Mathematics

13: Polar Reciprocal, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarReciprocal.nb first shows a transformation of the circle r = 3 into the circle r = 3sin (theta). Second, it shows the original and reciprocal graphs through the animation. Interesting stuff!

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09: Solving Trig Equations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SolvingTrigEquations.nb develops the idea of solving trigonometric equations with special angles by looking at a sequence of problems. The student is asked to think about solutions and to do more problems along the way.

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09: Slope Field, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SlopeField.nb does just what it says! Enter a differential equation in the form y = … and choose the window. It is also possible to choose the number of marks in each direction.

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Structure Formulas For Wave Operators, Marius Beceanu, Wilhelm Schlag

Mathematics and Statistics Faculty Scholarship

We establish quantitative estimates on the structure function arising in the representation of the intertwining wave operators of a Schroedinger operator in three dimensions. Regularity of zero energy is assumed throughout. This paper is related to, and corrects some inaccuracies in, the first author's work this https URL

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Discussion Of "Bridging The Gap Between Theory And Practice In Basic Statistical Process Monitoring", L. A. Jones-Farmer, Nathaniel Stevens

No abstract provided.

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Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, Nathaniel Stevens, C. M. Anderson-Cook

Mathematics

When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. New graphical summaries provide strategies for visualizing the results.

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On The Combinatorics Of Demoulin Transforms And (Discrete) Projective Minimal Surfaces, A Mccarthy, W Schief

Sciences Papers and Journal Articles

The classical Demoulin transformation is examined in the context of discrete differential geometry. We show that iterative application of the Demoulin transformation to a seed projective minimal surface generates a Z² lattice of projective minimal surfaces. Known and novel geometric properties of these Demoulin lattices are discussed and used to motivate the notion of lattice Lie quadrics and associated discrete envelopes and the definition of the class of discrete projective minimal and Q-surfaces (PMQ-surfaces). We demonstrate that the even and odd Demoulin sublattices encode a two-parameter family of pairs of discrete PMQ-surfaces with the property that one discrete PMQ-surface …

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A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

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A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

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Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them, both …

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Strategies For Using Data Analytics In Testing The Readability Levels Of Textbooks: It’S Time To Get Serious, Emily Wefelmeyer, Mary Beth Backus

Other Student Works

The idea that education in America is deteriorating is emotionally charged and controversial. While there is no disputing that education levels in the United States continue to rise, there is also a pervasive notion that this was accomplished by gradually reducing the readability level and general difficulty of textbooks. One tool often employed in the defense of education is the employment of readability indices in the evaluation of textbooks. There are a variety of these readability indices that serve the purpose of indicating a grade level for a particular piece of writing (Kinkaid, et. al., 1975). It’s relatively easy to …

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A Dressing Method For Soliton Solutions Of The Camass-Holm Equation, Rossen Ivanov, Tony Lyons, Nigel Orr

Conference papers

The soliton solutions of the Camassa-Holm equation are derived by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by other methods.

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Weihrauch Reducibility And Finite-Dimensional Subspaces, Sean Sovine

Theses, Dissertations and Capstones

In this thesis we study several principles involving subspaces and decompositions of vector spaces, matroids, and graphs from the perspective of Weihrauch reducibility. We study the problem of decomposing a countable vector space or countable matroid into 1-dimensional subspaces. We also study the problem of producing a finite-dimensional or 1-dimensional subspace of a countable vector space, and related problems for producing finite-dimensional subspaces of a countable matroid. This extends work in the reverse mathematics setting by Downey, Hirschfeldt, Kach, Lempp, Mileti, and Montalb´an (2007) and recent work of Hirst and Mummert (2017). Finally, we study the problem of producing a …

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The Pareto-G Extended Weibull Distribution, Oluwaseun Elizabeth Otunuga

Theses, Dissertations and Capstones

In this thesis, the Pareto family of extended Weibull distribution is introduced and discussed extensively. This family consists of the Pareto (Type I) Extended Weibull Distribution or PEW for short, and the Pareto (Type II) Extended Weibull Distribution or otherwise called the Lomax Extended Weibull Distribution or LEW for short. The numbers of the parameters of PEW or LEW depend on the number of parameters for the extended Weibull distribution and type of the Pareto distribution. Some properties of these distributions, such as the hazard rate function, the survival function, moments, skewness, kurtosis, mean deviation and entropies are discussed. The …

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Local Sensitivity Analysis Of Acute Inflammation, James Martin

Theses, Dissertations and Capstones

The inflammatory response is the body's response to some pathogen or foreign invader. When infected by a pathogen, a healthy individual will mount a response with immunological factors to eliminate it. An inflammatory response that is either too strong or too weak can be detrimental to the individual's health. We will look at a qualitative mathematical model of the inflammatory response, in scenarios that represent varying disorders of the immune system. Using sensitivity analysis we determine which parameters of this model are most influential in the different scenarios. By determining which parameters are most influential we can suggest possible targets …

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Common Core And Stem Opportunities, Lane H. Walker, Helene J. Sherman

The Mathematics Enthusiast

There is an increasing need for educators at all levels to equip more students with problem-solving skills that better fit our changing work force. Students are largely unaware of many science-, technology-, engineering-, and math-related (STEM) careers. They often do not understand the importance of those careers or what skills are required to pursue them. Students are exposed to some of those skills if they take Career Technical Education (CTE) classes, but rarely do they see the connections in their core math classes. Math teachers have pointed to their dense curricula as making STEM integration impractical. A study of the …

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Introduction To The Special Issue On Teaching Inquiry (Part I): Illuminating Inquiry, Brian P. Katz, Elizabeth Thoren

Mathematics: Faculty Scholarship & Creative Works

We provide an introduction to the special issue on Teaching Inquiry, through its motivation and themes. We focus here on Part I: Illuminating Inquiry.

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Introduction To The Special Issue On Teaching Inquiry (Part Ii): Implementing Inquiry, Brian P. Katz, Elizabeth Thoren

Mathematics: Faculty Scholarship & Creative Works

We provide an introduction to the special issue on Teaching Inquiry, through its motivation and themes, focusing here on Part II: Implementing Inquiry.

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Mathematical Creativity For The Youngest School Children: Kindergarten To Third Grade Teachers’ Interpretations Of What It Is And How To Promote It, Yinjing Shen, Carolyn Pope Edwards

The Mathematics Enthusiast

Creativity is important for young children learning mathematics. However, much literature has claimed creativity in the learning of mathematics for young children is not adequately supported by teachers in the classroom due to such reasons as teachers’ poor college preparation in mathematics content knowledge, teachers’ negativity toward creative students, teachers’ occupational pressure, and low quality curriculum. The purpose of this grounded theory study was to generate a model that describes and explains how a particular group of early childhood teachers make sense of creativity in the learning of mathematics and how they think they can promote or fail to promote …

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Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher

The Mathematics Enthusiast

System Dynamics (SD) modeling is a powerful analytical method used by professional scientists, academics, and governmental officials to study the behavior patterns of complex systems. Specifically through use of the Stella software, it is a method that I and others have used for over two decades with high school, and even middle school, math and science students. In this paper I describe an introduction to SD modeling intended for an algebra class (in either middle or high school). In the body of the paper, a nested sequence of simple bank account examples, increasing in complexity, is used to demonstrate a …

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Examining The Interaction Of Mathematical Abilities And Mathematical Memory: A Study Of Problem-Solving Activity Of High-Achieving Swedish Upper Secondary Students, Attila Szabo, Paul Andrews

The Mathematics Enthusiast

In this paper we investigate the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii (1976). Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students’ selected their problem-solving methods; where these methods failed to …

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Mathematical Modeling Cycles As A Task Design Heuristic, Jennifer A. Czocher

The Mathematics Enthusiast

There are many approaches to task design (Watson & Ohtani, 2015) from a large number of local and global design heuristics. The purpose of this paper is to present how mathematical modeling cycles, a popular way of describing mathematical modeling processes, were used as a task design heuristic.

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Pattern Avoidance, Emma Christensen

All College Thesis Program, 2016-2019

A set partition avoids a pattern if no subdivision of that partition standardizes to the pattern. There exists a bijection between set partitions and restricted growth functions (RGFs) on which Wachs and White defined four statistics of interest to this work. We first characterize the restricted growth functions of several avoidance classes based on partitions of size four, enumerate these avoidance classes, and consider the distribution of the Wachs and White statistics across these avoidance classes. We also investigate the equidistribution of statistics between avoidance classes based on multiple patterns.

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2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

Graduate Handbook on the MAEM Program at Otterbein University.

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A Proposed Local Instruction Theory For Teaching Instantaneous Speed In Grade Five, Huub De Beer, Koeno Gravemeijer, Michiel Van Eijck

The Mathematics Enthusiast

In answer to a call for innovative science and technology education in primary education, we started a design research project to explore how to teach instantaneous speed in grade five. In this article we present the results of a series of teaching experiments that were conducted to design, try out, and improve a local instruction theory on teaching instantaneous speed in grade five. In a retrospective analysis, looking for patterns in the whole data set, encompassing all experiments, we identified a set of key learning moment of the students. Based on these patterns, a potentially viable local instruction theory was …

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First Passage Statistics For The Capture Of A Brownian Particle By A Structured Spherical Target With Multiple Surface Traps, Alan E. Lindsay, Andrew Bernoff, Michael J. Ward

All HMC Faculty Publications and Research

We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small …

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A Remark On Non-Integral P-Adic Slopes For Modular Formsune Remarque Sur Les Pentes P-Adiques Non Entières Des Formes Modulaires, John Bergdall, Robert Pollack

Mathematics Faculty Research and Scholarship

We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral p-adic slope.

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Investigating Difference Equations, Dave Ruch

Discrete Mathematics

No abstract provided.

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Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

Analysis

No abstract provided.

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Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

Analysis

No abstract provided.

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Full-Text Articles in Mathematics

13: Polar Reciprocal, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

09: Solving Trig Equations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

09: Slope Field, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

Structure Formulas For Wave Operators, Marius Beceanu, Wilhelm Schlag

Mathematics and Statistics Faculty Scholarship

Discussion Of "Bridging The Gap Between Theory And Practice In Basic Statistical Process Monitoring", L. A. Jones-Farmer, Nathaniel Stevens

Mathematics

Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, Nathaniel Stevens, C. M. Anderson-Cook

Mathematics

On The Combinatorics Of Demoulin Transforms And (Discrete) Projective Minimal Surfaces, A Mccarthy, W Schief

Sciences Papers and Journal Articles

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

Strategies For Using Data Analytics In Testing The Readability Levels Of Textbooks: It’S Time To Get Serious, Emily Wefelmeyer, Mary Beth Backus

Other Student Works

A Dressing Method For Soliton Solutions Of The Camass-Holm Equation, Rossen Ivanov, Tony Lyons, Nigel Orr

Conference papers

Weihrauch Reducibility And Finite-Dimensional Subspaces, Sean Sovine

Theses, Dissertations and Capstones

The Pareto-G Extended Weibull Distribution, Oluwaseun Elizabeth Otunuga

Theses, Dissertations and Capstones

Local Sensitivity Analysis Of Acute Inflammation, James Martin

Theses, Dissertations and Capstones

Common Core And Stem Opportunities, Lane H. Walker, Helene J. Sherman

The Mathematics Enthusiast

Introduction To The Special Issue On Teaching Inquiry (Part I): Illuminating Inquiry, Brian P. Katz, Elizabeth Thoren

Mathematics: Faculty Scholarship & Creative Works

Introduction To The Special Issue On Teaching Inquiry (Part Ii): Implementing Inquiry, Brian P. Katz, Elizabeth Thoren

Mathematics: Faculty Scholarship & Creative Works

Mathematical Creativity For The Youngest School Children: Kindergarten To Third Grade Teachers’ Interpretations Of What It Is And How To Promote It, Yinjing Shen, Carolyn Pope Edwards

The Mathematics Enthusiast

Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher

The Mathematics Enthusiast

Examining The Interaction Of Mathematical Abilities And Mathematical Memory: A Study Of Problem-Solving Activity Of High-Achieving Swedish Upper Secondary Students, Attila Szabo, Paul Andrews

The Mathematics Enthusiast

Mathematical Modeling Cycles As A Task Design Heuristic, Jennifer A. Czocher

The Mathematics Enthusiast

Pattern Avoidance, Emma Christensen

All College Thesis Program, 2016-2019

2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

A Proposed Local Instruction Theory For Teaching Instantaneous Speed In Grade Five, Huub De Beer, Koeno Gravemeijer, Michiel Van Eijck

The Mathematics Enthusiast

First Passage Statistics For The Capture Of A Brownian Particle By A Structured Spherical Target With Multiple Surface Traps, Alan E. Lindsay, Andrew Bernoff, Michael J. Ward

All HMC Faculty Publications and Research

A Remark On Non-Integral P-Adic Slopes For Modular Formsune Remarque Sur Les Pentes P-Adiques Non Entières Des Formes Modulaires, John Bergdall, Robert Pollack

Mathematics Faculty Research and Scholarship

Investigating Difference Equations, Dave Ruch

Discrete Mathematics

Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

Analysis

Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

Analysis