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Showing papers in "American Mathematical Monthly in 1972"


Journal ArticleDOI

211 citations


Journal ArticleDOI
TL;DR: In this article, the authors define a graph as a simple graph and define the following properties of a graph: Simple graph, Simple Graph, simple graph, Konigsberg bridge problem, Utilities problem, Finite and Infinite graphs, Regular graph, Matrix representation of graphs Adjacency matrix, Incidence matrix and examples.
Abstract: Introduction Definition of a Graph, Simple Graph, Konigsberg bridge problem, Utilities problem, Finite and Infinite graphs, Regular graph, Matrix representation of graphs Adjacency matrix, Incidence matrix and examples; Paths and Circuits Isomorphism, Sub graphs, Walk, Path, Circuit, Connected graph, Euler line and Euler graph; Operations on graphs Union of two graphs, Intersecton of two graphs and ring sum of two graphs; Hamiltonian circuit, Hamiltonian path, Complete graph, Traveling salesmen problem. Trees and fundamental circuits, cutsets.

203 citations



Journal ArticleDOI

141 citations


Journal ArticleDOI
Peter D. Lax1
TL;DR: In this paper, the formation and decay of shock waves are discussed and a model of the wave formation and the decay is proposed. The American Mathematical Monthly: Vol. 79, No. 3, pp. 227-241.
Abstract: (1972). The Formation and Decay of Shock Waves. The American Mathematical Monthly: Vol. 79, No. 3, pp. 227-241.

133 citations



Journal ArticleDOI
TL;DR: The Derivative of a Determinant as mentioned in this paper is a derivative of a determinant that is derived from a deterministic determinant, and it can be seen as an alternative to determinant.
Abstract: (1972). The Derivative of a Determinant. The American Mathematical Monthly: Vol. 79, No. 10, pp. 1124-1126.

93 citations


Journal ArticleDOI
TL;DR: Theorems of Bony and Brezis on Flow-Invariant Sets as mentioned in this paper have been studied in the context of flow-invariant sets and flow invariant sets.
Abstract: (1972). The Theorems of Bony and Brezis on Flow-Invariant Sets. The American Mathematical Monthly: Vol. 79, No. 7, pp. 740-747.

88 citations


Journal ArticleDOI
Philip J. Davis1
TL;DR: The discovery of mathematical logic convinced many mathematicians and philosophers that this was the royal road to foundations and Gottlob Frege in his masterpiece The Foundations of Arithmetic not only sketched the logical deduction of arithmetic but inveighed against psychologism andhistoricism in philosophy.
Abstract: The discovery of mathematical logic convinced many mathematicians and philosophers that this was the royal road to foundations. Thus convinced, they were anxiousto rid philosophy of mathematics of all empirical considerations. None was more adamant than Gottlob Frege who in his masterpiece The Foundations of Arithmetic not only sketched the logical deduction of arithmetic but inveighed against psychologism andhistoricism in philosophy. Frege remarked in passing

88 citations


Journal ArticleDOI
TL;DR: In this article, the integration of finite terms in finite terms has been discussed in the context of the American Mathematical Monthly: Vol. 79, No. 9, pp. 963-972.
Abstract: (1972). Integration in Finite Terms. The American Mathematical Monthly: Vol. 79, No. 9, pp. 963-972.

79 citations


Journal ArticleDOI
TL;DR: In this article, the Pythagorean triples in unique factorization domains are presented. But they do not specify the order in which the triples are derived from the original triples.
Abstract: (1972). Pythagorean Triples in Unique Factorization Domains. The American Mathematical Monthly: Vol. 79, No. 5, pp. 503-505.

Journal ArticleDOI
TL;DR: The Hadamard Maximum Determinant Problem (MDP) as mentioned in this paper is a variant of the maximum determinant problem, and it has been shown to be NP-hard.
Abstract: (1972). The Hadamard Maximum Determinant Problem. The American Mathematical Monthly: Vol. 79, No. 6, pp. 626-630.

Journal ArticleDOI
TL;DR: In this article, the authors present thirteen colorful variations on the four-color conjecture, which they call "13 colorful variants on Guthrie's Four-Color Conjecture".
Abstract: (1972). Thirteen Colorful Variations on Guthrie's Four-Color Conjecture. The American Mathematical Monthly: Vol. 79, No. 1, pp. 2-43.

Journal ArticleDOI
TL;DR: The Historical Development of Algebraic Geometry as discussed by the authors is a history of algebraic geometry with a focus on algebraic geometrical geometry and algebraic algebraic graph theory.
Abstract: (1972). The Historical Development of Algebraic Geometry. The American Mathematical Monthly: Vol. 79, No. 8, pp. 827-866.

Journal ArticleDOI
TL;DR: In this article, what is a reciprocity law and how it relates to reciprocity laws are discussed, and the authors propose a model of reciprocity based on reciprocity in the American Mathematical Monthly.
Abstract: (1972). What is a Reciprocity Law? The American Mathematical Monthly: Vol. 79, No. 6, pp. 571-586.


Journal ArticleDOI
TL;DR: The Sums of Finite Sets of Integers (SFSI) as discussed by the authors is a collection of finite sets of integers that can be seen as a subset of the Integers.
Abstract: (1972). Sums of Finite Sets of Integers. The American Mathematical Monthly: Vol. 79, No. 9, pp. 1010-1012.

Journal ArticleDOI
TL;DR: In this paper, certain Rational Functions Whose Power Series Have Positive Coefficients are discussed. But they do not have positive coefficients in the power series. The American Mathematical Monthly: Vol. 79, No. 4, pp. 327-341.
Abstract: (1972). Certain Rational Functions Whose Power Series Have Positive Coefficients. The American Mathematical Monthly: Vol. 79, No. 4, pp. 327-341.



OtherDOI
TL;DR: Pasch and Peano as discussed by the authors described the origins of modern axiomatics in the American Mathematical Monthly: Vol. 79, No. 2, pp. 133-136.
Abstract: (1972). The Origins of Modern Axiomatics: Pasch to Peano. The American Mathematical Monthly: Vol. 79, No. 2, pp. 133-136.

Journal ArticleDOI
TL;DR: In this article, the edge-colouring problem is formulated as an edge coloring problem, and the solution is shown to be NP-hard, but it is possible to solve it.
Abstract: (1972). An Edge-Colouring Problem. The American Mathematical Monthly: Vol. 79, No. 9, pp. 1018-1020.

Journal ArticleDOI
TL;DR: In this paper, a weak parallelogram law for lp is proposed, which is a weaker version of the weak parity law for p. The American Mathematical Monthly: Vol 79, No. 9, pp. 1012-1015.
Abstract: (1972). A Weak Parallelogram Law for lp. The American Mathematical Monthly: Vol. 79, No. 9, pp. 1012-1015.

Journal ArticleDOI
TL;DR: In this article, the authors proposed the Acquaintance Graph Party Problem (AGP) and proved that it is NP-hard to solve the graph party problem with respect to friendship graphs.
Abstract: (1972). Acquaintance Graph Party Problem. The American Mathematical Monthly: Vol. 79, No. 10, pp. 1113-1117.


Journal ArticleDOI



Journal ArticleDOI
TL;DR: A survey of mutually related problems, conjectures and results dealing with variants of the notion of the cut-number m(P) of a polytope P is presented in this paper.
Abstract: : A survey of mutually related problems, conjectures and results is presented, dealing with variants of the notion of the cut-number m(P) of a polytope P . Here m(P) is the least number of hyperplanes needed to intersect all edges of the polytopes P . Cut-numbers and similar notions are of interest in many contexts, ranging from pattern recognition through graph theory to functional analysis. (Author)

Journal ArticleDOI
TL;DR: In this paper, the Geometry of Radon's Theorem is discussed and the authors propose a solution to the problem of the Radon Theorem in terms of the number of vertices.
Abstract: (1972). The Geometry of Radon's Theorem. The American Mathematical Monthly: Vol. 79, No. 9, pp. 949-963.