Mathematics Commons^™

Why Does Ramanujan, The Man Who Knew Infinity, Matter?, Ken Ono

Dalrymple Lecture Series

Dr. Ken Ono is the Thomas Jefferson Professor of Mathematics at the University of Virginia, the Asa Griggs Candler Professor of Mathematics at Emory University, and the vice president of the American Mathematical Society.He is an associate producer of the film The Man Who Knew Infinity starring Dev Patel and Jeremy Irons about Srinivasa Ramanujan, a self-trained two-time college dropout who left behind three notebooks filled with equations that mathematicians are still trying to figure out today. Ramanujan claimed that his ideas came to him as visions from an Indian goddess. This lecture is about why Ramanujan matters. The answers …

Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Models For Describing Molecular Self-Assembly, Margherita Maria Ferrari

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Loop Homology Of Bi-Secondary Structures, Andrei Bura

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Oscillation In Mathematical Epidemiology, Meredith Greer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Concise Workbook For College Algebra 2nd Edition, Fei Ye

Open Educational Resources

This is the second edition of the book "A Concise Workbook for College Algebra". In this new edition, some tips and notes, more exercises and examples were added.

Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, Ferhan Atici, Ngoc Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, Claudia Kolakowski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu

Mathematics Colloquium Series

In ecology, regime shifts are continual rapid change between different long-lasting dynamics. For instance, rapid evolutionary changes have been observed in a wide variety of organisms, both in predators and in prey. Another example is disease outbreak, where a system exhibits qualitative changes after long periods of apparent quiescence. Using the theory of slow-fast dynamics, for systems of differential equations with sufficiently large separation of time scales we derive conditions under which regime shifts occur. This is joint work with Shigui Ruan and Gail Wolkowicz.

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

It can be proven that linear dynamical systems exhibit either stable behavior, or unstable behavior, or oscillatory behavior, or transitional behavior. Interesting, the same classification often applies to nonlinear dynamical systems as well. In this paper, we provide a possible explanation for this phenomenon, i.e., we explain why a classification based on linear approximation to dynamical systems often works well in nonlinear cases.

Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev

Masters Theses & Specialist Projects

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we …

Toward Greater Reproducibility Of Undergraduate Behavioral Science Research, Bruce Evan Blaine

Mathematical and Computing Sciences Faculty/Staff Publications

Reproducibility crises have arisen in psychology and other behavioral sciences, spurring efforts to ensure research findings are credible and replicable. Although reforms are occurring at professional levels in terms of new publication parameters and open science initiatives, the credibility and reproducibility of undergraduate research deserves attention. Undergraduate behavioral science research projects that rely on small convenience samples of participants, overuse hypothesis testing for drawing meaning from data, and engage in opaque statistical computing are vulnerable to producing nonreproducible findings. These vulnerabilities are reviewed, and practical recommendations for improving the credibility and reproducibility of undergraduate behavioral science research are offered.

Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier

Journal of Catholic Education

Catholic schools primarily should be in the business of making saints. This article identifies and explores a meaningful, engaging point of contact between mathematics and theology for high school math classes, the Fibonacci Sequence. This sequence serves as an engaging introduction to sequences and series; more importantly, the topic can be used as a springboard to theological discussions. The paper will provide a brief historical background to the Fibonacci Sequence, an explanation of how it can be used in a high school math classroom, and an exploration of three different theological touchpoints that the Fibonacci Sequence offers.

College Algebra (Atlm), Shreyas Desai, Anthonia Ekwuocha, Noel Whelchel

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Twelve ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel

Mathematics and Statistics Faculty Publications and Presentations

Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and consensus --- discrete and continuous --- in …

Survey Of Calculus (Ga Southern), Paul Hadavas

Mathematics Grants Collections

This Grants Collection for Survey of Calculus was created under a Round Twelve ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Mathematical Modeling (Fvsu), Samuel Cartwright, Bhavana Burell

Mathematics Grants Collections

This Grants Collection for Mathematical Modeling was created under a Round Thirteen ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Quasilinearization And Boundary Value Problems At Resonance, Kareem Alanazi, Meshal Alshammari, Paul W. Eloe

Mathematics Faculty Publications

A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

Modeling Of Free Chlorine Consumption And Escherichia Coli O157:H7 Cross-Contamination During Fresh-Cut Produce Wash Cycles, Mohammadreza Dehghan Abnavi, Ali Alradaan, Daniel Munther, Chandrasekhar R. Kothapalli, Partha Srinivasan

Mathematics and Statistics Faculty Publications

Controlling the free chlorine (FC) availability in wash water during sanitization of fresh produce enhances our ability to reduce microbial levels and prevent cross-contamination. However, maintaining an ideal concentration of FC that could prevent the risk of contamination within the wash system is still a technical challenge in the industry, indicating the need to better understand wash water chemistry dynamics. Using bench-scale experiments and modeling approaches, we developed a comprehensive mathematical model to predict the FC concentration during fresh-cut produce wash processes for different lettuce types (romaine, iceberg, green leaf, and red leaf), carrots, and green cabbage as well as …

Moving Off Collections And Their Applications, In Particular To Function Spaces, Aaron Fowlkes

Theses and Dissertations

The main focus of this paper is the concept of a moving off collection of sets. We will be looking at how this relatively lesser known idea connects and interacts with other more widely used topological properties. In particular we will examine how moving off collections act with the function spaces Cp(X), C0(X), and CK (X). We conclude with a chapter on the Cantor tree and its moving off connections.

Many of the discussions of important theorems in the literature are expressed in terms that do not suggest the concept …