Using Manipulatives in Undergraduate Mathematics Courses

Students in undergraduate mathematics classes not only benefit from the use of manipulatives in the classroom, but also enjoy them. This paper specifically outlines one successful activity that used manipulatives in a large section of a precalculus course and then explores possibilities in other courses. It also addresses the use of mathematics manipulatives as a platform to introduce both active and cooperative learning in a large lecture setting

Transport Coefficients in Large NfN_f Gauge Theory: Testing Hard Thermal Loops

We compute shear viscosity and flavor diffusion coefficients for ultra-relativistic gauge theory with many fermionic species, Nf >> 1, to leading order in 1/Nf. The calculation is performed both at leading order in the effective coupling strength g^2 Nf, using the Hard Thermal Loop (HTL) approximation, and completely to all orders in g^2 Nf. This constitutes a nontrivial test of how well the HTL approximation works. We find that in this context, the HTL approximation works well wherever the renormalization point sensitivity of the leading order HTL result is small.Comment: 31 pages, including 9 figures. Error in vacuum self-energy, arising from trusting Arthur Weldon, fixed, thank you Tony Rebhan. Results and conclusions slightly but not significantly change

Transport Coefficients in Hot QCD

I give a physical explanation of what shear viscosity is, and what physics determines its value. Then I explain why determining the shear viscosity of the Quark-Gluon Plasma is interesting. I outline the leading-order calculation of the QGP shear viscosity (and baryon number diffusion constant), explaining why the quite complicated physics of parton splitting and Landau-Pomeranchuk-Migdal interference effects are required for its calculation. Then I briefly explore the range of applicability, emphasizing the importance of plasma instabilities.Comment: 10 pages, invited talk given at the conference "Strong and Electroweak Matter," Helsinki, Finland 16-19 June 200

Problems with lattice methods for electroweak preheating

Recently Garcia Bellido et. al. have proposed that electroweak baryogenesis may occur at the end of inflation, in a scenario where the reheat temperature is too low for electroweak symmetry restoration. I show why the scenario is difficult to test reliably by classical field techniques on the lattice.Comment: 10 pages with 3 figure

Electroweak Bubble Wall Friction: Analytic Results

We present an entirely analytic, leading log order determination of the friction an electroweak bubble wall feels during a first order electroweak phase transition. The friction is dominated by W bosons, and gives a wall velocity parametrically ~ alpha_w, and numerically small, ~ .01 -- 0.1 depending on the Higgs mass.Comment: 8 pages, no figures. Slight revision of introduction: published version (JHEP

Desiderata for an Every Citizen Interface to the National Information Infrastructure: Challenges for NLP

In this paper, I provide desiderata for an interface that would enable ordinary people to properly access the capabilities of the NII. I identify some of the technologies that will be needed to achieve these desiderata, and discuss current and future research directions that could lead to the development of such technologies. In particular, I focus on the ways in which theory and techniques from natural language processing could contribute to future interfaces to the NII. Introduction The evolving national information infrastructure (NII) has made available a vast array of on-line services and networked information resources in a variety of forms (text, speech, graphics, images, video). At the same time, advances in computing and telecommunications technology have made it possible for an increasing number of households to own (or lease or use) powerful personal computers that are connected to this resource. Accompanying this progress is the expectation that people will be able to more..