Showing papers in "American Mathematical Monthly in 1958"
TL;DR: An effective rule (or algorithm) for distinguishing sentences from nonsentences is obtained, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or at least for fragments of such languages.
Abstract: (1958). The Mathematics of Sentence Structure. The American Mathematical Monthly: Vol. 65, No. 3, pp. 154-170.
1,432 citations
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TL;DR: A(D) as discussed by the authors is a function space with norm ∥ ∥ [Definition I, 3, 1] which defines the topology of major interest in the space; a neighborhood basis of a point x is the family of sets {y: ∥ x - y ∥ ≦ e}.
Abstract: Each of the function spaces mentioned in the introduction of th preceding chapter has (with one exception, A(D)) a norm ∥ ∥ [Definition I, 3, 1] which defines the topology of major interest in the space; a neighborhood basis of a point x is the family of sets {y: ∥ x - y ∥ ≦ e} where e > 0.
1,062 citations
TL;DR: In this paper, Pseudo-inverses in Associative Rings and Semigroups are discussed in the context of semigroups, and pseudo-Inverses are shown to be pseudo-dual in a semigroup.
Abstract: (1958). Pseudo-Inverses in Associative Rings and Semigroups. The American Mathematical Monthly: Vol. 65, No. 7, pp. 506-514.
615 citations
582 citations
505 citations
281 citations
169 citations
TL;DR: Inverses of Vandermonde matrices as discussed by the authors have been studied extensively in the literature, see, e.g., the American Mathematical Monthly: Vol. 65, No. 2, pp. 95-100.
Abstract: (1958). Inverses of Vandermonde Matrices. The American Mathematical Monthly: Vol. 65, No. 2, pp. 95-100.
155 citations
97 citations
58 citations
TL;DR: The Teaching of Concrete Mathematics as mentioned in this paper is a popular text for concrete mathematics courses, with a focus on the teaching of concrete mathematical concepts and its application in computer science. The American Mathematical Monthly: Vol. 65, No. 1, pp. 1-9.
Abstract: (1958). The Teaching of Concrete Mathematics. The American Mathematical Monthly: Vol. 65, No. 1, pp. 1-9.
TL;DR: In this article, the Coefficients of Reciprocal Power Series (RPS) were used to define the reciprocal power series, and the coefficients of the RPS were analyzed.
Abstract: (1958). On the Coefficients of Reciprocal Power Series. The American Mathematical Monthly: Vol. 65, No. 2, pp. 90-94.