Showing papers in "American Mathematical Monthly in 1988"
2,331 citations
TL;DR: Approche diagrammatique des invariants dans la theoryie des nœuds as mentioned in this paper, relations avec la theorie des graphes, la physique et d'autres sujets.
Abstract: Approche diagrammatique des invariants dans la theorie des nœuds. Relations avec la theorie des graphes, la physique et d'autres sujets. Construction du polynome de Jones et de son algebre associee. Generalisations du polynome de Jones
251 citations
TL;DR: In this paper, when does a polynomial over a finite field permute the elements of the field? The American Mathematical Monthly: Vol 95, No 3, pp 243-246
Abstract: (1988) When Does a Polynomial over a Finite Field Permute the Elements of the Field? The American Mathematical Monthly: Vol 95, No 3, pp 243-246
149 citations
TL;DR: In this paper, Gert Almkvist and Bruce Berndt discuss the arithmetic-geometric mean, the ellipses, pi, and the Ladies Diary of Gert and Bruce.
Abstract: Paper 8: Gert Almkvist and Bruce Berndt, “Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, pi, and the Ladies Diary,” American Mathematical Monthly, vol. 95 (1988), pg. 585–608. Copyright 1988 Mathematical Association of America. All Rights Reserved.
127 citations
101 citations
TL;DR: The SEEK program as discussed by the authors is a special program for students from poor areas of the city, and it has coordinated its mathematics efforts since 1969, with the help of the CCNY Seminar on General Topology and Topological Algebra.
Abstract: RALPH KOPPERMAN: I received my Ph.D. from M.I.T. in 1965, and came to The City College in 1967. SEEK is a special program for students from poor areas of the city, and I have coordinated its mathematics efforts since 1969. My research interest has always been in limits, which I first tried to study through infinitary languages (logic). I was able to publish in the field, but was not happy with the results of that research, and went into point-set topology in 1980. I was a founding member of the CCNY Seminar on General Topology and Topological Algebra in 1981, and have been involved with it ever since.
89 citations
TL;DR: In this article, the authors propose a method for constructing isospectral manifold. But this method requires the construction of a set of isosveto-manifolds.
Abstract: (1988). Constructing Isospectral Manifolds. The American Mathematical Monthly: Vol. 95, No. 9, pp. 823-839.
89 citations
TL;DR: In this article, the authors show 35 examples of patterns that seem to appear when we look at several small values of n, in various problems whose answers depend on n. The question is, in each case: do you think that the pattern persists for all n, or do you believe that it is a figment of the smallness of the values in the examples? Caution: examples of both kinds appear; they are not all figments!
Abstract: This article is in two parts, the first of which is a do-it-yourself operation, in which I'll show you 35 examples of patterns that seem to appear when we look at several small values of n, in various problems whose answers depend on n. The question will be, in each case: do you think that the pattern persists for all n, or do you believe that it is a figment of the smallness of the values of n that are worked out in the examples? Caution: examples of both kinds appear; they are not all figments! In the second part I'll give you the answers, insofar as I know them, together with references. Try keeping a scorecard: for each example, enter your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all. This first part contains no information; rather it contains a good deal of disinformation. The first part contains one theorem:
72 citations
TL;DR: In this paper, five approaches to the theory of Bernoulli polynomials have been proposed, and these can be associated with three different types of polynomial classes.
Abstract: Beginning with Jacob Bernoulli's discovery before 1705 of the polynomials that bear his name, there have been five approaches to the theory of Bernoulli polynomials. These can be associated with th...
61 citations
TL;DR: In this article, a conjecture de J.H. Wilkinson relative un probleme d'optimisation sous contrainte dans l'elimination de Gauss is discussed.
Abstract: Etude d'une conjecture de J.H. Wilkinson relative un probleme d'optimisation sous contrainte dans l'elimination de Gauss
57 citations
TL;DR: The Jordan-Brouwer separation theorem for smooth hypersurfaces has been studied in this paper, where it is shown that smooth hypergraphs can be represented by a smooth polygon.
Abstract: (1988). The Jordan-Brouwer Separation Theorem for Smooth Hypersurfaces. The American Mathematical Monthly: Vol. 95, No. 1, pp. 39-42.
TL;DR: In this paper, area-minimizing surfaces, faces of Grassmannians, and Calibrations are discussed. But they focus on the face of the Grassmannian.
Abstract: (1988). Area-minimizing Surfaces, Faces of Grassmannians, and Calibrations. The American Mathematical Monthly: Vol. 95, No. 9, pp. 813-822.
TL;DR: In this article, a glossary of notation is presented for tensors in linear spaces, and a calculus of differential forms on fiber bundles is presented. But this glossary is restricted to fiber bundles.
Abstract: Preface Glossary of notation Introduction 1. Tensors in linear spaces 2. Manifolds 3. Transformations 4. The calculus of differential forms 5. Applications of the exterior calculus 6. Classical electrodynamics 7. Dynamics of particles and fields 8. Calculus on fiber bundles 9. Gravitation Bibliography Index.
TL;DR: In this paper, Integrals, an Introduction to Analytic Number Theory, is presented as an introduction to analytic number theory and analytically number theory, with a focus on Integrals.
Abstract: (1988). Integrals, an Introduction to Analytic Number Theory. The American Mathematical Monthly: Vol. 95, No. 4, pp. 308-315.
TL;DR: A fountain is an arrangement of n coins in rows such that there are exactly k coins in the bottom row, and such that each coin in a higher row touches exactly two coins in a lower row as discussed by the authors.
Abstract: In Richard Guy's article in last month's Monthly [6] there appeared a number of elegant questions, one of which we will answer here. An (n, k) fountain is an arrangement of n coins in rows such that there are exactly k coins in the bottom row, and such that each coin in a higher row touches exactly two coins in the next lower row. In FIG. 1 below we show a (28,12) fountain. Let f(n, k) be the number of (n, k) fountains, and let f(n) = Ekf k) be the number of fountains of n coins.
TL;DR: In this article, the equilateral triangle, the right isoceles triangle, and the 30-60-90 triangle are special in that they can be folded into replicas of themselves.
Abstract: The equilateral triangle, the right isoceles triangle, and the 30-60-90 triangle are special in that they can be folded into replicas of themselves. We describe polynomial mappings which are equiva...
TL;DR: The Sequence of Pedal Triangles as discussed by the authors is a sequence of triangulation of the sequence of triangle. The American Mathematical Monthly: Vol. 95, No. 7, pp. 609-620.
Abstract: (1988). The Sequence of Pedal Triangles. The American Mathematical Monthly: Vol. 95, No. 7, pp. 609-620.
TL;DR: Gleason as mentioned in this paper is a member of the National Academy of Sciences and a former president of the American Mathematical Society (AMS) who has worked in several areas including topological groups, Banach algebras, finite geometries, and coding theory.
Abstract: Dr. Gleason graduated from Yale in 1942 and then served four years . . j in the Navy. After the war he went to Harvard as a Junior Fellow in the ;;, Society of Fellows. Except for an interlude in the Navy from 1950-52, he has been at Harvard ever since. He now holds the Hofis Professorship of Mathematicks and Natural Philosophy, a chair that was endowed in 1727. Although he has no doctor's degree, he says that George Mackey was the equivalent of his dissertation supervisor. He has worked in several areas including topological groups, Banach algebras, finite geometries, and coding theory. He received the Newcomb Cleveland prize of the AAAS in 1952. He is a member of the National Academy of Sciences and is a former president of the American Mathematical Society.
TL;DR: In this paper, a proof of the Lucas-Lehmer Test is presented, based on a theorem prover, and a proof for the Lucas Lehmer test is given.
Abstract: (1988). A Proof of the Lucas-Lehmer Test. The American Mathematical Monthly: Vol. 95, No. 9, pp. 855-856.
TL;DR: In this paper, the authors show that every Latin Square of Order n a Partial Latin Transversal of Size n - 1 is a partial Latin transversal with size n − 1.
Abstract: (1988). Has Every Latin Square of Order n a Partial Latin Transversal of Size n - 1? The American Mathematical Monthly: Vol. 95, No. 5, pp. 428-430.
[...]
TL;DR: In this paper, the authors revisited UC Spaces Revisited and proposed a new approach to the UC Spaces revisited problem, which they called UC Space Revisited (UCSPV).
Abstract: (1988). UC Spaces Revisited. The American Mathematical Monthly: Vol. 95, No. 8, pp. 737-739.
TL;DR: Convergence-Preserving Functions The American Mathematical Monthly (AMM): Vol 95, No 6, pp 542-544 as mentioned in this paper, 1988] and Convergence-preserving Functions
Abstract: (1988) Convergence-Preserving Functions The American Mathematical Monthly: Vol 95, No 6, pp 542-544
TL;DR: Toward a Lean and Lively Calculus is a report of a conference held at Tulane University, January 2-6, 1986, organized by Ron Douglas, and supported by the Sloan Foundation, and lays down a program for the development of a new calculus text along the lines of the Chem Study materials in Chemistry.
Abstract: Deep concerns in mathematical education have converged, like currents in the ocean, to generate both a certain amount of froth and a strong force for reform of calculus instruction. First there are the dual concerns of adapting to the needs of the burgeoning number of computer science majors and of making use of new technologies in microcomputers and hand-held calculators. Second is alarm at the decline of the presentation of calculus into an arcane study of detailed techniques of differentiation, integration, and tests for convergence of series, with artificial set-piece problems that may be checked by making sure the answer is simple. Students see little of the towering intellectual achievement of the subject, and they cannot see how to formulate physical problems of change and constancy as mathematical ones involving differentiation and integration. Moreover, even many of the best students remain unable to unite English expressions and mathematical symbolism in a single coherent sentence, much less in an acceptable student paper on a mathematical subject. Toward a Lean and Lively Calculus is a report of a conference held at Tulane University, January 2-6, 1986, organized by Ron Douglas, and supported by the Sloan Foundation. It grew out of the continuous-versus-discrete debate initiated by Tony Ralston and continued at a Sloan Conference at Williams College in 1982 [4], in Forums in this Journal [3], [5], [2], at a panel discussion organized by Ron Douglas and Steve Maurer at the 1985 AMS/MAA meetings in Anaheim, and other places. The Introduction of the report summarizes the conference and lays down a program for the development of a new calculus text along the lines of the Chem Study materials in Chemistry. The time frame proposed for this is already obsolete, and the proposed funding pattern has been altered by the probable involvement of the National Science Foundation in FY88 through the Mathematical Science Directorate. This funding was discussed at a Sloan Conference in Washington in October of 1987. There were three workshops at the Tulane Conference: Content, Methods, and Implementation. They necessarily suffered from simultaneity; the Methods and Implementation participants did not know what would be in the Content report. In fact, the Content Workshop Report gives syllabi for a new Calculus I, a new "standard" Calculus II, and alternate second semester courses involving multivariable calculus (Calculus IIM) and computer symbolic manipulation (Calculus IIC). Most of the workshop time was devoted to Calculus I, and this syllabus is presented in more detail. We comment on this one and refer the reader to the book for the others.
TL;DR: In this paper, two discrete analogs of the Jordan curve theorem are presented, which are easy to prove by an induction argument coupled with some geometric intuition, and they are shown to play the role of a simple closed curve.
Abstract: The Jordan curve theorem is one of those frustrating results in topology: it is intuitively clear but quite hard to prove. In this note we will look at two discrete analogs of the Jordan curve theorem that are easy to prove by an induction argument coupled with some geometric intuition. One of the surprises is that when we discretize the plane we get two Jordan curve theorems rather than one, a consequence of the interplay between two natural products in the category of graphs. Topology in this context has been studied by Farmer in [2]. To state the discrete versions, we need to know what the discrete analog of the plane is and what plays the role of a simple closed curve. Since the plane is the topological product of two lines, we take as our discrete analog the product of two discrete lines. We will use undirected graphs for our analogs of spaces, with vertices for points and edges connecting points which are to be thought of as touching.
TL;DR: A Principal Ideal Domain that is not a Euclidean Domain this article is a principal ideal domain that does not have an ideal domain and is not an ideal space-time domain.
Abstract: (1988). A Principal Ideal Domain That Is Not a Euclidean Domain. The American Mathematical Monthly: Vol. 95, No. 9, pp. 868-871.
TL;DR: In this article, the Wronskian work is discussed and why does the Wronkian Work? The American Mathematical Monthly: Vol. 95, No. 1, pp. 46-49.
Abstract: (1988). Why Does the Wronskian Work? The American Mathematical Monthly: Vol. 95, No. 1, pp. 46-49.