Mathematics Commons^™

Spatial Training And Calculus Ability: Investigating Impacts On Student Performance And Cognitive Style, Lindsay J. Mccunn, Emily Cilli-Turner

Journal of Educational Research and Practice

Undergraduate calculus is a foundational mathematics sequence that previews the sophistication students will need to succeed in higher-level courses. However, students often struggle with concepts in calculus because they are more abstract and visual than those in other foundational mathematics courses. Additionally, women continue to be underrepresented in the STEM fields. This study builds on previous work indicating a malleability in spatial ability by testing whether improvement occurs in students’ spatial and mathematics ability after implementing spatial training in calculus courses. The researchers also measured associations between spatial training and self-reported cognitive style. While spatial training did not significantly improve …

Modelling The Effects Of Complacency And Educational Countermeasures On The Spread Of Hiv, Brooklyn M. Clive, Ryan Lumbert

S.U.R.E Posters

In this project, we consider a system of five ordinary differential equations which describe the population dynamics of HIV/AIDS when individuals are tested for the virus and then moved onto antiretroviral therapy. We include a Holling Type-II response to model the complacency of the population in response to the number of AIDS cases. We prove global stability of the disease-free equilibrium when the basic reproductive ratio is less than one. We then derive an optimal control problem and solve it theoretically using Pontryagin's Maximum Principle and numerically using the Forward-Backward Sweep Method. We conclude with a discussion on the impact …

Bootstrap Percolation In The Random Geometric Graph, Meirose Barnette, John T. Herndon

S.U.R.E Posters

Bootstrap percolation on a graph is a process which models the spread of an "infection" given an initially infected set of vertices of the graph. To state the problem more precisely, suppose G is a graph, k is a natural number, and I_0 is a set of initially infected vertices. Then for any discrete time t, we define I_t to be I_{t-1} along with any vertex outside of I_{t-1} which has at least k edges to vertices of I_{t-1}. This type of process may be used to model the spread of a disease by taking people as vertices, interactions between …

Effectiveness Of Mayer’S Problem Solving Model With Visual Representation Teaching Strategy In Enhancing Year Four Pupils’ Mathematical Problem Solving Ability, Sharmilla Palanisamy

Student Works (2020-2029)

This study aims to determine the effectiveness of Mayer’s problem solving Model with Visual Representation (MMVR) teaching strategy in enhancing Year 4 students’ mathematical problem solving ability in Klang Valley, and its interaction with gender. A quasi-experimental research design was employed in this study. A sample of 203 Year 4 students consisting of 101 males and 102 females from a private school in Klang Valley were drawn using a convenient sampling technique with two classes assigned as the experimental groups namely Mayer’s problem solving Model (MM) and MMVR groups, and the other one as the control group. The MM group …

Abstract Algebra: Theory And Applications, Thomas W. Judson

eBooks

Tom Judson's Abstract Algebra: Theory and Applications is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Rob Beezer has contributed complementary material using the open source system, Sage.

An HTML version on the PreText platform is available here.

The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone

Masters Theses & Specialist Projects

There exists a natural correspondence between the bases for a given finite-dimensional representation of a complex semisimple Lie algebra and a certain collection of finite edge-colored ranked posets, laid out by Donnelly, et al. in, for instance, [Don03]. In this correspondence, the Serre relations on the Chevalley generators of the given Lie algebra are realized as conditions on coefficients assigned to poset edges. These conditions are the so-called diamond, crossing, and structure relations (hereinafter DCS relations.) New representation constructions of Lie algebras may thus be obtained by utilizing edge-colored ranked posets. Of particular combinatorial interest are those representations whose corresponding …

Hereditarily Irreducible Maps, Hussam Abobaker, Włodzimierz J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A map f:X→Y from a continuum X onto a continuum Y is said to be hereditarily irreducible, if f(A)⊊f(B) for any subcontinua A and B such that A⊊B. We investigate properties of hereditarily irreducible maps between continua. Special attention is given to maps between graphs and maps from the interval.

A Fictitious Points One-Step Mps-Mfs Technique, Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C. S. Chen

Faculty Publications

© 2020 The method of fundamental solutions (MFS) is a simple and efficient numerical technique for solving certain homogenous partial differential equations (PDEs) which can be extended to solving inhomogeneous equations through the method of particular solutions (MPS). In this paper, radial basis functions (RBFs) are considered as the basis functions for the construction of a particular solution of the inhomogeneous equation. A hybrid method coupling these two methods using both fundamental solutions and RBFs as basis functions has been effective for solving a large class of PDEs. In this paper, we propose an improved fictitious points method in which …

Classification Of Triples Of Lattice Polytopes With A Given Mixed Volume, Gennadiy Averkov, Christopher Borger, Ivan Soprunov

Mathematics and Statistics Faculty Publications

We present an algorithm for the classification of triples of lattice polytopes with a given mixed volumemin dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number of which is finite for fixed m. Following this algorithm, we enumerate all irreducible triples of normalized mixed volume up to 4 that are inclusion-maximal. This produces a classification of generic trivariate sparse polynomial systems with up to 4 solutions in the complex torus, up to monomial changes of variables. By a recent result of Esterov, this leads to a description of all …

Energy Spectrum Of Linear Internal Wave Field In The Vicinity Of Continental Slope, Ranis N. Ibragimov, Austin Biondi, Nathan Arndt, Maria Castillo, Guang Lin, Vesselin Vatchev, Sheng Zhang

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of the research was to investigate two-dimensional modeling of efficiency of mixing, resulting from the reflection of a linear internal wave field (IWF) off a continental slope. Efficiency of deep ocean mixing was associated with the energy balance of the radiating IWF into an interior of the ocean in the vicinity of a sloping bottom topography. Since waves are generated not only at the fundamental frequency but also at all of its harmonics ωn = nω less than buoyancy frequency N and greater than Coriolis frequency f, our analysis includes, in general, an infinite number of …

Pattern Of Health Behavior And Its Association With Self-Rated Health: Evidence From The 2018 Behavioral Risk Factor Surveillance System In The United States, Linh Nguyen, Mamunur Rashid, M Mazharul Islam

Annual Student Research Poster Session

Physical inactivity, tobacco use, and alcohol consumption are linked with increased morbidity and mortality. To improve public health services, we need to keep policymakers updated with health-related issues. Yet, there are limited numbers of recent research on the combination of those lifestyle behaviors as the determinants of self-rated health (SRH) in the US. Therefore, this study (1) examines the pattern of physical activities, smoking, alcohol consumption, and SRH, and (2) investigates the association between the behaviors and SRH status among US citizens. We extracted data from the latest state-based survey of the 2018 Behavioral Risk Factor Surveillance System (BRFSS), which …

Making Artificial Cips Data With A Generative Adversarial Neural Network, Austin Hedges

Fall Showcase for Research and Creative Inquiry

Polar mesospheric clouds (PMCs) have been studied for thirteen years by NASA's Aeronomy of Ice in the Mesosphere (AIM) satellite. The Cloud Imaging and Particle Size (CIPS) instrument onboard AIM has taken many images of PMCs over this time. Such a large number of images makes CIPS data ideal for training neural networks which require large datasets. CIPS images were used to train a Generative Adversarial Network (GAN) to train towards being able to generate purely artificial CIPS-like images.

Non-Local Approximation, Iris Hammond

Fall Showcase for Research and Creative Inquiry

Using previous research done by Dr. Ledford, we investigated interpolation techniques with various multi-quadric kernels. Ultimately, we extended a previous Lemma for polynomials of degree M+1.

Mapping Disparities In Covid-19: Determining The Demographic, Economic, Educational, Housing, Quality Of Life, And Health Factors That Relate To Disparities In Covid-19 Infections And Deaths, Kate Stanley, Naima Shifa

Annual Student Research Poster Session

Background: Throughout the pandemic, minority groups, particularly African Americans and Hispanic/Latino Americans have experienced disproportionately high infection and death rates as compared to their white and Asian counterparts. Though this phenomenon could be attributed to high rates of pre-existing conditions in black and Hispanic communities, there are other underlying factors that cause such disparity. We set out to determine whether or not various demographic, economic, educational, health, housing, and quality of life indicators were correlated with higher rates of COVID-19 infection.

Methods: We used USAFacts COVID-19 data to select the 150 United States counties with the highest infection rates. We …

Convex Analysis Of Minimal Time And Signed Minimal Time Functions, D. V. Cuong, B. S. Mordukhovich, Mau Nam Nguyen, M. L. Wells

Mathematics and Statistics Faculty Publications and Presentations

In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets with respect to constant dynamics. Then we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.

Quasilinearization Applied To Boundary Value Problems At Resonance For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Riemann-Liouville fractional differential equation. Under suitable hypotheses, the method of upper and lower solutions is employed to establish uniqueness of solutions. A shift method, coupled with the method of upper and lower solutions, is applied to establish existence of solutions. The quasilinearization algorithm is then applied to obtain sequences of lower and upper solutions that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance.

A Data Analytic Framework For Physical Fatigue Management Using Wearable Sensors, Zahra Sedighi Maman, Ying-Ju Chen, Amir Baghdadi, Seamus Lombardo, Lora A. Cavuoto, Fadel M. Megahed

Mathematics Faculty Publications

The use of expert systems in optimizing and transforming human performance has been limited in practice due to the lack of understanding of how an individual's performance deteriorates with fatigue accumulation, which can vary based on both the worker and the workplace conditions. As a first step toward realizing the human-centered approach to artificial intelligence and expert systems, this paper lays the foundation for a data analytic approach to managing fatigue in physically-demanding workplaces. The proposed framework capitalizes on continuously collected human performance data from wearable sensor technologies, and is centered around four distinct phases of fatigue: (a) detection, where …

A Two-Stage Machine Learning Framework To Predict Heart Transplantation Survival Probabilities Over Time With A Monotonic Probability Constraint, Hamidreza Ahady Dolatsaraa, Ying-Ju (Tessa) Chen, Christy Evans, Ashish Gupta, Fadel M. Megahed

Mathematics Faculty Publications

The overarching goal of this paper is to develop a modeling framework that can be used to obtain personalized, data-driven and monotonically constrained probability curves. This research is motivated by the important problem of improving the predictions for organ transplantation outcomes, which can inform updates made to organ allocation protocols, post-transplantation care pathways, and clinical resource utilization. In pursuit of our overarching goal and motivating problem, we propose a novel two-stage machine learning-based framework for obtaining monotonic probabilities over time. The first stage uses the standard approach of using independent machine learning models to predict transplantation outcomes for each time-period …

A Novel Framework Using Neutrosophy For Integrated Speech And Text Sentiment Analysis, Florentin Smarandache, Kritika Mishra, Ilanthenral Kandasamy, Vasantha Kandasamy W.B.

Branch Mathematics and Statistics Faculty and Staff Publications

With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a …

Inequalities Between Mixed Volumes Of Convex Bodies: Volume Bounds For The Minkowski Sum, Gennadiy Averkov, Christopher Borger, Ivan Soprunov

Mathematics and Statistics Faculty Publications

n the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1++Pd of d-dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,,Pd). This is a consequence of the well-known Aleksandrov-Fenchel inequality. Esterov also posed the problem of determining a sharper bound. We show how additional relations between mixed volumes can be employed to improve the bound to O(md), which is asymptotically sharp. We furthermore prove a sharp exact upper bound in dimensions 2 …

Hive Minded: Like Neurons, Honey Bees Collectively Integrate Negative Feedback To Regulate Decisions, Talia M. Borofsky , '18, Victor J. Barranca, Rebecca Z. Zhou , '19, D. Von Trentini, R. L. Broadrup, C. Mayack

Mathematics & Statistics Faculty Works

Collective decision making is essential for multicellular and self-organized society coordination, but how this occurs when most of the individuals have limited knowledge of the external environment remains elusive. Using empirical data to inform a neuroscience-based firing-rate model, we found that integration of negative feedback and network dynamics in a honeybee, Apis mellifera, hive demonstrates strong similarities to the neuronal interactions of the human brain, where very brief perturbations of feedback in the system result in more rapid and accurate decisions. We show that honey bees used an inhibitory ‘stop’ signal towards dancing honey bees that reduced both waggle dancing …

Math 310: Applied Regression Analysis, Yu Wang

Open Educational Resources

Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.

Shutter Plot: A Visual Display Of Summary Statistics Over A Scatter Plot, Mamunur Rashid, Jyotirmoy Sarkar

Mathematics Faculty Publications

While a dot plot of one variable is naturally extended to a scatter plot of two variables, how should a box plot of one variable be extended to two variables? We propose a shutter plot that depicts the means and the standard deviations of both variables, the two regression lines and the coefficients of correlation and determination over a scatter plot. By showing all relevant summary statistics simultaneously, a shutter plot captures all aspects of a linear relationship, including flagging potential outliers, and helps the readers make good decisions.

Variable-Order Fractional Partial Differential Equations: Analysis, Approximation And Inverse Problem, Xiangcheng Zheng

Theses and Dissertations

Variable-order fractional partial differential equations provide a competitive means in modeling challenging phenomena such as the anomalous diffusion and the memory effects and thus attract widely attentions. However, variable-order fractional models exhibit salient features compared with their constant-order counterparts and introduce mathematical and numerical difficulties that are not common in the context of integer-order and constant-order fractional partial differential equations.

This dissertation intends to carry out a comprehensive investigation on the mathematical analysis and numerical approximations to variable-order fractional derivative problems, including variable-order time-fractional, space-fractional, and space-time fractional partial differential equations, as well as the corresponding inverse problems. Novel techniques …

Learning To Leverage Obstacles, Resources, And Strategies In Math Classes With Multilingual Learners, Aaron T. Wilson, Hyung Won Kim, Mayra Ortiz Galarza, Josef A. Sifuentes

School of Mathematical & Statistical Sciences Faculty Publications

Mathematics teachers must be ready for diverse classrooms, where students who are multilingual learners (MLs) bring new dimensions to the teaching and learning. While MLs face obstacles to learning particular to their linguistic and cultural background, they also bring resources and strengths to bear that can be applied to teaching and learning. We have developed a Challenge-Based Instructional activity to help teachers leverage their experiences of teaching math to ML students, to better understand the obstacles and resources, and to select more effective pedagogical strategies particular to this context. This paper reports the benefits teachers gain in implementing this activity.

On Triangular Paperfolding Patterns, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

We introduce patterns on a triangular grid generated by paperfolding operations. We show that in case these patterns are defined using a periodic sequence of foldings, they can also be generated using substitution rules and compute eigenvalues and eigenvectors of the corresponding matrices. We also prove that densities of all basic triangles are equal in these patterns.

Local Dimensions And Quantization Dimensions In Dynamical Systems, Mrinal Kanti Roychowdhury, Bilel Selmi

School of Mathematical & Statistical Sciences Faculty Publications

Let μ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of Rk. We study the Hausdorff and the packing dimensions, and the quantization dimensions of μ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure μ and generalize many known results about local dimensions and quantization dimensions of measures.

True-False Set Is A Particular Case Of The Refined Neutrosophic Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set.

Decision Making On Teachers’ Adaptation To Cybergogy In Saturated Interval- Valued Refined Neutrosophic Overset /Underset /Offset Environment, Florentin Smarandache, Nivetha Martin, Priya R.

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic overset, neutrosophic underset and neutrosophic offset introduced by Smarandache are the special kinds of neutrosophic sets with values beyond the range [0,1] and these sets are pragmatic in nature as it represents the real life situations. This paper introduces the concept of saturated refined neutrosophic sets and extends the same to the special kinds of neutrosophic sets. The proposed concept is applied in decision making on Teacher’s adaptation to cybergogy. The decision making environment is characterized by different types of teachers, online teaching skills and various training methods. Fuzzy relation is used to match the most suitable method to …