Mathematics Commons^™

Developing A Stem Teacher Recruitment Pipeline, Kimberly Shaw, Cindy Ticknor, Tim Howard

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

The Columbus Region Academy of Future Teachers of STEM (CRAFT-STEM), a Phase I Robert Noyce Teacher Scholarship Program, combines internships and scholarships, an exciting summer STEM Honors Camp, a new Teaching Connections Seminar, and an impressive array of existing resources to recruit, prepare, and graduate an increasing number of STEM teachers committed to serving high need high schools.

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

The aim of this session is to demonstrate the tools used to help reinforce and recreate students’ conceptual knowledge of fractions, specifically targeting the unit of reference. These manipulatives will provide teachers with instructional support for Common Core Standards, which emphasize critical thinking skills and various representations of knowledge, specifically with fractions. Participants will become actively engaged in learning about these tools, including jumping on a number line floor mat, working with circular fraction pieces and placing fractions on a number line rope. By representing knowledge through circular and linear methods, students will use critical thinking skills and support will …

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …

Trig-Star, James M. Anderson

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …

A Classification Tool For Predictive Data Analysis In Healthcare, Mason Lemoyne Victors

Theses and Dissertations

Hidden Markov Models (HMMs) have seen widespread use in a variety of applications ranging from speech recognition to gene prediction. While developed over forty years ago, they remain a standard tool for sequential data analysis. More recently, Latent Dirichlet Allocation (LDA) was developed and soon gained widespread popularity as a powerful topic analysis tool for text corpora. We thoroughly develop LDA and a generalization of HMMs and demonstrate the conjunctive use of both methods in predictive data analysis for health care problems. While these two tools (LDA and HMM) have been used in conjunction previously, we use LDA in a …

Why ℓ1 Is A Good Approximation To ℓ0: A Geometric Explanation, Carlos Ramirez, Vladik Kreinovich, Miguel Argaez

Departmental Technical Reports (CS)

In practice, we usually have partial information; as a result, we have several different possibilities consistent with the given measurements and the given knowledge. For example, in geosciences, several possible density distributions are consistent with the measurement results. It is reasonable to select the simplest among such distributions. A general solution can be described, e.g., as a linear combination of basic functions. A natural way to define the simplest solution is to select a one for which the number of the non-zero coefficients c_i is the smallest. The corresponding "l₀-optimization" problem is non-convex and therefore, difficult to …

Immersed Finite Element Methods For Parabolic Equations With Moving Interface, Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang

Mathematics and Statistics Faculty Research & Creative Works

This article presents three Crank-Nicolson-type immersed finite element (IFE) methods for solving parabolic equations whose diffusion coefficient is discontinuous across a time dependent interface. These methods can use a fixed mesh because IFEs can handle interface jump conditions without requiring the mesh to be aligned with the interface. These methods will be compared analytically in the sense of accuracy and computational cost. Numerical examples are provided to demonstrate features of these three IFE methods. © 2012 Wiley Periodicals, Inc.

Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

Some new results are presented for the oscillatory and asymptotic behavior of higher-order half-linear differential equations with a noncanonical operator. We study the delayed and advanced equations subject to various conditions. © 2013 Zhang et al.

How To Find Killing Vectors, Charles G. Torre

How to... in 10 minutes or less

We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.

Estimating Third Central Moment C3 For Privacy Case Under Interval And Fuzzy Uncertainty, Ali Jalal-Kamali, Vladik Kreinovich

Departmental Technical Reports (CS)

Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric ({\em skewed}). How can we gauge the skeweness? For symmetric distributions, the third central moment C₃ = E[(x - E(x))³] is equal to 0; thus, this moment is used to characterize skewness. This moment is usually estimated, based on the observed (sample) values x₁, ..., x_n, as C₃ = (1/n) * ((x₁ - E)³ + ... + (x_n - E)³), where E = (1/n) * (x₁ + ... + x_n). In many …

How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson

How to... in 10 minutes or less

We show how to compute the Levi decomposition of a Lie algebra in Maple using the command LeviDecomposition. A worksheet and corresponding PDF can be found below.

A Model Of Dendritic Cell Therapy For Melanoma, Lisette G. De Pillis, Angela Gallegos, Ami E. Radunskaya

All HMC Faculty Publications and Research

Dendritic cells are a promising immunotherapy tool for boosting an individual’s antigen-specific immune response to cancer. We develop a mathematical model using differential and delay-differential equations to describe the interactions between dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cells between lymph, blood, and tumor compartments. Our model reflects experimental results both for dendritic cell trafficking and for immune suppression of tumor growth in mice. In addition, in silico experiments suggest more effective immunotherapy treatment protocols can be achieved by modifying dose location and schedule. A sensitivity analysis of the model reveals which patient-specific …

Borel's Conjecture In Topological Groups, Fred Galvin, Marion Scheepers

Mathematics Faculty Publications and Presentations

We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number κ, let BCκ denote this generalization. Then BCℵ₀ is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, ¬BCℵ₁ is equivalent to the existence of a Kurepa tree of height ℵ₁. Using the connection of BCκ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results:

1. If it is consistent that there is a 1-inaccessible cardinal then it is consistent that BCℵ₁.

2. If it is consistent that BCℵ₁, then it is consistent that …

Moments For The Parabolic Anderson Model: On A Result By Hu And Nualart, Daniel Conus

Communications on Stochastic Analysis

No abstract provided.

Differentiability Of Stochastic Reflecting Flow With Respect To Starting Point, Andrey Pilipenko

Communications on Stochastic Analysis

No abstract provided.

Proving Existence Results In Martingale Theory Using A Subsequence Principle, Alexander Sokol

Communications on Stochastic Analysis

No abstract provided.

Parallel Mutation-Reproduction Processes In Random Environments, Ying Wang

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For The Shell Model Of Turbulence Perturbed By Lévy Noise, Utpal Manna, Manil T Mohan

Communications on Stochastic Analysis

No abstract provided.

Characterization Theorems For Differential Operators On White Noise Spaces, Abdessatar Barhoumi, Alberto Lanconelli

Communications on Stochastic Analysis

No abstract provided.

Stochastic Burgers Equation With Polynomial Nonlinearity Driven By Lévy Process, Erika Hausenblas, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.