February 12-13, 2021

This international conference was for all faculty and students who are interested in using modeling to motivate, teach, and learn differential equations. SIMIODE EXPO 2021 is part of our Community of Practice in SIMIODE.

We post links to Slides and Videos from the talks here.

SIMIODE EXPO 2021 was a virtual online conference and included contributed paper sessions, minicourses, poster sessions, break out rooms, panel discussions, lounge areas, one-on-one conversations with instant ZOOM connection for “hallway” conversations, small group gatherings, and more – all but the smell of hot coffee!! This ability to converse was available from the start of the conference on Friday through Sunday morning.

  • Organizing Committee in Appreciation

    Rob Krueger, Concordia University, St. Paul MN USA
    Terrance Pendleton, Drake University, Des Moines IA USA
    Dina Yagodich, Frederick Community College, Frederick MD USA
    Jennifer Garbett, Lenoir Rhyne University, Hickory NC USA
    Vinodh Chellamuthu, Dixie State University, St. George UT USA
    Aditi Ghosh, University of Wisconsin, Whitewater WI USA
    Arati Pati, University of St. Thomas, Houston TX USA
    Tracy Weyand, Rose-Hulman Institute of Technology, Terre Haute IN USA
    Brian Winkel, SIMIODE, Cornwall NY USA

The conference program ran from 3:30 PM (Eastern US Time) through 9:00 PM on Friday, 12 February 2021, and from 10:00 AM through 7:00 PM on Saturday, 13 February 2021, with time for friendly conversations and meet-ups. All but a few sessions were recorded and available for Registered Attendees. There were 297 attendees. Registration costs were $25US for students and $45US for non-students.

The final schedule is shown here, along with (Slides) and (Video) which presenters have shared.

General Themes/Threads in Breakout Session Rooms

(R1) Room 1:
New to modeling
(R2) Room 2:
Actions, practice, and tips at and above the basics
(R3) Room 3:
(R4) Room 4:
Student focus and SCUDEM
(LR) Lounge Rooms 1-4:
Mingle and Meet

SIMIODE EXPO 2021 Conference Schedule

We had 30 minute minicourses with 5 minute break in areas of interest to those teaching differential equations with modeling as well as Breakout Sessions consisting of two 20 minute sessions with 5 minute break between sessions and 15 minute break before next session.

Day 1: 12 February 2021

Opening Ceremony Greeting All times are (Eastern US Time).     (Slides)     (Video)

(MR) 3:30 PM - 4:00 PM Introductions, SOCOCO Platform Orientation, Notions


4:00 PM - 5:20 PM Two 30 minute sessions with 5 minute break between sessions, 10 minute break before next session OR one 60 minute session with 10 minute break before next session.

  • (M-R1) Minicourse on Applications of Differential Equations
    Glenn Ledder, University of Nebraska, Lincoln NE USA   (Slides)     (Video)
    An Epidemiological Model for COVID-19

    Abstract: We develop a model for COVID-19 population dynamics by extending the standard SEIR model to allow for the subclassification of the Infectious class to separate out asymptomatic infectives, symptomatic infectives, and hospitalized infectives. The model is implemented with a suite of Matlab programs consisting of a function program that runs a simulation and driver scripts that plot simulation results, compare results with different parameter values, and track changes in outcomes as a function of a parameter. Students use the program suite to do virtual experiments to assess the effects of public health policies and community behavior on key outcomes such as simultaneous hospitalizations and overall death counts. The program drivers are designed to require only a bare minimum of coding by students so as to focus students' efforts on interpretation of results. The programs can also run on the online implementation of Octave. See COVID-19 Education Module for more details, including a spreadsheet implementation that can be used with non-science students.

    Brian Winkel, SIMIODE, Cornwall NY USA    (Slides)   (Video)
    Introduction to Differential Equations of Stochastic Processes

    Abstract: We describe efforts to introduce the mathematics of stochastic processes leading to an inifinite number of simple first-order differential equations. In this manner we obtain models of random processes such as number of V-2 rockets falling on London in WW II, number of no-hitters per season in Major League Baseball, particle emissions in nuclear physics experiments, police blotter growth, Poisson Process, and more.

  • (M-R2) Minicourse on extended topics - Laplace Transform, Control Theory,  Delays
    Kurt Bryan, Rose-Hulman Institute of Technology, Terre Haute IN USA    (Slides)    (Video)
    The Language of Laplace Transforms in an Introduction to Control Theory

    Abstract: Control Theory is ubiquitous in modern technology, and PID ("Proportional-Integral-Derivative") control is one of the most common classes of control algorithms. This type of control is often applied to systems that are governed by differential equations, and the analysis of PID control is made much easier by using Laplace transforms. I'll show a simple application that illustrates the mathematics involved, and how PID control makes a wonderful example of the utility of the Laplace transform that one can use in an undergraduate ODE course.

    Nsoki Mavinga, Swarthmore College, Swarthmore PA USA    (Slides)   (Video)
    Delay Differential Equations in Epidemiology

    Abstract: Many problems in epidemiology give rise to delay differential equations (DDEs). These are differential equations in which the current rate of change of the system depends not only on the current state but also on the history of the system; i.e. the system has memory. In this minicourse, we will discuss some key tools necessary to understand the applications involving DDEs. We will go through an example that illustrates the need and implementation of DDE in certain infectious diseases.

  • (M-R3) Minicourse on MathBio Wetlab Team Taught Course
    Becky Sanft, University of North Carolina, Ashville NC USA and Anne Walter, St. Olaf College, Northfield MN USA    (Slides)    (Video)
    Adventures in Co-Teaching a Data-Driven Modeling Course

    Abstract: Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities, written collaboratively by a mathematician and biologist, provides supporting materials for a course taken simultaneously by students majoring in the mathematical sciences and those in the life sciences. The text is designed to actively engage students in the process of modeling through a collection of case studies and wet labs connecting mathematical models to real data. This work emanated from a course that we co-taught at St. Olaf College. In this session we will provide a brief overview of this course and discuss key factors that supported the development of this course, continuing challenges, and how this model might be adapted at various institutions.

    Becky Sanft, University of North Carolina, Ashville NC USA and Anne Walter, St. Olaf College, Northfield MN USA   (Slides)   (Video)
    Case Study: A Model of Immunotherapy in Prostate Cancer

    Abstract: In this session we will guide you through a case study on immunotherapy in prostate cancer that is adaptable to a variety of teaching contexts. We will formulate a system of differential equations that describe the interactions among tumor vaccine cells, immune response, and prostate cancer cells. Data from a prostate-specific antigen (PSA) test will be used to estimate model parameters, and the model will be applied to explore vaccination schedules with the goal of stabilizing the number of tumor cells. Student participants will have the opportunity to engage in the modeling process and see the utility of models for understanding complex systems, making predictions, and identifying further questions. Faculty participants will see a condensed version of how this case study is used in the classroom.

  • (M-R4) Creative Thinking
    Mike Naylor, Matematikkbølgen, Vanvikan NORWAY    (Slides)    (Video)
    How Mathematics Inspires Art

    Abstract: We will start with a pattern arising from the solution to a puzzle, and see what happens when we take that pattern in all kinds of directions. The result? Art, music, poetry, sculpture, landscape, architecture and literature . . . all inspired by one mathematical pattern!

    Sofya Kerzhner, Baltimore City Community College, Owings Mills MD USA    (Slides)    (Video)
    Unlocking Creativity and Enhancing Flexible Thinking through Art

    Abstract:This experiential workshop is an interactive session focused on helping all participants, including students, faculty, and staff, unlock their creativity. After a demonstration, participants will dive into creating their own artwork. The workshop will expose participants to unforgettable art samples. All participants will discover their potential and unknown talents.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

Breakout Session 1 

5:30 PM - 6:15 PM Two 20 minute sessions with 5 minute break between sessions

  • (B1-MR) How do I cover the 'normal' stuff?
    Rosemary Farley, Manhattan College, Riverdale NY USA     (Slides)    (Video)
    Using a Modeling First Approach and Maple in a Traditional Differential Equations Class

    Abstract: Our differential equations course is required of every student in the School of Engineering. As a required course, there is a syllabus with topics that have to be covered in preparation for a cumulative final. All the traditional methods of solving differential equations by hand must be covered.

    We will explain how we incorporated the modeling first approach into our differential equations classroom while still covering the traditional topics required. We will explain how we managed to devote one-third of our class time to the use of a modeling first approach together with the extensive use of the computer algebra system Maple while still preparing students for a traditional common final. We will provide several examples of modeling problems from the SIMIODE scenarios that we adapted to our needs and time restrictions. We will give examples of how we created test questions that reflected ideas from our modeling first scenarios.

    Patrice Tiffany, Manhattan College, Riverdale NY USA (Slides)
    Modeling in Differential Equations in a Virtual Setting

    Abstract: Mathematical modeling is a critical tool in our world. Mathematical modeling is also a valuable pedagogical tool. The differential equations course, by its nature lends itself to be a modeling rich course. Must we abandon this modeling approach when we transfer to a remote platform? I do not believe so. We cannot transform the course by means of just a document camera. However, the course can be transformed to a viable remote experience. The new course may be more structured. The group work may be mirrored in break out sessions and the students’ work may be monitored more closely. This modeling unit introduces the separation of variables technique through group work. I use the SIMIODE scenario that models the spread of Ebola in western Africa. From there, the students go on to individual projects where they model the spread of COVID in individual states in the U.S. I will show how an in-class data driven modeling unit was transformed onto a remote platform.

  • (B1-R1) Student Activities - Sources, engagement, level, management
    Anna Davis, Ohio Dominican University, Columbus OH USA, Justin Greenly, Franciscan University, Steubenville OH USA, L. Felipe Martins, Cleveland State University, Cleveland OH USA, Paul Zachlin, Lakeland Community College, Kirtland OH USA    (Slides)    (Video)
    Our Ohio OER on ODE

    This talk will describe the materials compiled and created by the Ohio Open Ed Collaborative for an introductory course in ordinary differential equations in Ordinary Differential Equations Course Content. The materials consist of a dynamic adaptation of a classic text by William Trench using the interactive, web-based Ximera platform, and several hands-on student activities accompanied by dynamic worksheets. The authors will describe their experiences with using the text and hands-on activities in their classrooms.

    W. Y. Chan, Texas A&M University – Texarkana, Texarkana TX USA    (Slides)    (Video)
    Using Projects, Class Problems, and Other Resources in Teaching Mathematical Modeling

    Abstract: Mathematical modeling is an interesting and exciting course to teach. Students have a lot of flexibility to create their own models based on a set of physical rules and assumptions. Through this, they can practice their problem-solving skills. One of the challenges of teaching this course is to prepare for suitable teaching materials: exercises, projects, discussion topics, and other assessments. This course is quite different from other mathematics classes to fit the need of students with various academic backgrounds. To keep students’ participation, class problems and projects are assigned to assist students to understand the ideas behind building mathematical models and envision their applications. In this talk, we are going to share some experience and effort to instruct this course.

  • (B1-R2) Student Activities - Sources, engagement, level, management 
    Mark Nelson, University of Wollongong, Wollongong, New South Wales AUSTRALIA     (Slides)   (Video)
    Modelling using differential equations: undergraduate projects

    Abstract: The School of Mathematics and Applied Statistics at the University of Wollongong offers undergraduate students enrolled on mathematics related degrees four mechanisms to take an individual project supervised by a member of staff. Firstly, some students are allowed to take a project as an elective instead of a regular subject. Secondly, students can apply for a scholarship to undertake a summer project (this does not count towards the credit requirements for graduation). Thirdly, third-year students on many math related degrees are required to take a capstone project. Finally, students who stay on for a fourth year of undergraduate study (known as the honours year) are required to take a substantial project.

    In this presentation I will address questions such as these. “Where do I get the ideas for my projects from?" “How do I teach my students?" “How are student projects assessed?” “Should students undertake research as part of their project?”

    Christopher Scott Vaughen, Montgomery County Community College, Blue Bell PA USA     (Slides)    (Video)
    Solving the Rocket Equation with Mathematica and Kerbal Space Program

    Abstract: In this presentation we set up a differential equation to model a rocket launch, solve the equation with Euler's method using Excel and Wolfram Programming Lab and compare the results with a launch in the computer game Kerbal Space Program. We share a workbook I wrote and is inspired by the computer game Kerbal Space Program which itself is a model solar system.

  • (B1-R3) Reaching out to Cognate Area sources, courses, and colleagues
    Mentewab Ayalew, Spelman College, Atlanta GA USA    (Video)
    Integration of biology, mathematics, and computing in the classroom through the creation and repeated use of transdisciplinary modules

    Abstract: The integration of biology with mathematics and computer science mandates the training of students capable of comfortably navigating among these fields. We address this formidable pedagogical challenge with the creation of transdisciplinary modules that guide students toward solving realistic problems with methods from different disciplines. Knowledge is gradually integrated as the same topic is revisited in biology, mathematics, and computer science courses. We illustrate this process with a module on the homeostasis and dynamic regulation of red blood cell production, which was first implemented in an introductory biology course and will be revisited in the mathematics and computer science curricula.

  • (B1-R4) Student Career Path - Post Baccalaureate
    Kim Shurupoff, Elizabeth Olson, Sara Taylor, National Security Agency, Fort Meade MD USA    (Video)
    National Security Agency Employment Opportunities for Mathematicians

    Abstract: Mathematics can be more than just a subject in school; it can be a career. The government is the number one single employer of mathematicians in the country. Many of those mathematicians end up at the National Security Agency (NSA), where they find careers in research, cybersecurity, and cryptanalysis. This talk will be an introduction to the roles of mathematicians at NSA, followed by a Q&A session.

    The speakers will also be available in the Poster Session to chat about full-time and summer internship opportunities, what it's like to work at the NSA, and answer questions.

    Marco Martinez, North Central College, Naperville IL USA     (Slides)    (Video)
    Actuarial Science Opportunities

    Abstract: If you like math, are skilled with numbers, and are interested in a fulfilling and rewarding career, then a career as an Actuary might be for you! Actuaries are leading professionals who manage today's complex risks using a combination of strong analytical skills, business knowledge, and understanding of human behavior. A career as an Actuary is hard to beat in almost every category: work environment, employment outlook, job security, growth opportunity, salary, and much more. If you want to be an actuary, start preparing now! In this talk we will describe how you can become an actuary.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

6:45 PM - 7:15 PM Keynote Speaker

Brian Macdonald, Statistics and Data Science, Carnegie Mellon University, Pittsburgh PA USA     (Slides)     (Video)
An overview of data science problems in the sports industry

Abstract: We give an overview of how mathematics, statistics, and data science can be used in the sports industry for teams, leagues, and media companies, as well as how sports analytics problems can be used in education. We discuss metrics used by a team’s front office, coaching staff, and scouting department to help them make better and faster decisions, and used by media organizations to analyze those decisions. We also discuss the kinds of data and optimization problems that are encountered on the business side of an organization in departments like sales and marketing. We will finish by discussing resources for educators and students and learning opportunities for students in the area of sports analytics. Brian Macdonald is the former Director of Sports Analytics at ESPN, Bristol CT USA.

7:30 PM - 9:00 PM After Dinner Relax

  • MathBowl  conducted by Paul Fonstad, Franklin College, Franklin IN USA.    (Video)
    Download and print out MathBowl Questions and Response Sheet   for an enjoyable time.
  • Breakout Social Groups - opportunities to gather for informal discussions on issues of interest 
    (R1) Tracy Weyand, Rose-Hulman Institute of Technology Terre Haute IN USA
    Discussion group for faculty on how to get started with modeling in coursework.
    (R2) Ian Ebert, San Jacinto College, Pasadena TX USA
    Discussion group for students on sharing experiences and reactions to using modeling in learning mathematics with modeling in coursework.
    (R3) Brian Winkel, SIMIODE, Cornwall NY USA     (Slides)
    Discussion group on where to get ideas and sources for modeling activities.

9:00 PM - 11:00 PM Opportunities to visit in small groups and reunite with friends

Day 2: 13 February 2021

Opening Ceremony All times are (Eastern US Time)     (Slides)    (Video)

10:00 AM - 10:30 AM Introductions, SOCOCO Platform Orientation, Notions

Breakout Session 2 

10:30 AM - 11:15 AM Two 20 minute sessions with 5 minute break between sessions

  • (B2-R1) Modeling before, during, and after mathematics AND Contributions of the CODEE Community
    Christopher Brown, California Lutheran University, Thousand Oaks CA USA
    Best Practices of Data Analysis in the Differential Equations Course

    Abstract: In this talk I'll discuss my experiences bringing best practices of data analysis, especially predictive modeling frameworks, to a modeling-centric Differential Equations course. The key issue of interest is generalizability: analyzing model performance on data the model was not trained on. I'll introduce the notions of a train-test framework and cross-validation, and discuss how these intersect with model selection and refinement in practice. I'll also discuss avenues for introducing these topics in the differential equations course, to audiences with and without experience with coding.

    Beverly West, CODEE, Ithaca NY USA     (Slides)    (Video)
    CODEE — the other, more senior, differential equations group

    Abstract: Description of the historical and current work of the CODEE community including the CODEE Journal. We offer several of the presenters very favorite examples that got students really engaged.

  • Assessment and Evaluation of Learning Modeling - We will try again next year.
  • (B2-R3) Video Production Tools and Experiences
    Trefor Bazett, University of Victoria, Victoria BC CANADA     (Slides)    (Video)
    Online Classes vs YouTube: Opportunities and Challenges Engaging a Global Audience

    Abstract: When I first used YouTube to host the class videos for a small online class, I never imagined they would end up being watched millions of times globally. This created tremendous opportunities for mathematical outreach and engagement at a large scale. In this talk I am going to share my journey in the video medium, what I have learned about producing engaging videos for a larger audience, and what I have learned that I have taken back and included in my own teaching for my own classes. I will share my philosophies on creating videos, how to effectively include them in the pedagogical design of a course, and some practical tips to getting started in the video medium.

    Dina Yagodich, Frederick Community College, Frederick MD USA   (Video)
    Teaching by video - even post-pandemic

    Abstract: I have been teaching online since 2009, using a variety of tools to provide lecture content to classes. Whether you have great editing tools such as Camtasia or just a simple cell phone camera, it's possible to make engaging effective lecture videos for mathematics courses. In addition to the how, I'll speak about the why -- delivering content, engaging students, and where it fits into a course, both in fully online courses as well as face-to-face courses.

  • (B2-R4) Student Publication and Research Experiences / Student Career Path - Post Baccalaureate
    Chris McCarthy, Borough of Manhattan Community College – CUNY, New York NY USA    (Video)
    Student Research Experiences at a Two-year College

    Abstract: In this talk I will relate my experiences mentoring a variety of student research and honor's projects in the two-year college setting. Most projects involve differential equations modeling and range from the very simple, to the relatively advanced.

    Vinodh Chellamuthu and Noelle West, Dixie State University, St. George UT USA    (Video)
    Modeling the Effects of Passive Immunity in Birds for the Disease Dynamics of West Nile Virus

    Abstract: West Nile Virus (WNV) is a vector-borne disease that circulates among birds, and has spread across the world, causing several human infections and deaths. We developed a mathematical model to investigate how passive immunity and vertical transmission interact with the disease dynamics of WNV. Furthermore, this project was completed by an undergraduate student with the assistance of a faculty mentor. Our presentation will focus on how we created the model and how to pursue academic research at the undergraduate level.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

Breakout Session 3 

11:30 AM - 12:15 PM Two 20 minute sessions with 5 minute break between sessions

12:45 PM - 1:15 PM Keynote Speaker

Matt Boelkins, Grand Valley State University, Allendale MI USA and Editor PRIMUS     (Slides)     (Video)
More Linear Algebra

Abstract: In 2001, Gilbert Strang of MIT wrote the short essay "Too Much Calculus" in which he noted the imbalance of the mathematics curriculum: 3 or more semesters devoted to calculus, with only 1 semester for linear algebra. While calculus is awesome and important -- playing a key role in differential equations particularly -- linear algebra is arguably even more important, especially in the 21st century. Indeed, linear algebra is mathematics that makes the digital world work.

In this talk, we'll look at some examples that demonstrate the incredible importance of linear algebra in our world today, see some accessible examples of how computational technology opens doors to seeing the power of the subject, and advocate for two parallel positions: for students, however much linear algebra you have learned, learn more; for faculty, however much linear algebra you teach, teach more. Along the way, we'll share some free and open resources for students and faculty to use in pursuit of these goals.

1:30 PM - 2:15 PM Poster Session

Presenter, Title, Abstract
          Posters Detailed

Kim Shurupoff, Elizabeth Olson, Sara Taylor, National Security Agency, Fort Meade MD USA
Title: Network with NSA Cryptanalysts
Abstract: National Security Agency (NSA) representatives with backgrounds in mathematics will be available to chat with you about full-time and summer internship opportunities, what it's like to work at the NSA, and answer your questions.

Kate E. Johnson, University of California Davis, Davis CA, USA and Paul Johnson, Biostatistical Software Development, Clinical SAS Programmer
Title: Nonlinear Methods for the Reference Value on the Percent Lysis Axis
Abstract: Parameter estimates in cytotoxicity values are obtained from sets of natural killer cell values obtained for input 100%, 50%, 25%, 12.5% and 6.25% cytotoxicity levels. A reference value on the percent lysis axis is selected to compare curves using the horizontal separation between curves at that reference point. The SAS NLIN (SAS/ Stat, 2018) procedure is used for the estimation. The procedure uses numerical methods, such as Gauss Newton or Marquardt, to estimate the parameters of a nonlinear model by least squares. The first derivative matrix is the matrix of the first partial derivatives of the mean function f with respect to the model parameters. The nonlinear model is approximated by a series of linear models. The regressor matrix is the first derivative matrix. The parameter estimates are improved upon iteratively from a starting value, input by the user. Gender and slope differences are examined for the subjects' reference values on the percent lysis axis.

William Clark, Dixie State University, St. George UT USA
Title: Effects of Temperature on Population Mobility and Spread of Covid-19
Abstract: The Covid-19 outbreak has caused a global pandemic and compelled many to search for a deeper understanding of how ecological and sociological factors influence the disease's spread. Many governmental leaders have mandated social distancing and other regulations on everyday activity to stop the spread of the disease. Many studies have developed models and shown the effects of social distancing, the efficacy of masks, and the impact the ambient temperature has on the number of cases reported. Yet numbers continue to rise despite the regulations being imposed, which has led researchers to ask why, and what other factors contribute to the spread of infections? We propose that a significant cause of the recent spikes in positive cases has been the mobility of the population, most notably the returning of students in school and the drop in temperature occurring near the end of the year. This study aims to identify the effect that temperature has on the mobility of a population and the spread of Covid-19. We developed a mathematical model presenting the dynamics of positive Covid-19 cases in the state of Utah with the incorporation of social distancing, mask efficiency, and the relationship between temperature and the rate of infection. The nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used for the numerical solution of our proposed model. Our results suggest that the temperature effect has on a population's mobility plays a significant role in the Covid-19 disease dynamics and the attempt to mitigate the spread of the disease.

Brandon Payne, Dixie State University, St. George UT USA
Title: A Mathematical Model of COVID-19: Efficacy of Vaccination with Heterogeneous Populations
Abstract: Infections from the novel coronavirus disease 2019 (COVID-19) remain superfluous as the disease continues to spread profusely across the world. Currently, there is no available vaccine to protect against COVID-19. As scientists work to develop a vaccine, our goal is to explore scenarios for different levels of vaccine-effectiveness and varying proportions of vaccinated-populations in order to demonstrate the effectiveness of a vaccine in mitigating the spread of COVID-19. We develop a mathematical model to analyze the disease dynamics of COVID-19 in relation to vaccine-effectiveness. Furthermore, we performed a data fitting algorithm to estimate parameters within the model to best resemble current infection trends using data from the Center for Disease Control and Prevention (CDC). We incorporate a vaccinated population and demonstrate the mitigation of COVID-19 with the introduction of a vaccine. Our simulation results determine possible best-case scenarios at varying degrees of vaccine-effectiveness and proportions of vaccinated-populations. Moreover, to account for the disease’s varying infection and mortality rates based on an individual’s age, we further partition the population by age groups to determine which age groups are most vital to vaccinate. Our simulation also identifies the minimal required vaccine-efficacy for a given proportion of vaccinated individuals.

Mishal Ali, DePauw University, Greencastle IN USA
Title: Analysis of Dynamic Systems for the Synthesis of Phenobarbital
Abstract: The use of mathematical methods for the analysis of chemical reaction systems is one of the useful tools. Phenobarbital (a barbiturate medication also called phenobarb) is a prescription drug used to control seizures, relieve anxiety, treat epilepsy (in some countries), and prevent withdrawal symptoms in people dependent on other barbiturate drugs. We followed the strategy employed in the paper [1] but approaches it with different mathematical approaches: matrix analysis [2] and ODE system [3] which will help us understand the chemical stoichiometry of these synthesis reactions.


Justin Zhu, Harvard College, Cambridge MA USA
Title: Modeling Time-Varying Treatment Effects with Zero-Inflated Data
Abstract: Gaussian Process (GP) models have gained popularity for its flexibility to handle correlation among data sampled from distributions in the exponential family. The correlation frequently characterizes time-dependent data, such as step count data across different time horizons. In this project, we plan to analyze the effectiveness of Gaussian Process on zero-inflated Poisson (ZIP) step count data. To do so, we formulate the parameters, likelihood function, and predictive posterior distribution characterizing the Gaussian Process. A flexible GP should be able to successfully model any mixture of generative distributions from the exponential family and zero- inflated data. By being able to model the underlying generative distribution, we can better identify the time-varying treatment effect of mobile health interventions for step count data.

Alice Xu, Seven Lakes High School, Katy TX USA; Ruoxian (Susan) Huang, Eastside Catholic High School, Sammamish WA USA; and Raaghav Malik, Columbus Academy, Gahanna OH USA
Title: A Mathematical Model Regarding ge in Preferences of Refugee Settlements
Abstract: Where cultures meet, there is bound to be conflict to some extent. This especially applies in the case of refugees grouped together when seeking asylum, with different styles of life, socialization, and conflict resolution meeting in one place. This paper focuses specially on three types of conflict resolution(negotiation, mediation, and arbitration) and constructs a differential equation model to study how the interactions between populations cause the number of people following each resolution method to shift. It was found that when there is no existing outside authority or environmental bias towards a resolution method, the method with the greatest number of followers will also be the one to take over the final population. However, in the presence of an outside force promoting or discouraging certain methods, although some groups will be given advantages over others, the final outcome is also still partially under the influence of the initial population. Outside of stable equilibria representing situations where one method ends up taking over the entire population, we also found certain unstable equilibria that carry key information about the basins of attraction of the stable equilibria.

Panel Discussions

2:30 PM - 3:15 PM

  • (P-R1) Faculty Development Programs
    Guangming Yao, Clarkson University, Potsdam NY USA     (Slides)     (Video)
    Initiating Projects Elements for Students

    Abstract: I taught Differential Equations for a few years when I first started teaching at Clarkson University. We initiated projects elements for students in the course, which was a great experience. I would like to share, but more importantly to learn what other faculty's ideas and suggestions on improving my teaching on modeling with differential equations.

    Elizabeth Roan, Texas State University, San Marcos TX USA     (Slides)     (Video)
    Modeling in the Classroom from Different Perspectives

    Abstract: I interviewed 10 different STEM faculty (3 psychologists, 2 anthropologists, 3 geologists, and 2 economists) and asked about their conception of modeling and its prevalence in the classroom. I would like to share their stories and discuss what and how different aspects of these stores align with other faculty' exps. erience

  • (P-R2) Assessment and Evaluation of Student Success/Gains
    Jennifer Czocher, Texas State University, San Marcos TX USA     (Slides)
    What Can We Learn About Students That Grades Won't Teach Us?

    >Abstract: Universities and students expect that we use grades to communicate an assessment of students' learning in a course. So, naturally, there is an expectation that good innovations to curriculum and instruction should be measurable as grade increases. But that is very rarely the case! Not only are students busy, but grades are such a crude and inaccurate measure of benefits to students that improved pedagogy may not translate directly to better grades. In this talk, I'll give a very brief and broad overview of measures we can use to model students' gains even, and especially when, grades just don't show what we teachers see students getting out of a course.

    Robin Terrell Taylor, rTRES Consulting, Nashville TN USA     (Slides)
    Evaluation as a Tool for Assessing the Effectiveness of Teaching Interventions

    Abstract: Assessment and evaluation are processes of collecting data to inform understanding of changes, e.g., knowledge gains, attitudes, behaviors, beliefs, skills, that occur as the result of some interventions, such as new curricular techniques or scaffolding of new skills. In this panel discussion I will outline how evaluation methods can be utilized to understand program effectiveness with examples of best practices and lessons learned gained through my experience working as an evaluator of STEM education and workforce development programs.

  • (P-R3) Introduction of SIMIODE Online Text - Meet the Author
    Kurt Bryan, Rose-Hulman Institute of Technology, Terre Haute IN USA     (Slides)     (Video)
    Differential Equations: A Toolbox For Modeling The World

    Abstract: A discussion and presentation of the development, approaches, ideas, models, and features of SIMIODE's new online text which will be made available immediately to all conference attendees before the meeting. See details at Differential Equation: A Tool for Modeling the World.

  • (P-R4) SIMIODE and SCUDEM Benefits: Where to Start?
    Vinodh Chellamuthu, Dixie State University, St. George UT USA    (Video)
    ASaP SCUDEM: Advancing Students as Practitioners through SCUDEM

    Abstract: In this session, I will share my experiences recruiting and coaching students to participate in the SCUDEM. Furthermore, I will also share my experiences to what extent teaching a Differential Equations curriculum, using SIMIODE materials changed my students' perspective towards STEM education.

    Blain Patterson, Virginia Military Institute, Lexington VA USA     (Video)
    Recommendations from an Early Career Mathematician

    Abstract: Blain recently earned his PhD and started working at Virginia Military Institute in the fall of 2019. One of the various opportunities he was given during this time was to get involved with SIMIODE and SCUDEM. Since then, Blain has published modeling scenarios for SIMIODE and coached teams for SCUDEM. In this session, Blain will share his experiences as an early career mathematician and discuss the benefits of getting involved in these programs.

    Sarah Patterson, Virginia Military Institute, Lexington VA USA     (Video)
    Preparing Students to Participate in SCUDEM>

    Abstract: I required students in my Elementary Differential Equations class to participate in the SCUDEM competition in 2019 and virtually in 2020. I plan to discuss preparing students for the competition using the SIMIODE resources in /font>

  • (P-MR) Faculty Dynamics Research Opportunities - Primarily Undergraduate Institutions
    Kimberly Ayers, Carroll College, Helena MT USA; Han Li, Wesleyan University, Middletown CT USA; David McClendon, Ferris State University, Big Rapids MI USA; Andy Parrish, Eastern Illinois University, Charleston IL USA: Ami Radunskaya, Pomona College, Claremont CA USA     (Video)
    Support for Dynamics Research at Primarily Undergraduate Institutions

    Abstract: Little School Dymamics is a research community, sponsored by American Institute of Mathematics and the National Science Foundation, which stimulates, supports, and promotes dynamics research at Primarily Undergraduate Institutions (PUIs). We intend to accomplish this through a variety of activities constructed with the unique demands of our work environment in mind, ranging from colloquia to small research groups, and including ample opportunities for building new professional networks. Full participation is open to any mathematician whose research interests include dynamical systems and whose home institution is a PUI; adjunct and teaching faculty at other institutions are likewise encouraged to apply. Keeping in mind the varying obligations of faculty at PUIs, the organizers welcome, encourage, and value participation at any and all levels. Bound by a common discipline and shared experiences, we aim to develop a pool of talent and expertise on which participants can draw to further their own objectives and pursue new interests.

    In this session, we will do a brief overview of what the community will look like, followed by more informal discussion and questions and answers.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

Breakout Session 4 

3:30 PM - 4:15 PM Two 20 minute sessions with 5 minute break between sessions>

  • Working the room and engaging in group active learning - We will try again next year.
  • (B4-R2) Accessibility Issues - What to know, look for, offer, and learn about
    Amee Evans Godwin and Cynthia Jimes, Institute for the Study of Knowledge Management in Education (ISKME), Half Moon Bay CA USA     (Slides)     (Video)
    Accessibility of Digital Resources: A Framework for the Evaluation of STEM OER

    Abstract:This session will introduce participants to key issues related to accessibility of openly licensed digital curriculum. With the aim to address not only equitable access, but also use of resources by all learners, ISKME (Institute for the Study of Knowledge Management in Education), in partnership with SERC, an advisory group, and set of STEM faculty, has developed the Accessibility of STEM Open Educational Resources (OER) Guidebook. The guidebook seeks to support OER curators and authors in evaluating, creating, and describing open STEM content intended for their courses. The session will discuss the framework’s alignment with Universal Design for Learning guidelines, with W3C’s POUR framework, and with the principles of open education.

    Amee Evans Godwin and Cynthia Jimes, Institute for the Study of Knowledge Management in Education (ISKME), Half Moon Bay CA USA     (Slides)     (Video)
    OER Accessibility Framework - Applications for STEM

    Abstract: This session will focus on a walk-through of accessibility criteria, definitions, tips and practices, included in ISKME’s new framework and guide, Accessibility of STEM OER Guidebook, that are specifically related to STEM, and supporting authors and curators of open STEM content. The guidebook offers an extension of the P.O.U.R. framework (Perceivable, Operable, Understandable, Robust), called P.O.U.R. + STEM. The session will demonstrate how STEM open educational resources (OER) may be evaluated using the guidebook, and tools for remediating accessibility challenges that are identified through the evaluation process.

  • (B4-R3) Data sources - collecting, finding, real time, and incorporation
    Terrance Pendleton, Drake University, Des Moines IA USA     (Video)
    Show Me the Data--Examples (and Resources) for Data-Driven Modeling

    Abstract: In this talk, we demonstrate through a number of modeling scenarios how data can be used to drive the creation of mathematical models. We also discuss how data can serve as a tool for validating these models. Emphasis will be placed on locating good data sources for which mathematical models can be developed and tested.

    Rikki Wagstrom, Metropolitan State University, Saint Paul MN USA     (Slides)     (Video)
    Simulation Modeling Project in Advanced Mathematical Modeling Course

    Abstract: This presentation discusses a project that was first assigned in our team-based Advanced Mathematical Modeling course in Fall 2019. The context for the project is the investigation of queues in a local coffee shop/café associated with the café’s front-end operations. The course instructor collected initial data for the project, including arrival times of parties, party size, wait times associated with the cashier, cashier service times, and barista service times. Additional data pertaining to food and beverage ordering preferences, was later synthetically generated from basic information provided by the owner of the café. Provided with these data sets, student teams used Excel to develop and implement Monte Carlo simulation models to investigate queue formation and wait times associated with the cashier and barista. Student teams disseminated their findings in a report and poster presentation.

  • (B4-R4) Student Career Flow - Post PhD - II
    Rich Laverty, The Boeing Company, Ridley Park PA USA     (Slides)     (Video)
    The Finite Element Method in School, in Industry, and One Example of a Career in It

    Abstract: Few mathematical techniques have had greater impact on our daily lives than the Finite Element Method (FEM). It has been essential to the progress of our entire engineered world, from the dramatically powerful rockets that put man and machine into space to the mundane packaging that protects what we buy while in transit. At its core, the method is simply a way to approximate solutions to differential equations. And, as with most successful numerical methods its strength is the simplicity of its foundation, allowing it to be adapted to a large variety of problems.

    In universities, the Finite Element Method is taught regularly in Mathematics and Engineering departments, with predictable differences in emphasis, but still touching on the same essential tenets. Its use in industry is through large commercial software packages that efficiently create, solve, and post-process mathematical models. In this talk I want to highlight my experience with the FEM, as a student and teacher of the first, and only, class most professional users of the FEM will take. And contrast that with the requirements of using the method professionally with commercial software. Finally, I will bring in my personal experience in a rather narrow, but exciting corner of the FEM community.

    Jeffrey M. Alden, General Motors (GM), Ypsilanti MI USA     (Slides)     (Video)
    Analytics at GM, Briefly

    Abstract: A brief overview of an analytics career at GM with an example of using math to increase plant throughput with award winning results.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

Breakout Session 5 

4:30 PM - 5:15 PM Two 20 minute sessions with 5 minute break between sessions

  • Grading and Evaluation - Experiences, Examples, and Issues  - We will try again next year.>
  • (B5-R1) Modeling in other courses and levels - Track 1
    (A1) Leszek Gawarecki, Kettering University, Flint MI USA     (Slides)     (Video)
    Adventures in the "Islands" - Enhancing Student Engagement in Teaching Statistics

    Abstract: The factors for enhancing student engagement frequently identified are active and problem-based learning as well as real-life experience relevant to students' interests. The importance of using real data in teaching statistics has been repeatedly emphasized and its importance is growing. However, data collection, as part of a student project, faces serious practical problems. It is time-consuming, may require access to equipment, or raise ethical issues.

    Sometimes collected data is not even suitable to analyze the original research problem but making new observations is no longer possible. One solution is to retrieve already existing data, e.g., from the US Census Bureau or Github.

    We follow a more active and holistic approach of using a virtual environment, the "Islands", where students can design and perform experiments on inhabitants and observe their environment. The virtual population is dynamic and evolves according to mathematical models. It also exhibits surprisingly rich features. We propose practical recommendations for others who choose similar projects.

    (A2) Arati Pati, University of St. Thomas, Houston TX USA and Kehinde Ladipo, Humber College, Toronto Ontario CANADA
    Numerical Solution of Arterial Blood Flow

    Abstract: The normal human heart is a strong muscular two stage pump which pumps continuously through the circulatory system. It is a four chambered pump that controls blood through a series of valves in one direction. Blood flow through a blood vessel, such as vein and artery can be modeled by Poiseuille law which establishes a relationship between velocity of blood and the radius of the vessel. Our goal here is to solve the differential equations numerically by replacing with algebraic equations to obtain approximate solutions of velocity. In this talk, we will walk through the development of the simulation procedure to visualize how blood flows in steae dimension.

  • (B5-R1) Modeling in other courses and levels - Track 2
    (B2) Muhammad Nazam, Allama Iqbal Open University, Islamabad PAKISTAN     (Slides)     (Video)
    Existence Theorems and Their Applications

    Abstract:Existence theorem states the existence of an object, such as solution to a problem or equation. Generally it does not tell about the objects explicitly nor give a rule to find out such object. Existence theorems can be categorized into three parts.

    Type1: existence theorems that along with existence of an object or solution also provide a rule to find it out.

    Type 2: existence theorems that are settled by nonconstructive proofs which simply deduce the necessity of solutions without indicating any method for determining them.

    Type 3: existence theorems whose proofs depend on iteration processes to show existence of the objects.

    We shall discuss several examples and applications of such theorems.

  • (B5-R3) Technology use - depth, use, type,  in discovery, in analysis - Track 1
    (A1) Tim Lucas, Pepperdine University, Malibu CA USA     (Slides)    (Video)
    Using Mobile Apps to Enhance Learning in Differential Equations

    Abstract: It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. A key for these students to understand mathematical models that incorporate differential equations is visualizing slopefields, phase planes and solutions. Slopes is a mobile application with an intuitive interface, designed to visualize solutions to differential equations and support active learning in the classroom. Slopes is currently available for iPad, iPhone and Android phones, which are highly portable and feature larger touch screens that allow students to view and manipulate content easily. To study the possible benefits of the app, we implemented group activities using Slopes into an ordinary differential equations class, conducted observations and focus groups, and examined final poster projects on modeling topics. We found that students used Slopes to visualize solutions, aid in discussion and cooperation, and demonstrate understanding of differential equations concepts.

    (A2) Andrew Perry, Springfield College, Springfield MA USA     (Slides)    (Video)
    Numerical Solution of Ordinary Differential Equations Using Free Software

    Abstract: We will discuss some basic commands and techniques that might be used to find numerical solutions of ODE's using software that's available free of charge and relatively straightforward to use. This will be a non-technical introductory talk suitable for instructors or students of an introductory class in Differential Equations. We will consider Wolfram Alpha and R, as well as possibly other software.

  • (B5-R4) Student and coaches Sharing their SCUDEM Experiences
    Rob Krueger, Concordia University, St. Paul, St. Paul MN USA     (Slides)    (Video)
    Father and Son Venture into the Unknown

    Abstract: Even though I have been working with the SIMIODE community for the last several years, this was the first opportunity I had to coach a SCUDEM team. It turns out my son is a mathematics major at my school and participated on a team. We explore our first DEM.

    Anthony Stefan, Florida Institute of Technology, Melbourne FL USA     (Slides)    (Video)
    Participating in SIMIODE Challenge as Student, Coach, and Host (On Campus and Virtual)

    Abstract: We describe participation as part of a SCUDEM II 2018 team from Florida Southern College, Lakeland FL USA, and discuss the greatest takeaways from our participation: as to how we selected our problem, worked as a team with our different backgrounds, and developed our modeling approach. Furthermore, we share the opportunities our participation in SCUDEM has provided to us since SCUDEM II as professionals. Such opportunities include presentations, a publication, being a SCUDEM/SIMIODE intern for the Summer of 2020, graduate school, and our careers, and being a coach. Our internship was funded by SGCI and provided SIMIODE/SCUDEM with interns that were tasked with projects to develop and enhance future directions of SIMIODE and SCUDEM. We conclude by discussing what it is like to be a coach for SCUDEM, our method for organizing coaching materials (what resources and activities we use), and how to promote SCUDEM with its new virtual structure.

  • B5-MR) (B1) Students Sharing their SCUDEM Experiences and (B2) Technology use - depth, use, type,  in discovery, in analysis - Track 2
    (B1) Henry Bae, Chenming Zhen, and Miles Pophal, Florida Institute of Technology, Melbourne FL USA     (Slides)    (Video)
    Our SCUDEM V Experience and Model for "Spinning A Wheel"

    Abstract: For the SCUDEM V 2020 virtual challenge, we received outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations as well as our numerical results by applying the Heaviside equation for the swing motion of the bird. We further discuss the overall limitations and future work of the model we constructed, as well as the organization and experience we had oM V 2020.

    (B2) Boyan Kostadinov, New York City College of Technology, CUNY, Brooklyn NY USA     (Slides)    (Video)
    Fitting the SIRD Model Using Real COVID-19 Data with R and RStudio

    Abstract: We use real COVID-19 data to fit the SIRD model parameters and solve the system of differential equations. We use the R programming environment with RStudio to create an interactive R Markdown notebook and generate a PDF report with the project narrative, LaTeX expressions, code, numerical analysis, and results.

  • (LR) Lounge Rooms 1-4: Mingle and Meet

Closing Ceremony and Dinner    (Slides)    (Video)

5:30 PM - 7:00 PM Closing and Farewells - Future - Dinner with friends

Collaboration and Visiting Opportunities

7:00 PM - 11:00 PM Opportunities to visit in small groups and reunite with colleagues

The ability to have conversations was extended to Sunday morning Eastern US Time.


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