Showing papers in "American Mathematical Monthly in 1985"
AT&T1
TL;DR: The 3x + 1 problem and its generalizations were studied in this paper, where the authors propose a generalization of the 3x+1 problem to the 3 × 3 problem.
Abstract: (1985). The 3x + 1 Problem and its Generalizations. The American Mathematical Monthly: Vol. 92, No. 1, pp. 3-23.
489 citations
TL;DR: Balinski and Young as discussed by the authors developed a theory of fair representation that establishes various principles for translating state populations or vote totals of parties into a fair allocation of congressional seats using U.S. history as a guide.
Abstract: The issue of fair representation will take center stage as U.S. congressional districts are reapportioned based on the 2000 Census. Using U.S. history as a guide, the authors develop a theory of fair representation that establishes various principles for translating state populations --or vote totals of parties --into a fair allocation of congressional seats. They conclude that the current apportionment formula cheats the larger states in favor of the smaller, contrary to the intentions of the founding fathers and compromising the Supreme Court's \"\"one man, one vote\"\" rulings. Balinski and Young interweave the theoretical development with a rich historical account of controversies over representation, and show how many of these principles grew out of political contests in the course of United States history. The result is a work that is at once history, politics, and popular science. The book --updated with data from the 1980 and 1990 Census counts --vividly demonstrates that apportionment deals with the very substance of political power.
355 citations
TL;DR: In this paper, the authors present the Systems of Numeration (SNO) system, which is a generalization of the system of counting systems of numbers (SNS).
Abstract: (1985). Systems of Numeration. The American Mathematical Monthly: Vol. 92, No. 2, pp. 105-114.
224 citations
222 citations
TL;DR: Theorems of Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors are presented.
Abstract: (1985). Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors. The American Mathematical Monthly: Vol. 92, No. 10, pp. 711-717.
213 citations
TL;DR: Machiavelli and the Stable Matching Problem as mentioned in this paper were the first to be studied in the mathematical literature, and they were considered to be a classic example of the stable matching problem.
Abstract: (1985). Ms. Machiavelli and the Stable Matching Problem. The American Mathematical Monthly: Vol. 92, No. 4, pp. 261-268.
209 citations
TL;DR: In this paper, Halley's Iteration Method is discussed and a discussion of the effect of the iterative method on the performance of the algorithm is presented. The American Mathematical Monthly: Vol. 92, No. 2, pp. 131-134.
Abstract: (1985). On Halley's Iteration Method. The American Mathematical Monthly: Vol. 92, No. 2, pp. 131-134.
159 citations
TL;DR: The interesting series involving the Central Binomial Coefficient (CBCoI) as discussed by the authors is a series of articles about the CBCoI and its relationship with the central binomial coefficient.
Abstract: (1985). Interesting Series Involving the Central Binomial Coefficient. The American Mathematical Monthly: Vol. 92, No. 7, pp. 449-457.
132 citations
TL;DR: In this article, Algorithmic Thinking and Mathematical Thinking are discussed in the context of the American Mathematical Monthly: Vol. 92, No. 3, pp 170-181.
Abstract: (1985). Algorithmic Thinking and Mathematical Thinking. The American Mathematical Monthly: Vol. 92, No. 3, pp. 170-181.
96 citations
TL;DR: A number of ways have been suggested for reducing the huge amount of information carried by a shape down to a "skeleton" of crucial, possibly discrete, information which can be more readily assimilated.
Abstract: (1985). Local Symmetry of Plane Curves. The American Mathematical Monthly: Vol. 92, No. 10, pp. 689-707.
82 citations
TL;DR: Balinski and Young as discussed by the authors proposed Fair Representation: Meeting the Ideal of One Man, One Vote, 1985, The American Mathematical Monthly: Vol. 92, No. 4, pp. 302-303.
Abstract: (1985). Fair Representation: Meeting the Ideal of One Man, One Vote. By Michel L. Balinski and H. Peyton Young. The American Mathematical Monthly: Vol. 92, No. 4, pp. 302-303.
TL;DR: An elementary proof of the Cauchy-Kowalevsky Theorem is given in this paper, where it is shown that an elementary proof can be found in the form of
Abstract: (1985). An Elementary Proof of the Cauchy-Kowalevsky Theorem. The American Mathematical Monthly: Vol. 92, No. 2, pp. 115-126.
TL;DR: From the Calculus to Set Theory as discussed by the authors traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century.
Abstract: From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Moller-Pedersen.
TL;DR: This dissertation aims to explore the role of language in the development of knowledge and the role that language plays in the acquisition of knowledge.
Abstract: 1. Introduction.- 2. Sophie Germain.- 3. Respectfully Yours, Gauss.- 4. Setting the Prize.- 5. The One Entry.- 6. The Molecular Mentality.- 7. An Award with Reservations.- 8. Publication.- 9. Emergence of a Theory.- 10. Final Years.- Notes.
TL;DR: The Four-or-More Vertex Theorem has been studied extensively in the literature, e.g. as mentioned in this paper. But this paper is not related to the present paper.
Abstract: (1985). The Four-or-More Vertex Theorem. The American Mathematical Monthly: Vol. 92, No. 5, pp. 332-337.
[...]
TL;DR: The introduction to group theory and geometry can be found in this paper, where the author emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research.
Abstract: This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.
[...]
TL;DR: The Towers of Hanoi and Analysis of Algorithms as mentioned in this paper, a collection of algorithms from the World Wide Web, is an example of such an approach, and it can be found here.
Abstract: (1985). Towers of Hanoi and Analysis of Algorithms. The American Mathematical Monthly: Vol. 92, No. 6, pp. 407-420.
TL;DR: Another Note On The Inclusion Lp(μ) ⊂ Lq(μ), The American Mathematical Monthly: Vol. 92, No. 7, pp. 485-C76 as mentioned in this paper.
Abstract: (1985). Another Note On The Inclusion Lp(μ) ⊂ Lq(μ) The American Mathematical Monthly: Vol. 92, No. 7, pp. 485-C76.
TL;DR: Hormander et al. as discussed by the authors presented the analysis of linear partial differential operators (LPDO) and showed that LPDO is a class of linear PDEs.
Abstract: (1985). The Analysis of Linear Partial Differential Operators, Vols. I & II. By Lars Hormander. The American Mathematical Monthly: Vol. 92, No. 10, pp. 745-749.