement to Textbooks on the Differential and Integral Calculus"
1966 | pages: 149 | ASIN: B0007DSPK2 | PDF | 5,2 mb
This little book is a concession to those of my colleagues (unfortunately in the majority) who do not share my point of view on the following question.
While a rigorous and complete exposition of elementary mathematics can not, of course, be expected in the high schools, the mathematical courses in colleges and universities should acquaint the student not only with the subject matter and results of mathematics, but also with its methods of proof. Even one who studies mathematics mainly for its applications to physics and to other sciences, and who must therefore often discover auxiliary mathematical theorems for himself, can not continue to take steps securely along the path he has chosen unless he has learned how to walkâthat is, unless he is able to distinguish between true and false, between supposition and proof (or, as some say so nicely, between non-rigorous and rigorous proof).
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