Showing papers in "American Mathematical Monthly in 1970"
TL;DR: The book as mentioned in this paper is designed for a first course in number theory with minimal prerequisites and is designed to stimulate curiosity about numbers and their properties, including almost a thousand imaginative exercises and problems.
Abstract: Designed for a first course in number theory with minimal prerequisites, the book is designed to stimulates curiosity about numbers and their properties. Includes almost a thousand imaginative exercises and problems.
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TL;DR: The floating-point number system is contrasted with the real numbers as discussed by the authors, and the author then illustrates the variety of computational pitfalls a person can fall into who merely translates information gained from pure mathematics courses into computer programs, including summing a Taylor series, solving a quadratic equation, solving linear algebraic systems, solving ordinary and partial differential equations, and finding polynomial zeros.
Abstract: The floating-point number system is contrasted with the real numbers. The author then illustrates the variety of computational pitfalls a person can fall into who merely translates information gained from pure mathematics courses into computer programs. Examples include summing a Taylor series, solving a quadratic equation, solving linear algebraic systems, solving ordinary and partial differential equations, and finding polynomial zeros. It is concluded that mathematics courses should be taught with a greater awareness of automatic computation.
115 citations
TL;DR: In this paper, positive definite matrices have been studied in the context of Positive Definite Matrices (PDM) and positive definiteness matrices (PVDM).
Abstract: (1970). Positive Definite Matrices. The American Mathematical Monthly: Vol. 77, No. 3, pp. 259-264.
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TL;DR: The tradition of friendship between French and Roumanian scientists, particularly between our mathematicians, is old as discussed by the authors and I am very happy to be a link in this chain, which I hope will continue, stronger and more cordial, in the years to come.
Abstract: Thank you for your kind words on my behalf. I must admit that it is a great pleasure for me to escape from my duties as dean and spend a week in such a warm and friendly atmosphere. The tradition of friendship between French and Roumanian scientists, particularly between our mathematicians, is old. I am very happy to be a link in this chain, which I hope will continue, stronger and more cordial, in the years to come. Well, if you don't mind, I shall not make a very long speech, and I should be happy to answer at the end of it the questions which, no doubt, will be put to me. I don't pretend to deal with all the history of the works of Bourbaki, and I shall give you all a chance to ask questions on the points I merely touch upon.
TL;DR: In this article, the authors proposed dividing a square into triangles and then dividing the triangles into squares, based on the idea of dividing a triangle into triangles, and the American Mathematical Monthly: Vol 77, No. 2, pp. 161-164.
Abstract: (1970). On Dividing A Square Into Triangles. The American Mathematical Monthly: Vol. 77, No. 2, pp. 161-164.
TL;DR: (1970).
Abstract: (1970). An Approach to Empirical Logic. The American Mathematical Monthly: Vol. 77, No. 4, pp. 363-374.
TL;DR: A note on Commuting automorphisms of rings is given in this paper, where it is shown that the automorphism of rings can be expressed as a function of the number of rings.
Abstract: (1970). A Note on Commuting Automorphisms of Rings. The American Mathematical Monthly: Vol. 77, No. 1, pp. 61-62.
TL;DR: In this article, the groups which are the Union of Three Subgroups (U3S) are described. But they do not specify the three subgroups as a union of groups.
Abstract: (1970). Groups Which are the Union of Three Subgroups. The American Mathematical Monthly: Vol. 77, No. 1, pp. 52-57.
TL;DR: The Helly Type Theorems Derived from Basic Singular Homology (HTH) as discussed by the authors are derived from the basic singular homology (BSH) of the lambda calculus.
Abstract: (1970). Helly Type Theorems Derived from Basic Singular Homology. The American Mathematical Monthly: Vol. 77, No. 4, pp. 375-380.
TL;DR: In this paper, an analytic proof of Young's Inequality is presented in the context of the American Mathematical Monthly: Vol 77, No. 6, pp. 603-609.
Abstract: (1970). An Analytic Proof of Young's Inequality. The American Mathematical Monthly: Vol. 77, No. 6, pp. 603-609.
TL;DR: The American Mathematical Monthly: Vol. 77, No. 3, No 3, pp. 264-282 as discussed by the authors, is a seminal work in logic versus pedagogy.
Abstract: (1970). Logic Versus Pedagogy. The American Mathematical Monthly: Vol. 77, No. 3, pp. 264-282.
TL;DR: The Simple Continued Fraction Expansion of e.g., this article, is an extension of the e.i.d. expansion of E.e.d., and it is a simple continued fraction expansion.
Abstract: (1970). The Simple Continued Fraction Expansion of e. The American Mathematical Monthly: Vol. 77, No. 9, pp. 968-974.