Mathematics Commons^™

Math Rules, Blake Mayer

Humanistic Mathematics Network Journal

No abstract provided.

Geometric Shapes, Sam Dudley

Humanistic Mathematics Network Journal

No abstract provided.

A Minmax Principle, Index Of The Critical Point, And Existence Of Sign Changing Solutions To Elliptic Boundary Value Problems, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems.

We prove that, when isolated, the local degree of any solution given by this minmax principle is +1. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is asymptotically linear, we provide sufficient conditions for:

i) the existence of at least four solutions (one of which changes sign exactly once),

ii) the existence of at least five solutions (two of which change sign), and …

Newton's Cubic Roots, Lisette G. De Pillis

All HMC Faculty Publications and Research

No abstract included in this article

Average-Case Lower Bounds For Noisy Boolean Decision Trees, William Evans, Nicholas Pippenger

All HMC Faculty Publications and Research

We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise, thus yielding stronger lower bounds. It also applies to many more functions than do previous results. The method yields a simple proof of the result (previously established by Reischuk and Schmeltz) that almost all Boolean functions of n arguments require $\Me(n \log n)$ queries, and strengthens this bound from the …

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su

All HMC Faculty Publications and Research

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …

Tree-Based Multicasting In Wormhole-Routed Irregular Topologies, Ran Libeskind-Hadas, Dominic Mazzoni '99, Ranjith Rajagopalan '99

All HMC Faculty Publications and Research

A deadlock-free tree-based multicast routing algorithm is presented for all direct networks, regardless of interconnection topology. The algorithm delivers a message to any number of destinations using only a single startup phase. In contrast to existing tree-based schemes, this algorithm applies to all interconnection topologies, requires only fixed-sized input buffers that are independent of maximum message length, and uses a single asynchronous flit replication mechanism. The theoretical basis of the technique used here is sufficiently general to develop other tree-based multicasting algorithms for regular and irregular topologies. Simulation results demonstrate that this tree-based algorithm provides a very promising means of …

On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

The Reform Calculus Debate And The Psychology Of Learning Mathematics, James M. Cargal

Humanistic Mathematics Network Journal

No abstract provided.

Teaching Mathematics Appreciation To Nonscience Majors, Josefina Alvarez

Humanistic Mathematics Network Journal

No abstract provided.

Poems, David L. Finn

Humanistic Mathematics Network Journal

No abstract provided.

Borsuk-Ulam Implies Brouwer: A Direct Construction, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article.

A Situational Pedagogy For Elementary Mathematics, Vincent Haag

Humanistic Mathematics Network Journal

No abstract provided.

The Object And The Study Of Mathematics, Pinar Karaca

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Ethnomathematics--Challenging Eurocentrism Inmathematics Education, Edited Byarthur B. Powell And Marilyn Frankenstein, Karen Dee Michalowicz

Humanistic Mathematics Network Journal

No abstract provided.

A Tribute To Karl Menger, Seymour Kass

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Garbage Pizza, Patchwork Quilts, And Math Magic: Stories About Teachers Who Love To Teach And Children Who Love To Learn, By Susan Ohanian, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Reflections Of Glenmount Reform Effort, Gail Black, Ruth Miller

Humanistic Mathematics Network Journal

No abstract provided.

Resource Review: Research On Children's Learning As A Tool To Improve Math And Science Teaching, Cynthia Hudley

Humanistic Mathematics Network Journal

No abstract provided.

Helping Students With Attention Deficit Disorder Succeed In A College Mathematics Class, Pamela E. Matthews

Humanistic Mathematics Network Journal

No abstract provided.

John Dewey, The Math And Science Standards, And The Workplace, Bernard A. Fleishman

Humanistic Mathematics Network Journal

No abstract provided.

Inspiration In England, Mary Mcdermott

Humanistic Mathematics Network Journal

No abstract provided.

A Course In Mathematical Ethics, Robert P. Webber

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Nexus: Architecture And Mathematics, Edited By Kim Williams, Joseph Malkevitch

Humanistic Mathematics Network Journal

No abstract provided.

A Sign-Changing Solution For A Superlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

What Kind Of Thing Is A Number?: A Talk With Reuben Hersh, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

Math Lingo Vs. Plain English: Multiple Entendre, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: The Crest Of The Peacock: Non-European Roots Of Mathematics,By George Gheverghese Joseph, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.