Mathematics Commons^™

Mathematicians Can Be Wrong, Tony Dunlop, Ken Kaminsky

Humanistic Mathematics Network Journal

No abstract provided.

To My Students, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Cantor’S Coat, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

A New Family Of Irrational Numbers With Curious Properties, Vera W. De Spinadel, José M. Paz University Of Buenos Aires

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Fiction, Pat Mower

Humanistic Mathematics Network Journal

No abstract provided.

The Möbius Metaphor, Julian Fleron

Humanistic Mathematics Network Journal

No abstract provided.

A Day In The Life Of Diophantus (C. 251 A.D.), Rebecca Pekrul

Humanistic Mathematics Network Journal

No abstract provided.

News Extra: Ancient Document Discovered"Could Be The Greatest Of All Time If Validated" Says Professor, Shawn Dolezilek

Humanistic Mathematics Network Journal

No abstract provided.

Limericks On The "Century Of Genius", Thomas J. Lipp

Humanistic Mathematics Network Journal

No abstract provided.

Book Announcement: Women, Art And Geometry In Southern Africa, By Paulus Gerdes

Humanistic Mathematics Network Journal

No abstract provided.

Leibniz: His Philosophy And His Calculi, Eric Ditwiler

Humanistic Mathematics Network Journal

No abstract provided.

Magic "Squares" Indeed, Arthur T. Benjamin, Kan Yasuda '97

All HMC Faculty Publications and Research

No abstract provided in this article.

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

On The Number Of Radially Symmetric Solutions To Dirichlet Problems With Jumping Nonlinearities Of Superlinear Order, Alfonso Castro, Hendrik J. Kuiper

All HMC Faculty Publications and Research

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem

Δu+f(u)=h(x)+cφ(x)

on the unit ball Ω⊂R^N with boundary condition u=0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u)<μ, where μ is the smallest positive eigenvalue for Δψ+μψ=0 in Ω with ψ=0 on ∂Ω. It is shown that, given any integer k≥0, the value c may be chosen so large that there are 2k+1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

An Inverse Function Theorem, Alfonso Castro, J. W. Neuberger

All HMC Faculty Publications and Research

In this note we present a local surjectivity result which is applicable to differential equations for which full boundary conditions may not be known. Our method uses continuous steepest descent and Sobolev gradients.

The Bordalo Order On A Commutative Ring, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

If R is a commutative ring with identity and ≤ is defined by letting a ≤ b mean ab = a or a = b, then (R,≤) is a partially ordered ring. Necessary and sufficient conditions on R are given for (R,≤) to be a lattice, and conditions are given for it to be modular or distributive. The results are applied to the rings Z_n of integers mod n for n ≥ 2. In particular, if R is reduced, then (R,≤) is a lattice iff R is a weak Baer ring, and (R,≤) is a distributive lattice iff R …