Showing papers in "American Mathematical Monthly in 1976"
761 citations
328 citations
TL;DR: In this article, the authors present a Diophantine representation of the set of prime numbers in terms of a set of numbers, and show that it is possible to compute the cardinality of the prime numbers.
Abstract: (1976). Diophantine Representation of the Set of Prime Numbers. The American Mathematical Monthly: Vol. 83, No. 6, pp. 449-464.
78 citations
TL;DR: The American Mathematical Monthly: Vol. 83, No. 6, pp. 409-448 as discussed by the authors, is a collection of historical ramblings in algebraic geometry and related algebra.
Abstract: (1976). Historical Ramblings in Algebraic Geometry and Related Algebra. The American Mathematical Monthly: Vol. 83, No. 6, pp. 409-448.
71 citations
57 citations
TL;DR: In this paper, the teaching of elementary calculus using the nonstandard analysis approach is discussed, and the authors propose a method for teaching elementary calculus with non-standard analysis in the classroom.
Abstract: (1976). The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach. The American Mathematical Monthly: Vol. 83, No. 5, pp. 370-375.
51 citations
48 citations
TL;DR: The fixed point property for non-expansive mapping as mentioned in this paper is a property of non-Expansive Mappings that can be expressed as a fixed-point property for Non-Expanding Mappings.
Abstract: (1980). The Fixed Point Property for Non-Expansive Mappings, II. The American Mathematical Monthly: Vol. 87, No. 4, pp. 292-294.
45 citations
TL;DR: In this paper, Commutativity in Finite Rings is studied in the context of finite rings, and the authors show that it is commutative in finite rings with respect to finite rings.
Abstract: (1976). Commutativity in Finite Rings. The American Mathematical Monthly: Vol. 83, No. 1, pp. 30-32.
39 citations
TL;DR: In this article, Probability and Statistics: Experimental Results of a Radically Different Teaching Method (RDT) is presented. The American Mathematical Monthly: Vol. 83, No. 9, pp. 733-739.
Abstract: (1976). Probability and Statistics: Experimental Results of a Radically Different Teaching Method. The American Mathematical Monthly: Vol. 83, No. 9, pp. 733-739.
38 citations
TL;DR: Part of a continuing experience of collaboration with two neurophysiologists from U.C.L.A., H. Bryant Jr. and J. Segundo is described, one of measuring the degree of association of points of two different sorts distributed along a straight line in an irregular manner.
Abstract: Modern applied statistics typically involves elements of computation, probability theory, statistical theory and collaboration with specialists in the subject matter of some substantive field. In this article I shall describe part of a continuing experience of collaboration with two neurophysiologists from U.C.L.A., H. L. Bryant Jr. and J. P. Segundo. In formal terms, the problem considered is one of measuring the degree of association of points of two different sorts distributed along a straight line in an irregular manner.
TL;DR: In this paper, a bound for the chromatic number of a graph is given, where the number is defined as the number of vertices in a graph that can be represented by a graph.
Abstract: (1976). A Bound for the Chromatic Number of a Graph. The American Mathematical Monthly: Vol. 83, No. 4, pp. 265-266.
TL;DR: In this article, the authors presented a paper on Rational Triangulation and Rational Triangles, which was published in the American Mathematical Monthly: Vol. 83, No. 7, pp. 517-521.
Abstract: (1976). On Rational Triangles. The American Mathematical Monthly: Vol. 83, No. 7, pp. 517-521.
TL;DR: In this paper, the relevance of mathematics involves both the various applications of mathematics and the position of mathematics in the spectrum of human values, and they take it that relevance must refer, at least implicitly, to a relation with some body of values or purposes.
Abstract: “Relevance” has been a favorite concept in the last few years. Questions about the relevance of an institution, an activity, or a subject are often asked (and less often answered). We take it that relevance must refer, at least implicitly, to a relation with some body of values or purposes. Thus a subject may be relevant in the first instance by way of its applications to another subject—which in its turn may then be tested for its further relevance, ultimately to human welfare or to an overriding conception of the good. In short, the relevance of mathematics involves both the various applications of mathematics and the position of mathematics in the spectrum of human values.
TL;DR: In this paper, an Entire Function Bounded in Every Direction (EFL) is described, which is a function bounded in every direction in the Euclidean plane, and it can be expressed as follows:
Abstract: (1976). An Entire Function Bounded in Every Direction. The American Mathematical Monthly: Vol. 83, No. 3, pp. 192-193.
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TL;DR: In this paper, a characterisation of the convergence of successive approximate approximations is presented, based on the Convergence of Successive Approximations (COSA).
Abstract: (1976). A Characterization of the Convergence of Successive Approximations. The American Mathematical Monthly: Vol. 83, No. 4, pp. 273-273.
TL;DR: The growth function of the organism is a function f such that f(t) is the number of cells in the organism at time t, and it is assumed that its growth rate, and that of its parts, is governed by internal, inherited factors.
Abstract: When an organism is growing under optimal conditions it may be assumed that its growth rate, and that of its parts, is governed by internal, inherited factors. The growth function of the organism is a function f such that f(t) is the number of cells in the organism at time t. In the last few years such growth functions have been actively studied by some researchers interested in mathematical models for biological development. We report on some of the results obtained.
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TL;DR: In this paper, a group ring is defined as a group of rings, and the group ring can be represented as a circle with a group circle, and a group is a set of rings.
Abstract: (1976). What is a Group Ring? The American Mathematical Monthly: Vol. 83, No. 3, pp. 173-185.
TL;DR: In this article, the authors consider the question "Are all complete binary trees Graceful?" and show that they are all complete Binary Trees Graceful, i.e., they are complete trees.
Abstract: (1976). Are All Complete Binary Trees Graceful? The American Mathematical Monthly: Vol. 83, No. 1, pp. 35-37.
TL;DR: The Mathematics Clinic at the University of California, Berkeley, has been used to train students for industrial and governmental problems as discussed by the authors, with an emphasis on training for non-academic employment.
Abstract: Introduction. Recently much has been said and written about the mismatch between traditional academic training in mathematics (both at the undergraduate and graduate levels) and the current and predicted job market for mathematicians. Evidence of this mismatch is widespread. In [1] a steady decline in graduate mathematics enrollments, accompanied by a general shift of student interest toward applied mathematics, is reported. Several new MS and PhD programs are being initiated ([2], [3]) with emphasis on training for non-academic employment. Thought is being given to the special preparation needed to train mathematicians for industrial careers [4] and to the role of the industrial mathematician [5], and new courses in which industrial mathematics is simulated are being designed [6]. In this article we describe experience with a new course developed at the Claremont Colleges, in whi'ch industrial and governmental problems are addressed, studied, and solved by teams of students working under faculty supervision. This approach was pioneered within the Engineering Department at Harvey Mudd College, beginning with a pilot activity in 1964 and led to the formation of the Engineering Clinic at that College. During the current academic year, the Engineering Clinic will operate a wide variety of Clinic projects involving about 70 students each semester. The Mathematics Clinic is patterned after this highly successful model. In response to the changing national funding patterns and job markets, the Claremont Graduate School developed, in 1973, four new Master's programs aimed at training students for immediate employment in industry, government, and two-year college teaching. At the same time, joint BS and MA programs with the same objectives were developed in concert with several of the undergraduate Claremont Colleges. Three of these four concentrations involve various aspects of applied mathematics, and the notion of a Mathematics Clinic was deemed of central importance in these concentrations. A first project was operated at Harvey Mudd College during 1973-74. In 1974-75, the Mathematics Clinic was developed jointly by Claremont Graduate School and Harvey Mudd College, and during the current academic year, Clinic projects are being operated which involve an average of 20 students each semester. Reaction on the part of students, faculty, and Clinic clients is overwhelmingly positive so far. Student participation in real-world problems provides stimulation simply not achievable in a traditional classroom environment. Clients, too, feel excitement through participation in an educational venture which they judge to be more meaningful than conventional ones. In addition, relationships are formed which may very well lead to jobs for the students and to a reduction in expensive on-the-job training for the employer. Furthermore, Clinic projects produce income which not only covers average project expenses but also provides stipends for graduate students and helps to offset some overhead expenses. Income this year from the Engineering Clinic will total approximately $200,000, while income from the Mathematics Clinic will total about $50,000.
TL;DR: In this article, the American Mathematical Monthly: Vol. 83, No. 10, pp. 798-801, discusses comments and complements of a paper by Gurewitz et al.
Abstract: (1976). Comments and Complements. The American Mathematical Monthly: Vol. 83, No. 10, pp. 798-801.