Finances & Algebra Too!,
2013
Wofford College
Finances & Algebra Too!, Anne J. Catlla, Jonathan Foster, Charlene Frazier
Arthur Vining Davis High Impact Fellows Projects
The focus of this project is to provide an application-based approach to teaching algebra 2. Students will study algebraic concepts and functions through the lens of personal finance. After each unit of study, students will complete a financial application project that will go into each student’s “financial” portfolio.
Towards A Better Understanding Of Space-Time Causality: Kolmogorov Complexity And Causality As A Matter Of Degree,
2013
The University of Texas at El Paso
Towards A Better Understanding Of Space-Time Causality: Kolmogorov Complexity And Causality As A Matter Of Degree, Vladik Kreinovich, Andres Ortiz
Departmental Technical Reports (CS)
Space-time causality is one of the fundamental notions of modern physics; however, it is difficult to define in observational physical terms. Intuitively, the fact that a space-time event e=(t,x) can causally influence an event e'=(t',x') means that what we do in the vicinity of e changes what we observe at e'. If we had two copies of the Universe, we could perform some action at e in one copy but not in another copy; if we then observe the difference at e', this would be an indication of causality. However, we only observe one Universe, in which we either perform …
Mapcores 2012-2013 Assessment Report,
2013
College of Saint Benedict/Saint John's University
Mapcores 2012-2013 Assessment Report, Kristen Nairn, Pamela L. Bacon, Jim Crumley, Lynn Ziegler
MapCores Faculty Publications
This is a report showing the assessment results for the MapCores (MAthematics, Physics, COmputer science REsearch Scholars) program at the College of Saint Benedict. Started in 2009, MapCores is a cohort-based program designed to increase women's interest and achievement in mathematics, physics, computer science and engineering. The report was submitted for the National Science Foundation grant number 0965705.
Self-Directed Learning Readiness And Self-Determination For Selected Rehabilitation Professional Students: The Impact Of Clinical Education,
2013
Otterbein University
Self-Directed Learning Readiness And Self-Determination For Selected Rehabilitation Professional Students: The Impact Of Clinical Education, Shelley S. Payne, Peter Rundquist, William V. Harper, Julie Gahimer
Mathematics Faculty Scholarship
In a time of rapidly changing medical information, practitioners must have learning skills that enable them to be effective life-long learners. A part of an examination of a final clinical internship for rehabilitation professionals was a pre-post measure of learner self-direction and self-determination. Two instruments, the Self-Directed Learning Readiness Scale (SDLRS) and the Academic Motivation Scale (AMS- reported as Self-Determination Index (SDI) were used with a sample of Doctorate of Physical Therapy (DPT) and Master of Occupational Therapy (MOT) students. Pre-testing occurred just prior to and post-testing just after the subjects’ final clinical assignments. Both groups increased mean scores from …
A Borsuk-Ulam Equivalent That Directly Implies Sperner's Lemma,
2013
Willamette University
A Borsuk-Ulam Equivalent That Directly Implies Sperner's Lemma, Kathryn L. Nyman, Francis Su
All HMC Faculty Publications and Research
We show that Fan’s 1952 lemma on labelled triangulations of the n-sphere with n + 1 labels is equivalent to the Borsuk–Ulam theorem. Moreover, unlike other Borsuk–Ulam equivalents, we show that this lemma directly implies Sperner’s Lemma, so this proof may be regarded as a combinatorial version of the fact that the Borsuk–Ulam theorem implies the Brouwer fixed-point theorem, or that the Lusternik–Schnirelmann–Borsuk theorem implies the KKM lemma.
Quantitative Approaches To Sustainability Seminars,
2013
Harvey Mudd College
Quantitative Approaches To Sustainability Seminars, Rachel Levy
All HMC Faculty Publications and Research
How can mathematicians contribute to education of about sustainability? Mathematicians study climate change, energy-related technologies, models of energy availability, production and consumption, and even the political and social aspects of sustainable legislation and practices. However, at this point, few courses on sustainability can be found in math department offerings. When we consider problems that our current and future students will face, energy sustainability certainly seems important. But how many of these ideas reach our classrooms?
[Sabbatical Report],
2013
Western Kentucky University
[Sabbatical Report], Alex Lebedinsky
Sabbatical Reports
During the sabbatical leave I collaborated with Dr. Ferhan Atici of the Mathematics department on a new theory of mathematical modeling called Time Scale Calculus (TSC). Dr. Atici and I are also working on another article (titled) "Cagan-type rational expectation model on complex discrete time domains."
Voter Compatibility In Interval Societies,
2013
Harvey Mudd College
Voter Compatibility In Interval Societies, Rosalie J. Carlson
HMC Senior Theses
In an interval society, voters are represented by intervals on the real line, corresponding to their approval sets on a linear political spectrum. I imagine the society to be a representative democracy, and ask how to choose members of the society as representatives. Following work in mathematical psychology by Coombs and others, I develop a measure of the compatibility (political similarity) of two voters. I use this measure to determine the popularity of each voter as a candidate. I then establish local “agreeability” conditions and attempt to find a lower bound for the popularity of the best candidate. Other results …
Imprecise Probabilities In Engineering Analyses,
2013
University of Liverpool
Imprecise Probabilities In Engineering Analyses, Michael Beer, Scott Ferson, Vladik Kreinovich
Departmental Technical Reports (CS)
Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which …
The Use Of Statistics In Experimental Physics,
2013
Ithaca College
The Use Of Statistics In Experimental Physics, Thomas J. Pfaff, Maksim Sipos, M. C. Sullivan, B. G. Thompson, Max Tran
Publications and Research
Most mathematicians are aware of the importance of statistics in biological sciences, business, and economics, but are less aware that statistics is used every day in experimental physics. This paper gives three interesting examples of how statistics plays a vital role in physics. These examples use the basic statistical tools of residuals analysis and goodness of fit.
Approximate Similarity Reduction,
2013
Georgia Southern University
Approximate Similarity Reduction, Rui Zhang
College of Graduate Studies: Theses & Dissertations
The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.
Variational Methods On Elastic Curves,
2013
Georgia Southern University
Variational Methods On Elastic Curves, Daniel D. Rocker
College of Graduate Studies: Theses & Dissertations
In this thesis we investigate elastic curves. These are curves with minimal bending energy as measured by the total squared curvature functional. We show that these can be computed by evolving curves in the direction of the negative gradient in certain Hilbert space settings. By discretizing the curves and using numerical integration, we compute approximate minimizers and display using computer graphics. We propose a conjecture based on the rotation number of a curve that predicts the critical point curves that minimize bending energy.
Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis,
2013
Old Dominion University
Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader
Chemistry & Biochemistry Theses & Dissertations
Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …
Study Of Spatiotemporal Signatures Between Objects To Improve Video Segmentation In Complex Environments,
2013
Old Dominion University
Study Of Spatiotemporal Signatures Between Objects To Improve Video Segmentation In Complex Environments, Adam Robert Reckley
Electrical & Computer Engineering Theses & Dissertations
Background subtraction is often considered to be a required stage of any video surveillance system being used to detect objects in a single frame and/or track objects across multiple frames in a video sequence. Most current state-of-the-art techniques for object detection and tracking utilize some form of background subtraction that involves developing a model of the background at a pixel, region or frame level and designating any elements that deviate from the background model as foreground. Most existing approaches are capable of segmenting a number of distinct components, but are unable to distinguish between the desired object of interest and …
Weighted Shifts Of Finite Multiplicity,
2013
Western Michigan University
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Dissertations
We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.
Student Centered Mathematics In An Isolated Skill Environment-Constructivist Methods In Mathematics,
2013
Bemidji State University
Student Centered Mathematics In An Isolated Skill Environment-Constructivist Methods In Mathematics, Amy Katherine Sorenson
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 Elementary and Middle Mathematics Education"
Improving Student Achievement Through Feedback,
2013
Bemidji State University
Improving Student Achievement Through Feedback, Jennifer L. Mchlachlan
Mathematics Graduate Theses
This paper reviews the current research that exists on feedback given to students in an educational setting. Questions examined were what characteristics make feedback effective, what are the effects on student achievement if feedback is available to students in a math classroom and does timing of the feedback given play a role in its effectiveness. Results showed that feedback is effective if it is descriptive, including both strengths and weaknesses. Feedback given in small doses throughout the learning process, so as not to overwhelm students, has also proven effective. The research shows that the effect of feedback on student achievement …
Combinatorial Pooling Enables Selective Sequencing Of The Barley Gene Space,
2013
University of California - Riverside
Combinatorial Pooling Enables Selective Sequencing Of The Barley Gene Space, Stefano Lonardi, Denisa Duma, Matthew Alpert, Francesca Cordero, Marco Beccuti, Prasanna R. Bhat, Yonghui Wu, Gianfranco Ciardo, Burair Alsaihati, Steve Wanamaker, Josh Resnik, Serdar Bozdag, Ming-Cheng Luo, Timothy J. Close
Mathematics, Statistics and Computer Science Faculty Research and Publications
For the vast majority of species – including many economically or ecologically important organisms, progress in biological research is hampered due to the lack of a reference genome sequence. Despite recent advances in sequencing technologies, several factors still limit the availability of such a critical resource. At the same time, many research groups and international consortia have already produced BAC libraries and physical maps and now are in a position to proceed with the development of whole-genome sequences organized around a physical map anchored to a genetic map. We propose a BAC-by-BAC sequencing protocol that combines combinatorial pooling design and …
The String Landscape: On Formulas For Counting Vacua,
2013
University of Rochester
The String Landscape: On Formulas For Counting Vacua, Tamar Friedmann, Richard P. Stanley
Mathematics Sciences: Faculty Publications
We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with G2 holonomy. Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U (1) factors which are dual to each other. The vacua correspond to various symmetry breaking patterns of grand unified theories. Counting these dual vacua is equivalent to counting the number of conjugacy classes of elements of finite order inside Lie groups. We also point out certain cases where the …
2013 (Spring),
2013
University of Dayton
2013 (Spring), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2013 Spring Colloquium.
