Analyzing the Impact of Active Learning in General Education Mathematics Courses

This talk shares the preliminary results of a study that explores the general perceptions and attitudes of students in general education mathematics courses taught using primarily active learning- based methods (like group work, projects, and discovery learning), and compares them with those enrolled in a general education mathematics course taught in a more traditional and lecture-based method. We present an analysis of survey data collected throughout the semester, which explores the disposition and mindset of students, their mathematical confidence and anxiety, and perceptions of pedagogical methods used for the teaching of mathematics. We also explored how these perceptions and dispositions changed throughout the course by comparing pre, mid, and post surveys

First measurements of high frequency cross-spectra from a pair of large Michelson interferometers

Measurements are reported of the cross-correlation of spectra of differential position signals from the Fermilab Holometer, a pair of co-located 39 m long, high power Michelson interferometers with flat, broadband frequency response in the MHz range. The instrument obtains sensitivity to high frequency correlated signals far exceeding any previous measurement in a broad frequency band extending beyond the 3.8 MHz inverse light crossing time of the apparatus. The dominant but uncorrelated shot noise is averaged down over $2\times 10^8$ independent spectral measurements with 381 Hz frequency resolution to obtain $2.1\times 10^{-20} \ \mathrm{m}/\sqrt{\mathrm{Hz}}$ sensitivity to stationary signals. For signal bandwidths $\Delta f > 11$ kHz, the sensitivity to strain $h$ or shear power spectral density of classical or exotic origin surpasses a milestone $PSD_{\delta h} < t_p$ where $t_p= 5.39\times 10^{-44}/\mathrm{Hz}$ is the Planck time.Comment: 5 pages, 3 figure

Interferometric Constraints on Quantum Geometrical Shear Noise Correlations

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.Comment: Matches the journal accepted versio

MHz gravitational wave constraints with decameter Michelson interferometers

A new detector, the Fermilab Holometer, consists of separate yet identical 39-meter Michelson interferometers. Strain sensitivity achieved is better than 10[superscript -21]/√Hz between 1 to 13 MHz from a 130-h data set. This measurement exceeds the sensitivity and frequency range made from previous high frequency gravitational wave experiments by many orders of magnitude. Constraints are placed on a stochastic background at 382 Hz resolution. The 3σ upper limit on Ω[subscript GW], the gravitational wave energy density normalized to the closure density, ranges from 5.6×10[superscript 12] at 1 MHz to 8.4×10[superscript 15] at 13 MHz. Another result from the same data set is a search for nearby primordial black hole binaries (PBHB). There are no detectable monochromatic PBHBs in the mass range 0.83–3.5×10[superscript 21]  g between the Earth and the Moon. Projections for a chirp search with the same data set increase the mass range to 0.59-2.5×10[superscript 25]  g and distances out to Jupiter. This result presents a new method for placing limits on a poorly constrained mass range of primordial black holes. Additionally, solar system searches for PBHBs place limits on their contribution to the total dark matter fraction.United States. Dept. of Energy (Contract DE-AC02-07CH11359)United States. Dept. of Energy (Early Career Research Program FNAL FWP 11-03)Templeton FoundationNational Science Foundation (U.S.) (Grants PHY- 1205254 and DGE-1144082)National Aeronautics and Space Administration (Grant NNX09AR38G)Fermi Research AllianceUniversity of Chicago. Kavli Institute for Cosmological PhysicsUniversity of Chicago. Fermilab Strategic Collaborative InitiativesScience Support ConsortiumNational Science Foundation (U.S.). Graduate Research Fellowship Program (Grant DGE-0638477)Universities Research Association (U.S.). Visiting Scholars Progra

The JWST Early Release Science Program for the Direct Imaging and Spectroscopy of Exoplanetary Systems

The direct characterization of exoplanetary systems with high-contrast imaging is among the highest priorities for the broader exoplanet community. As large space missions will be necessary for detecting and characterizing exo-Earth twins, developing the techniques and technology for direct imaging of exoplanets is a driving focus for the community. For the first time, JWST will directly observe extrasolar planets at mid-infrared wavelengths beyond 5 μm, deliver detailed spectroscopy revealing much more precise chemical abundances and atmospheric conditions, and provide sensitivity to analogs of our solar system ice-giant planets at wide orbital separations, an entirely new class of exoplanet. However, in order to maximize the scientific output over the lifetime of the mission, an exquisite understanding of the instrumental performance of JWST is needed as early in the mission as possible. In this paper, we describe our 55 hr Early Release Science Program that will utilize all four JWST instruments to extend the characterization of planetary-mass companions to ∼15 μm as well as image a circumstellar disk in the mid-infrared with unprecedented sensitivity. Our program will also assess the performance of the observatory in the key modes expected to be commonly used for exoplanet direct imaging and spectroscopy, optimize data calibration and processing, and generate representative data sets that will enable a broad user base to effectively plan for general observing programs in future Cycles

The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems: Best Practices for Data Collection in Cycle 2 and Beyond

We present a set of recommended best practices for JWST data collection for members of the community focussed on the direct imaging and spectroscopy of exoplanetary systems. These findings and recommendations are based on the early analysis of the JWST Early Release Science Program 1386, "High-Contrast Imaging of Exoplanets and Exoplanetary Systems with JWST." Our goal is for this information to be useful for observers in preparation of JWST proposals for Cycle 2 and beyond. In addition to compiling a set of best practices from our ERS program, in a few cases we also draw on the expertise gained within the instrument commissioning programs, as well as include a handful of data processing best practices. We anticipate that this document will be regularly updated and resubmitted to arXiv.org to ensure that we have distributed our knowledge of best-practices for data collection as widely and efficiently as possible.Comment: Not yet submitted for publication. Intended only to be a community resource for JWST Cycle 2 proposal