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Physical Sciences and Mathematics Commons™

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2002

Claremont Colleges

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Articles 1 - 30 of 52

Full-Text Articles in Physical Sciences and Mathematics

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su Dec 2002

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su

All HMC Faculty Publications and Research

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.

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Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison Nov 2002

Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison

All HMC Faculty Publications and Research

Presentation of two simple combinatorial proofs.

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Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su Oct 2002

Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su

All HMC Faculty Publications and Research

We develop a procedure for implementing an efficient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments, assuming that players have quasi–linear utility functions. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.

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A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su Oct 2002

A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su

All HMC Faculty Publications and Research

We prove the following conjecture of Atanassov (Studia Sci. Math. Hungar.32 (1996), 71–74). Let T be a triangulation of a d-dimensional polytope P with n vertices v1, v2,…,vn. Label the vertices of T by 1,2,…,n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F. Then there are at least n−d full dimensional simplices of T, each labelled with d+1 different labels. We …

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The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt Sep 2002

The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt

All HMC Faculty Publications and Research

We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.

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Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman Sep 2002

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

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Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro Sep 2002

Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro

All HMC Faculty Publications and Research

In this article we provide sufficient conditions for a superlinear Dirichlet problem to have infinitely many nonradial solutions. Our hypotheses do not require the nonlinearity to be an odd function. For the sake of simplicity in the calculations we carry out details of proofs in a ball. However, the proofs go through for any annulus.

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From The Editor, Issue 26, 2002, Alvin White Jun 2002

From The Editor, Issue 26, 2002, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego Jun 2002

History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego

Humanistic Mathematics Network Journal

The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics as an academic discipline. The initial point of departure includes the analysis of some traditional definitions of the concept of 'history' taken from standard dictionaries. This concise dissection attempts to suggest the complexity of the discipline.

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Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein Jun 2002

Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein

Humanistic Mathematics Network Journal

No abstract provided.

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Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap Jun 2002

Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap

Humanistic Mathematics Network Journal

No abstract provided.

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Loopy, George W. Hart Jun 2002

Loopy, George W. Hart

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Look At Mathematics And Theology, Philip J. Davis Jun 2002

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

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Pat's Prologues: Introductions To The First Two Airings Of Math Medley, A Radio Talk Show, Patricia Clark Kenschaft Jun 2002

Pat's Prologues: Introductions To The First Two Airings Of Math Medley, A Radio Talk Show, Patricia Clark Kenschaft

Humanistic Mathematics Network Journal

No abstract provided.

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Notes On Formal Constructivism, D. Joyner, P. Lejarraga Jun 2002

Notes On Formal Constructivism, D. Joyner, P. Lejarraga

Humanistic Mathematics Network Journal

Our aim is to sketch some ideas related to how we (as in, we two) think we (as in, we humans) think. "That theory is useless. It isn't even wrong." - Wolfgang Pauli. Our hope in this paper is to provide a theory, admittedly somewhat vague, of how we think about mathematics. We also hope our ideas do not cause the reader to be reminded of Pauli's quote above. These notes were motivated by the interesting book by Changeaux and Connes.

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Calculus, Sarah Glaz Jun 2002

Calculus, Sarah Glaz

Humanistic Mathematics Network Journal

No abstract provided.

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Aphorisms, Lee Goldstein Jun 2002

Aphorisms, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey Jun 2002

Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey

Humanistic Mathematics Network Journal

No abstract provided.

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When Is A Math Problem Really "Real"?, Michael E. Goldberg Jun 2002

When Is A Math Problem Really "Real"?, Michael E. Goldberg

Humanistic Mathematics Network Journal

No abstract provided.

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"Magic In A Box", Lacie Juris Jun 2002

"Magic In A Box", Lacie Juris

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown Jun 2002

Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon Jun 2002

Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon

Humanistic Mathematics Network Journal

This paper describes my efforts to incorporate problem-solving portfolios into my liberal arts mathematics course. I begin with a description of the components of the portfolios and the factors I consider in evaluating them. I then address some of the more significant obstacles I have encountered as well as what I consider to be among the major benefits. A selection from one student’s portfolio is appended.

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Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht Jun 2002

Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht

Humanistic Mathematics Network Journal

No abstract provided.

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Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis Jun 2002

Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis

Humanistic Mathematics Network Journal

This paper describes a divisibility rule for any prime number as an engaging problem-solving activity for preservice secondary school mathematics teachers.

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Equation Story, Whitney Perret Jun 2002

Equation Story, Whitney Perret

Humanistic Mathematics Network Journal

No abstract provided.

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Special Section: On The Publication Of The 26th Issue Of The Humanistic Mathematics Network Journal, Sandra Z. Keith Jun 2002

Special Section: On The Publication Of The 26th Issue Of The Humanistic Mathematics Network Journal, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

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Does A Mathematical/Scientific Worldview Lead To A Clearer Or More Distorted View Of Reality?: Purposive Musings Inspired From Readings In The Urantia Book, The Cosmic Family, Volume I, And Elsewhere, Jeru Jun 2002

Does A Mathematical/Scientific Worldview Lead To A Clearer Or More Distorted View Of Reality?: Purposive Musings Inspired From Readings In The Urantia Book, The Cosmic Family, Volume I, And Elsewhere, Jeru

Humanistic Mathematics Network Journal

No abstract provided.

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Teaching As Though Students Mattered: A Biography Of Alvin White As Told To Sandra Keith, Alvin White, Sandra Z. Keith Jun 2002

Teaching As Though Students Mattered: A Biography Of Alvin White As Told To Sandra Keith, Alvin White, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

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Humanistic Mathematics: Personal Evolution And Excavations, Stephen I. Brown Jun 2002

Humanistic Mathematics: Personal Evolution And Excavations, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Letters And Comments, Issue 26, 2002, Dick Tahta Jun 2002

Letters And Comments, Issue 26, 2002, Dick Tahta

Humanistic Mathematics Network Journal

No abstract provided.

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