Mathematics Commons^™

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

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

Humanistic Mathematics Network Journal

No abstract provided.

Aphorisms, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

When Is A Math Problem Really "Real"?, Michael E. Goldberg

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.

"Magic In A Box", Lacie Juris

Humanistic Mathematics Network Journal

No abstract provided.

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.

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.

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 Network Journal

No abstract provided.

Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article

A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli

CMC Faculty Publications and Research

A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.

Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan

Pomona Faculty Publications and Research

We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph K_n in R³ contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of K_r in R³ contains a knot Q with |a₂(Q)| ≥ m, where a₂(Q) denotes the second coefficient of the Conway polynomial of Q.

Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger

All HMC Faculty Publications and Research

If G = (V, E) is a graph, the incidence graphI(G) is the graph with vertices I ∪ E and an edge joining v ∈ V and e ∈ E when and only when v is incident with e in G. For G equal to K_n (the complete graph on n vertices) or K_n,n (the complete bipartite graph on n + n vertices), we enumerate the matchings (sets of edges, no two having a vertex in common) in I(G), both exactly (in terms of generating …

Asymmetric Two-Colourings Of Graphs In S³, Erica Flapan, David Linnan Li

Pomona Faculty Publications and Research

We prove that for any non-planar graph H, we can choose a two-colouring G of H such that G is intrinsically chiral, and if H is 3-connected and is not K_3,3 or K₅, then G is intrinsically asymmetric. No such asymmetric two-colouring is possible for K_3,3 or K₅.

A Minimal Regular Ring Extension Of C(X), Melvin Henriksen, Robert M. Raphael, R. G. Woods

All HMC Faculty Publications and Research

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τ_δ) of continuous real-valued functions on the space (X,Τ_δ), where Τ_δ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τ_δ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τ_δ) are characterized. Necessary, and different sufficient, conditions for the equality …

A Local Inversion Principle Of The Nash-Moser Type, 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 [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser 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.

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin

All HMC Faculty Publications and Research

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum l_F is replaced by l_B =l_F − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …

Math Major, Math Major, Arthur T. Benjamin

All HMC Faculty Publications and Research

Sung to the tune of "Matchmaker" from Fiddler on the Roof:

Math major, math major, make me some math.

Find me a prime, sketch me a path.

Math major, math major look through your books,

And make me some perfect math.

Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman

All HMC Faculty Publications and Research

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem

Nuclear Magnetic Resonance And Humanistic Mathematics: A Farewell, Linley Erin Hall

Humanistic Mathematics Network Journal

No abstract provided.

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.