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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
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.
Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison
Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison
All HMC Faculty Publications and Research
Presentation of two simple combinatorial proofs.
Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su
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.
A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su
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 …
The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt
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.
Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman
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.
Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro
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.
From The Editor, Issue 26, 2002, Alvin White
From The Editor, Issue 26, 2002, Alvin White
Humanistic Mathematics Network Journal
No abstract provided.
History Of Mathematics, An Intuitive Approach, Alejandro R. Garciadiego
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.
Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein
Comments On Zal Usiskin's Article In The Humanistic Mathematics Network Journal For May, 2001, Robert Stein
Humanistic Mathematics Network Journal
No abstract provided.
Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap
Humanizing Mathematics: The Humanistic Impression In The Course For Mathematics Teaching, Ada Katsap
Humanistic Mathematics Network Journal
No abstract provided.
Loopy, George W. Hart
A Brief Look At Mathematics And Theology, Philip J. Davis
A Brief Look At Mathematics And Theology, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Pat's Prologues: Introductions To The First Two Airings Of Math Medley, A Radio Talk Show, Patricia Clark Kenschaft
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.
Notes On Formal Constructivism, D. Joyner, P. Lejarraga
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.
Calculus, Sarah Glaz
Aphorisms, Lee Goldstein
Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey
Book Review: My Dance Is Mathematics By Joanne Growney, Sally Lipsey
Humanistic Mathematics Network Journal
No abstract provided.
When Is A Math Problem Really "Real"?, Michael E. Goldberg
When Is A Math Problem Really "Real"?, Michael E. Goldberg
Humanistic Mathematics Network Journal
No abstract provided.
"Magic In A Box", Lacie Juris
"Magic In A Box", Lacie Juris
Humanistic Mathematics Network Journal
No abstract provided.
Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown
Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown
Humanistic Mathematics Network Journal
No abstract provided.
Portfolio Assessment In Liberal Arts Mathematics, Mike Kenyon
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.
Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht
Marcy's Dots: A Problem On National Test Revisited, Patricia Baggett, Andrzej Ehrenfeucht
Humanistic Mathematics Network Journal
No abstract provided.
Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis
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.
Equation Story, Whitney Perret
Equation Story, Whitney Perret
Humanistic Mathematics Network Journal
No abstract provided.
Special Section: On The Publication Of The 26th Issue Of The Humanistic Mathematics Network Journal, Sandra Z. Keith
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.
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.
Teaching As Though Students Mattered: A Biography Of Alvin White As Told To Sandra Keith, Alvin White, Sandra Z. Keith
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.
Humanistic Mathematics: Personal Evolution And Excavations, Stephen I. Brown
Humanistic Mathematics: Personal Evolution And Excavations, Stephen I. Brown
Humanistic Mathematics Network Journal
No abstract provided.
Letters And Comments, Issue 26, 2002, Dick Tahta
Letters And Comments, Issue 26, 2002, Dick Tahta
Humanistic Mathematics Network Journal
No abstract provided.