Mathematics Commons^™

A Hypnotist Teaches Math: The Effect Of Person Centered Math Support Classes On At-Risk Community College Students, Ron Bell

Humanistic Mathematics Network Journal

The same elements which make Ericksonian hypnosis a highly effective therapeutic tool are found to be at work in an algebra support class called Math Success Orientation. Interpersonal dynamics of Carl Rogers’ person centered approach to counseling are also part of the philosophy of the class which has a four semester track record of improving both grades and attitude in at risk, math avoidant community college students. The article relates the history of the course with illustrations of how the elements of Person Centered Mathematics operate in the classroom. An appendix demonstrates the effect of the class on student grades

An Inverse Function Theorem Via Continuous Newton’S Method, Alfonso Castro, J. W. Neuberger

All HMC Faculty Publications and Research

We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [4] is that we use continuous steepest descent while [4] uses a combination of Newton type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.

"Stairway To Seven", Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

On The Preparation Of High School Mathematics Teachers, Edna Maura Zuffi

Humanistic Mathematics Network Journal

In this paper I discuss some results got in 1997/98 with Brazilian mathematics school teachers. The research was done to investigate their mathematical language as related to the concept of function. A dichotomy was detected between “formal” and “practical” language they used to express their own conceptions of function, as well as to teach their students this subject. Also, I found teachers’ conceptual images “shrinking” as soon as they were far from their colleges or universities programs.

Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson

Humanistic Mathematics Network Journal

No abstract provided.

The Natural Role Of Mathematics In The Sciences: How Maharishi's Vedic Science Answers The Question Of The Unreasonable Effectiveness Of Mathematics In The Sciences, Catherine A. Gorini

Humanistic Mathematics Network Journal

Mathematicians and scientists have for a long time tried to understand why mathematics, a subjective creation of the human intellect, is so effective in the sciences, which study the objective, physical world. Satisfactory reasons have not been found because there has not been a comprehensive understanding of the relationship between the subjective and the objective aspects of life. In this paper we will see that Maharishi’s Vedic Science, by explaining the link between the subjective realm where mathematics is located and the objective world that science examines, can resolve this problem in a natural way.

A Sabbatical Experience: Nurturing A Partnership, R. Michael Krach

Humanistic Mathematics Network Journal

No abstract provided.

Uniqueness Of Volume-Minimizing Submanifolds Calibrated By The First Pontryagin Form, Daniel A. Grossman, Weiqing Gu

All HMC Faculty Publications and Research

One way to understand the geometry of the real Grassmann manifold G_k(R^k+n) parameterizing oriented k-dimensional subspaces of R^k+n is to understand the volume-minimizing subvarieties in each homology class. Some of these subvarieties can be determined by using a calibration. In previous work, one of the authors calculated the set of 4-planes calibrated by the first Pontryagin form p₁ on G_k(R^k+n) for all k,n ≥4, and identified a family of mutually congruent round 4-spheres which are consequently homologically volume-minimizing. In the present work, we associate to the family of calibrated …

A Geometry Course For Prospective Secondary School Teachers, Jeff Connor, Barbara Grover

Humanistic Mathematics Network Journal

No abstract provided.

Zero, Sheila A. Mcneill

Humanistic Mathematics Network Journal

No abstract provided.

Journal Review: Third International Anthology On Paradoxism, Joanne Growney

Humanistic Mathematics Network Journal

No abstract provided.

Students And Their Learning From Reading, Chris Fenwick

Humanistic Mathematics Network Journal

My aim in this article is to summarize work I have done over the last three years, focusing on the issue of helping students learn from whatever mathematics text they read. Although these types of texts generally contain 3 modes of communication, namely technical English, the language of mathematics itself and diagrams, I will focus this article only on the technical English of such texts. The idea, then, that students can develop techniques and strategies for learning from what they read is generally known as “reading to learn.”

A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain

Humanistic Mathematics Network Journal

No abstract provided.

Real Numbers, Math Lives, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Hotel Infinity, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin

All HMC Faculty Publications and Research

Mathematical Constance (A Poem Dedicated to Constance Reid)

I think that I shall never see

A constant lovelier than e,

Whose digits are too great too state,

They're 2.71828…

And e has such amazing features

It's loved by all (but mostly teachers).

With all of e's great properties

Most integrals are done with … ease.

Theorems are proved by fools like me

But only Euler could make an e.

I suppose, though, if I had to try

To choose another constant, I

Might offer i or phi or pi.

But none of those would satisfy.

Of all the …

What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Problems In Which Given Information Is Ignored, Howard Wachtel

Humanistic Mathematics Network Journal

A set of problems is presented and discussed for which there is a tendency for students to ignore part of the given information in the problem and to substitute some extraneous assumptions. Typical student reactions are also discussed.

The Need To Diversify The Ranks Of Teachers Of Mathematics, Frederick L. Uy

Humanistic Mathematics Network Journal

This paper intends to give rationales for the need to diversify the ranks of teachers of mathematics. It also suggests ideas that we can take to alleviate the situation that we currently are confronting.

Announcement: Association For Women In Mathematics Mentor Network

Humanistic Mathematics Network Journal

No abstract provided.

Educating The Public About School Mathematics, Zalman Usiskin

Humanistic Mathematics Network Journal

No abstract provided.

Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell

Humanistic Mathematics Network Journal

No abstract provided.

Representation, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

Funny Problems, Florentin Smarandache

Humanistic Mathematics Network Journal

No abstract provided.

Proof With Words: 2 + 11 - 1 = 12, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof with words: 2 + 11 – 1 = 12

TWo ELeVEn

Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su

All HMC Faculty Publications and Research

We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin²(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.

Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff

All HMC Faculty Publications and Research

We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D^−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D⁻¹), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with …