Mathematics Commons^™

Galactic Hippodrome, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Using Guided Inquiry In Teaching Mathematical Subjects, Stephanos Gialamas, Abour Cherif, Sarah Keller, Ann Hansen

Humanistic Mathematics Network Journal

No abstract provided.

What Does It Mean To Understand Mathematics?, Emam Hoosain

Humanistic Mathematics Network Journal

No abstract provided.

The Pythagorean Theorem And Area: Postulates Into Theorems, Paul A. Kennedy, Kenneth Evans

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Cultural Diversity In The Curriculum, Rick Gillman

Humanistic Mathematics Network Journal

No abstract provided.

To Myself, Abba Kovner

Humanistic Mathematics Network Journal

No abstract provided.

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.

Control Of Error Rates In Adaptive Analysis Of Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level 1 - α.

Test Of The Additive-Dominance Model Of Grain Weight And Grain Uniformity Of Oat, Avena Sativa L, Genotypes, Sowm Reuben

Tanzania Journal of Science

An investigation of the genetic mechanisms controlling grain weights for the primary and secondary grains uniformity expressed in primary: secondary individual grain weight (P: S IGW) ratio and % tertiary grains produced was conducted using a backcross experiment'. Two oat, parental genotypes, I.L82-1657 (pistillate) and 10589 Cn (staminate) with different grain weight characteristics were hybridized to obtain 6 backcross generations viz. P1, P2, F1, B1, B2 and F2. The scaling test indicated that overall average, primary and secondary individual grain weights and % tertiary grain weight produced failed to satisfy the additive - dominance model and digenic interactions were detected …

Automatic Closure Of Invariant Linear Manifolds For Operator Algebras, Allan P. Donsig, Alan Hopenwasser, David R. Pitts

Department of Mathematics: Faculty Publications

Kadison's transitivity theorem implies that, for irreducible representations of C*-algebras, every invariant linear manifold is closed. It is known that CSL algebras have this property if, and only if, the lattice is hyperatomic (every projection is generated by a nite number of atoms). We show several other conditions are equivalent, including the condition that every invariant linear manifold is singly generated.

We show that two families of norm closed operator algebras have this property. First, let L be a CSL and suppose A is a norm closed algebra which is weakly dense in Alg L and is a bimodule over …

A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler

Mathematics Faculty Publications

In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …

The Critical Components Of A School-College Partnership Formed To Reduce The Enrollment In Remedial Courses In Mathematics Of Incoming Freshman, Marcella Lavoi Melby

Mathematics Graduate Theses

"A Research paper submitted to the Faculty of the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Science in Education, Mathematics."

Stochastic Properties Of Spacings In A Single-Outlier Exponential Model, Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

Let X₁,..., X_n be independent exponential random variables with possibly different scale parameters. Kochar and Korwar [J. Multivar. Anal. 57 (1996)] conjectured that, in this case, the successive normalized spacings are increasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all except one of the parameters are identical. We also prove that the spacings are more dispersed and larger in the sense of hazard rate ordering when the vector of scale parameters is more dispersed in the sense of majorization.

Even Kakutani Equivalence And The Loose Block Independence Property For Positive Entropy Zᵈ Actions, Aimee S. A. Johnson, A. A. Şahin

Mathematics & Statistics Faculty Works

In this paper we define the loose block independence property for positive entropy Zᵈ actions and extend some of the classical results to higher dimensions. In particular, we prove that two loose block independent actions are even Kakutani equivalent if and only if they have the same entropy. We also prove that for d > 1 the ergodic, isometric extensions of the positive entropy loose block independent Zᵈ actions are also loose block independent.

Aspects Of Minimality In Abelian Groups, Seosamh Ó Hógáin

Doctoral

This thesis investigates those abelian groups which are minimal with respect to certain quasi-orders defined on Abk, the category of abelian groups of a given infinite cardinality k. Six such quasi-orders are defined and groups which are minimal with respect to these quasi-orders are called either quasi-minimal, with the associated concepts of purely and directly quasi-minimal groups, or simple minimal with the corresponding associated groups. A complete characterisation is derived for the quasi-minimal groups and, assuming GCH, for the purely quasi-minimal groups. Moreover, it is shown that the direct quasi-minimality of a group may be undecidable in ZFC. In the …

Constructing Critical Indecomposable Codes, Judy L. Walker

Department of Mathematics: Faculty Publications

Critical indecomposable codes were introduced by Assmus, who also gave a recursive construction for these objects. One of the key ingredients in the construction is an auxiliary code, which is an indecomposable code of minimum distance at least 3. In terms of actually being able to construct all critical indecomposable codes, however, Assmus leaves many unanswered questions about these auxiliary codes. In this paper, we provide answers to these questions, including a description of when two equivalent auxiliary codes can yield inequivalent critical indecomposable codes, and results on both the minimum length and the maximum number of critical columns of …

Interfering Solutions Of A Nonhomogeneous Hamiltonian System, Gregory S. Spradlin

Publications

A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity. A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomogeneous nonlinearity.

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 …

What Mathematical Paradoxes Teach Us About Paradoxes In Christianity, Paul Bialek

ACMS Conference Proceedings 2001

In Christian academic circles, we talk about the integration of our faith and learning. That is, we seek to discover and develop connections between our Christian faith and our particular discipline. This is notoriously difficult when the discipline is mathematics. I have found that asking myself these three questions has helped me to integrate my Christian faith with mathematics, although they could be applied to any discipline: (1) How does the fact that I am a Christian affect the way I view mathematics? (2) How does the fact that I am a mathematician affect the way I view Christianity? (3) …

Three Problems From Number Theory, Robert Brabenec

ACMS Conference Proceedings 2001

This paper discusses the experiences of Wheaton College mathematics and computer science department colloquium as they explored open-ended problems.

The Soviet Concept Of The Correlation Of Forces, James Bradley

ACMS Conference Proceedings 2001

This paper takes a look at the Soviet Union’s accumulation of nuclear weapons during the Cold War and what mathematical strategy they employed to make their choices.

Gravitational Acceleration In Hades, Andrew Simoson

ACMS Conference Proceedings 2001

Does acceleration due to gravity increase or decrease upon descending from Earth’s surface? The answer—as we show—depends on one’s model for Earth’s density. For our Earth, gravity increases before it collapses to zero at Earth center.

Theism & Mathematical Realism, John Byl

ACMS Conference Proceedings 2001

This paper examines connections between theism and mathematical realism. Mathematical realism, which offers the best account of mathematics, strongly supports theism. Theism, in turn, supports mathematical realism. Theism readily explains the intricate relations between mathematics, matter, and mind. The attributes of the biblical God provide justification for classical mathematics.

Mathematics Memory Verses: Weekly Devotionals For Math Class, Mark Colgan

ACMS Conference Proceedings 2001

Each Monday during the semester I start class with a short devotional on a verse that relates in some way to mathematics. After three weeks I choose one of the three at random for students to write out on their quiz for a possible bonus point. This encourages students to practice memorizing Scripture and it gives us the opportunity to discuss biblical principles that relate to some of the topics we are studying in the course.

I would like to share some of the Bible verses and weekly devotionals I have used in my mathematics classes. These can be organized …