From LaTeX to RMarkdown: Communication and Collaboration Tools for the Mathematical Sciences, presented by Omar De La Cruz Cabrera, Kent State University; Part A, Wednesday, 4:00–6:00 pm, and Part B, Friday, 4:00–6:00 pm. Producing high quality documents is part of everyday life for the mathematician and statistician, be it for research, teaching, and even for writing letters. We will introduce participants to tools that will allow them to:

• Simplify document production without sacrificing quality
• Streamline their research and collaboration process
• Improve the dissemination of their work to the public through interactivity
• Easily and conveniently create Reproducible Research documents
• These tools range from classics like LaTeX to new like RMarkdown and Plot.ly.

Topics included in this course are:

• Introduction to LaTeX
• Brief introduction to R (computational environment)
• Including R computations in LaTeX: Sweave and Knitr
• Simplifying: Markdown and RMarkdown
• Bibliographies and reference management
• Slideshows and presentations
• Interactive documents (interactive plots and graphics, Shiny apps)
• Version control, collaboration, and dissemination (using git and others)
• Useful cloud-based services (including Overleaf, Github, Zotero, AWS and others)

Inclusive Active Learning in Undergraduate Mathematics, presented by Nancy Kress, University of Colorado at Boulder, Rebecca Machen, University of Colorado at Boulder, Wendy Smith, University of Nebraska-Lincoln, and Matt Voigt, Clemson University; Part A, Wednesday, 9:00–11:00 am, and Part B, Friday, 9:00–11:00 am. This PEP will support participants to advance their use of active learning instructional practices with explicit attention to approaches that support inclusive learning communities. Promotion of positive experiences for all students, especially those who identify as members of underrepresented groups in mathematics, will be central throughout this PEP. This PEP will address early undergraduate mathematics course structures, policies, instructional practices and methods of assessment with emphasis aligned to the needs and interests of the participants. The course will be welcoming, appropriate and applicable for all participants interested in using active learning instructional practices including those considering active learning for the first time and those who have been using active learning approaches in their classes for many years. This PEP will be organized around the premise that we can all learn from each other and we all have experiences that, when shared, contribute to the learning of others in the group. Activities in this Inclusive Active Learning PEP will include the following:

• Opportunities to grapple with, discuss and role play responses to a variety of scenarios that describe challenging situations or potentially difficult conversations that can arise in active learning classrooms
• Opportunities to share, discuss and problem solve around challenges, concerns and/or prior experiences generated by session participants
• Opportunities to consider existing examples of teaching math for social justice and to adapt, design, develop and share lessons and materials for use in our own classrooms

Participants will leave with example scenarios that can be used to facilitate conversations with other members of their departments, new experiences related to navigating challenging situations and conversations that can arise in undergraduate mathematics classrooms, and lesson plans that can be used in their own classes. This will draw off of experiences and research results from two NSF funded IUSE projects. The Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project is currently conducting supplementary funded work focused on equity in active learning instructional contexts that includes facilitating a two-semester biweekly equity workshop with participants who are members of the SEMINAL research project. The Characteristics of Equitable Mathematics Project (CEMP) is studying the nature of instruction, student experiences and departmental contexts in mathematics departments identified as promoting especially positive experiences for women and students of color. The experiences and results gained from these projects will inform the design of this PEP, and empirical research results will be shared with participants.

Mathematical Modelling Of Real-World Infectious Disease Epidemics – An R Based Hands-On JMM PEP, presented by Ashok Krishnamurthy, Mount Royal University; Part A, Wednesday, 4:00–6:00 pm, and Part B, Friday, 4:00–6:00 pm. Mathematical modelling of infectious diseases is an interdisciplinary area of increasing interest. In this PEP we will describe and illustrate participants an understanding of infectious diseases and their value for public health. The course will be based on our real-world experience of tracking the spatial spread of measles in pre-vaccine England and Wales (1944-1966), Ebola in the Democratic Republic of Congo (2018-2020), and COVID-19 in Nigeria (2020-2021) using integro-differential equations.

By the end of this PEP, participants will be able to:

• know how to build a compartment model of epidemiology (for ex: SIR, SEIR, SEIRD, SVEIRD etc.) to track the spatial spread of an infectious disease outbreak.
• adopt the two basic ingredients for spatiotemporal tracking of infectious diseases via Bayesian data assimilation methods; (1) a mathematical model (to reproduce the process of interest) (2) incorporate observations (incidence, prevalence, recovery, and death data) to update epidemic state estimates
• apply ideas to a realistic scenario involving tracking COVID-19 in a particular country.

This JMM PEP assumes a basic understanding of compartmental models of epidemiology. We will primarily be using R program and the RStudio IDE. This interactive PEP will be delivered using real-world data and practical simulation exercises using the free, open-source software R. No prior detailed knowledge of modelling infectious diseases or epidemiology is required. Some amount of programming will be involved (students with complementary skills will be encouraged to form teams) and basic understanding from Calculus, Linear Algebra and Introductory Statistics may be beneficial.

Recruiting and Mentoring Majors in the Mathematical Sciences, presented by Jason Aubrey and William Y. Velez, University of Arizona; Part A, Thursday, 8:00–10:00 am and Part B, Saturday, 9:00–11:00 am. In this PEP, the organizers will explain the model of intensive advising and recruiting of math and data science majors at the University of Arizona. These activities are organized under the umbrella of a “Math Center.” A description of the Math Center at the University of Arizona will be given, listing the duties/ activities/ responsibilities of the Math Center and how it is funded. We will then explore how participants can implement similar activities in their departments. Topics will include the following.

Recruiting students into the major:

• First year students: Why should a first-year student declare mathematics as a major? We will discuss letters of invitation that can be sent to incoming students, and what a welcoming letter should look like. An example of such a letter will be presented for critique. Participants will be given the task of writing their departmental letter inviting students into the major. This will involve looking at their own website and making suggestions as to how the website can appear more informative.
• Students beyond the first year: Students add the mathematics major later on in their course of study. Review of letter of invitation for students beyond their first year. Obstacles that departments and universities impose.
• Recruiting minority students into the major: Given the minority status, there are opportunities available that can be used to motivate students to pursue the math major.
• The benefits for faculty of a Math Center: The Math Center has professionals that understand not only the rules and regulations of the university, but they are also knowledgeable of the opportunities for mathematics majors. A Math Center can be seen as a focal point for transforming students into professional mathematicians.

The undergraduate major: What does the undergraduate mathematics major program of study look like? What is it preparing students to do? Is the mathematics major preparing students for the past or for the future? Participants will look over their program of study for the undergraduate mathematics major and we will discuss similarities and differences. Participants should have reviewed their website for the undergraduate program of study and have that website available for discussion.

Mentoring: Students of mathematics often run into difficulty. Mentoring students in trouble presents challenges. How can faculty help these students? What are the local resources available to help students and how are faculty aware of them? Do students know how to effectively learn the material?

Teaching a Tiling Theory Course, presented by Colin Adams, Williams College; Part A, Wednesday, 1:00–3:00 pm and Part B, Thursday, 1:00–3:00 pm. Tiling theory is a wonderful way to get students to appreciate the beauty of mathematics. It has all the relevant ingredients:

1. There are beautiful pictures.
2. Open problems can be stated without having to spend months providing students with the necessary background.
3. There is deep mathematics that applies to the field.

Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such it makes for an ideal senior course for undergraduates. But it is also true that much of the material can be covered in a lower level course by skipping the more technical sections.

In this PEP, we will cover the necessary background on tilings. Possible topics include basic background, symmetries, frieze groups, wallpaper groups, monomorphic tilings, the Conway Criterion, uniform tilings, Laves tilings, non-edge-to-edge tilings, random tilings, tilings via patches, the Extension Theorem, the Periodicity theorem, and monohedral convex polygonal tiles. We will also cover aperiodic tilings and their relation to quasicrystals, including the Robinson, Penrose and Taylor-Socolar tilings. Then we will talk about tilings of the sphere, hyperbolic plane, and 3-space, including knotted tilings. Throughout, we will include open problems and possible projects for students. Participants will have the opportunity to work on tiling problems, design their own tilings and to play with some tiling software. They will come away with the background necessary to teach a course in the subject.

Visualizing Projective Geometry Through Photographs and Perspective Drawings, presented by Annalisa Crannell, Franklin and Marshall College, and Fumiko Futamura, Southwestern University; Part A, Wednesday, 4:00–6:00 pm and Part B, Friday, 1:00–3:00 pm. This PEP introduces hands-on, practical art puzzles that motivate the mathematics of projective geometry---the study of properties invariant under projective transformations, often taught as an upper-level course. This PEP seeks to strengthen the link between projective geometry and art. On the art side, we explore activities in perspective drawing or photography. These activities provide a foundation for the mathematical side, where we introduce activities in problem solving and proof suitable for a sophomore-level proofs class. In particular, we use a geometrical analysis of Renaissance art and of photographs taken by students to motivate several important concepts in projective geometry, including Desargues' Theorem and the use of numerical projective invariants. No artistic experience is required.

The ideas and materials presented in this PEP come from a larger set of materials developed by the proposers. We have used these materials in mathematics and art courses for liberal arts majors and projective geometry courses for mathematics majors at our respective institutions. The ideas presented in this PEP are appropriate for self-contained lessons in both types of courses.

DAY 1 (Desargues’s Theorem)
DAY 2 (Numerical invariants)

Worksheets with photographs and drawing exercises, course materials and suggestions for other homework assignments will be available as packets for participants to take home. Rulers, pencils and calculators will be provided for each participant.

Steps Toward Right Relationship with Native Peoples, presented by Sandra Laursen, University of Colorado Boulder; Omayra Ortega, Sonoma State University; Belin Tsinnajinnie, WestEd; and Stan Yoshinobu, University of Toronto; first session, Wednesday, 9:00 am–11:00 am and second session, Friday 9:00 am–11:00 am.

The minicourse will comprise two two-hour sessions, both fully online and hosted on Zoom. The goals are to raise participants’ levels of knowledge and concern about the historic and ongoing impact of colonization of Indigenous peoples; to recognize these impacts in ourselves and our institutions; and to explore actions that we can take, as mathematics educators and community members, to move toward right relationship between Native and non-Native peoples.

Session 1 features a scripted, interactive workshop, “Roots of Injustice, Seeds of Change,” developed and led by Native and non-Native leaders of Toward Right Relationship with Native Peoples. Using images, historical quotations, experiential elements, music, reflection and discussion, the session will trace the history of the United States from a Native perspective, especially the historic and ongoing impacts of the Doctrine of Discovery, the 15th-century justification for European subjugation of non-Christian peoples. In the Doctrine of Discovery lie the roots of injustice; in the U.N. Declaration on the Rights of Indigenous Peoples, lie the seeds of change. So how can we nurture these seeds to bring forth the fruits of right relationship among Native and non-Native peoples?

Session 2 provides a structured opportunity to grapple with that question, as participants consider steps we can take to foster right relationship within our classroom, professional and personal communities. One focus for action will be land acknowledgments as a way to center the importance of land to Native peoples, as impetus to learn about the history of the particular Native peoples connected to the specific places where we live and work, and as an opportunity to consider our own place in that history.

The organizers bring diverse organizational connections to this minicourse. Sandra Laursen is a volunteer for Toward Right Relationship with Native Peoples (TRR), a project of Friends Peace Teams led by Native and non-Native people to educate people and help communities work toward right relationship. Stan Yoshinobu is director of the Academy of Inquiry Learning (AIBL)and co-founder of the Love, Empathy, Respect Math Coalition. Belin Tsinnajinnie (Filipino/Diné) is a mathematics education researcher who has studied the mathematical identity of Indigenous and LatinX students and pathways to student success in tribal colleges. Omayra Ortega is president of the National Association of Mathematics and active in the Association for Women in Mathematics. Professors Ortega, Tsinnajinnie and Yoshinobu are experienced mathematics educators, and Dr. Laursen is an education researcher who has studied teaching, learning and equity issues in undergraduate mathematics education.