Calculus: A Modern Approach. TRUE FIRST EDITION, IN MIMEOGRAPHED FORM.

True First Edition, dated 1952 on title page. 255 pp, mimeographed. Loose leaf binder. Very Good. 'One great disappointment of Menger's intellectual life was the failure of his long and strenuous effort to reform both the teaching and the application of calculus and other undergraduate mathematics. Like the work on the algebra of functions and in fact closely associated with it, the reform effort resulted from Menger's experience in teaching calculus classes in the United States. Many teachers, upon finding that their students meet difficulties, blame the students themselves for all such difficulties, and blithely go on in their accustomed way. Menger, feeling that such a response was inadequate and unjust, analysed all aspects of the situation, and concluded that the traditional way of presenting the calculus was deeply flawed. He resolved to remedy this situation. After some years of preparation and testing, he began to teach what he called his 'modern approach' to calculus in 1952. Concurrently, he tried to influence the entire mathematical community by a series of articles and lectures. In them, and in the book he produced, originally in mimeographed form [offered here], for his class, he analyzed the manifold notions connected with the word 'variable' and carefully distinguished arguments and values of functions from the functions themselves. The latter being the actual objects treated in calculus, he introduced explicit symbols for certain important functions (most notably, the identity function) which because of their ubiquity had been taken for granted and so had remained undesignated. A feature of the book which is often overlooked and which is perhaps its most striking pedagogical innovation is the development of a complete 'miniature calculus' within which all the basic features of the calculus, including the so-called 'Fundamental Theorem', can be illustrated without bringing in limits. The few reviews the books received were generally favorable; some, such as the ones by Cain T. Adamson in the Mathematical Gazette and H. E. Bray in the American Mathematical Monthly (61, 1954, pp. 483-492) exceptionally so. Bray ended his review (of the second mimeographed edition) by saying: 'Unfortunately, the typography of the book is unattractive, but this fault will undoubtedly be remedied by an enterprising publisher who will print the book in the attractive format in which so many lesser books are now being offered.' In 1955 the book did get published as Calculus: A Modern Approach by Ginn and Company . . . it has now been long out of print and difficult to obtain' (Introduction to Karl Menger, Reminiscences of the Vienna Circle and the Mathematical Colloquium, Louise Golland, Abe Sklar, Brian McGuinness, eds., 1994, pp. xviii-xix). 'Written in characteristically vigorous style, it was a radical revision of textbooks of the period, scrapping some traditional notation. It received a lengthy, thoughtful, and cautiously favorable review in the Monthly by H. E. Bray but was never accorded serious attention. He sent a copy to Einstein, who replied that he liked it and recognized the need for some clarity in notation, but advised against attempting too much 'housecleaning'. That his book was ignored saddened Menger's later years. When Menger addressed the foundations of dimension theory, topology, projective n-space, or differential geometry, attention was paid by the best mathematical minds of his generation: Hahn, Brouwer, von Neumann, Gödel. The failure of the calculus endeavor strained his relations with the mathematical community' (Seymour Kass, 'Karl Menger', Notices of the AMS, Vol. 43, No. 5, 560-1). …