## JMM Professional Enhancement Programs (PEP)

JMM Professional Enhancement Programs (PEP) are open only to persons who register for the Joint Meetings and pay the Joint Meetings registration fee, in addition to the appropriate PEP fee. The AMS reserves the right to cancel any PEP that is undersubscribed. Participants should read the descriptions of each PEP thoroughly as some require participants to bring their own laptops and special software; laptops will not be provided in any PEP. The enrollment in each PEP is limited to 50; the cost is US\$100. A Complex Transition to Advanced Undergraduate Mathematics, presented by Bob Sachs, George Mason University, Hortensia Soto, Colorado State University, and Paul Zorn, St. Olaf College; Part A, Wednesday, 9:00–11:00 am, and Part B, Friday, 9:00–11:00 am. “Transition courses,” common requirements or electives for undergraduate mathematics majors and minors, aim to introduce students to a variety of methods and ways of thinking typical of advanced mathematics. Here “transition” refers to students’ progress from calculation-oriented work, as in elementary calculus, to more theoretical perspectives, as in real analysis, abstract algebra, topology, complex analysis, and beyond. Working with definitions, writing clearly, and reasoning carefully are all emphasized. The goal is sometimes described as helping students to develop “mathematical habits of mind.” Transition courses vary widely in mathematical content, which might include Boolean algebra, set theory, proof techniques, and some selection of basics from one or more of number theory, discrete mathematics, groups, sequences and series, etc. We propose (and are writing a textbook for) a transition course focused squarely on “$\C$-stuff”. We expect students to jump, without excessive ado, into algebra and geometry of complex numbers; complex functions, especially polynomials and rational functions; the fundamental theorem of algebra; basics of complex derivatives and integrals; and glimpses of some main theorems of complex analysis, including their discrete analogues. We propose also a variety of less standard optional topics, whether as moveable modules or as independent study/projects: Gaussian integers, Mobius transformations, discrete Fourier transforms, etc. We find “$\C\$-stuff” ideal for the goals of this course. The topic opens doors to multiple courses later in the curriculum. For example, topological ideas such as winding numbers point to higher-dimensional generalizations, but are reachable at this level. The course also reflects back on and reifies high school algebra and college calculus. This content benefits future high school teachers in particular, but it also develops all mathematics students’ perspectives on earlier material. Basic complex numbers and their properties are core to the 19th century development of mathematical subdisciplines along with physical applications.

Graphing and visualization of complex-valued functions present special challenges for students. Since domain and range are each two-dimensional, graphs cannot be as easily displayed as in single variable real calculus. Multiple representations (side-by-side domain and range pictures, animation, domain coloring, etc., can push students to think more carefully about what is depicted and what is missing. Doing so also encourages a deeper conception of functions, particularly as mappings, and helps develop abstract thinking. Examples using Mathematica and GeoGebra will be shown and some student responses included.

The PEP participants will work through and discuss questions and problem sets in small groups---as students might do. Because there is limited research and considerable variation among college instructors on both means and ends of transition courses, we will devote time to group discussion of pedagogical questions: strategies to promote active learning, foster productive struggle, invite inquiry and collaboration, and address student growth.

By the end of the PEP, we expect participants to have selected topics and resources for transition courses they might teach at their own institutions, or for modules they might use in other courses, including (of course) complex analysis but possibly also number theory, abstract algebra, real analysis, topology, etc.

Breaking the Cycle of Mechanisms of Inequality in Mathematics Teaching and Learning, presented by Nicole M. Joseph, Vanderbilt University and William Yslas Velez, University of Arizona; Part A, Wednesday, 1:00–3:00 pm, and Part B, Thursday, 1:00–3:00 pm. The field of mathematics continues to be plagued with underrepresentation and attrition among racialized and gendered students. African American, Hispanic, Native American, and Native Hawaiian/Pacific Islander students seldom find mathematics and statistics as an attractive major and career pathway because they are often discouraged and pushed out by high school counselors and mathematics teachers, undergraduate advisors, and higher education mathematics faculty. The mathematics field also promotes neutrality and objectivity in the teaching and learning space, rather than as a space of contestation whereby minoritized students experience intellectual and psychological harm (Leyva et al., 2021; Martin, 2019). In their study of 18 Black and Latina/o students’ perceptions of Calculus instruction as a racialized and gendered experience, Leyva and colleagues (2021) found two logics: (1) instructors hold more mathematical authority than students in classrooms and (2) Calculus coursework is used to weed out students ‘not cut out’ for STEM. These logics, coupled with the influence of broader sociohistorical forces, such as stereotypes, give rise to what these scholars call “mechanisms of inequality” through seemingly neutral instructional practices. Consequently, these introductory mathematics courses and the instructors who teach them reinforce racial-gendered distribution of classroom participation and STEM persistence. So, when a mathematics faculty advises “an entire class to drop down a course level or not take Calculus 2 if they cannot complete steps of a problem quickly,” (Leyva et al., 2021, p.31.), this discourse is racialized and gendered. Faculty think that they are helping students, being benevolent, but are in fact causing minority students to experience a unique form of discrimination. And when minoritized students internalize these logics, they say to themselves things like “oh, so, this is why Black and Latinx students are not in mathematics; they don’t belong here.

So, what can we do as a field to address these issues? First, we must be bold and brave to acknowledge minoritized experiences as real, legitimate, and that the field perpetuates these issues. Next, we need to come together to educate ourselves about ways to critically examine and disrupt instructional practices that subscribe to exclusionary logics and fuel mechanisms of inequality. This is hard work, and we need each other to learn and grow beyond equity-light discussions. It is important for mathematics instructors and faculty to understand that instructional practices are more than what they do, say, and teach in the classroom. Instruction happens during office hours, advising appointments, mentoring sessions, and other spaces where conversations about mathematics learning and college/career aspirations occur between mathematics faculty, advising personnel and racialized and gendered students.

This PEP aims to co-construct with its audience members a powerful and meaningful learning experience for breaking down these issues and disrupting the cycle of inequality in the mathematics community. Participants engage in short readings, small group discussion, scenario/video analyses, and their tangible product is an implementation plan for change within their own realms of influence. Proposed schedule is as follows:

Day 1:

• Co-Construct Norms for Courageous Conversations about Knotty Equity-Oriented Problems in Mathematics
• Watch & Discuss Videos on Mentoring Conversations

Day 2:

• Pre-Readings discussions in small groups
• Partner Work: Conceptualize, Develop, and Share Implementation Plan for Change (We will use Critical Friends and Wows/Wonders Protocols.)

Developing Mathematics Programs for Workforce Preparation in Data Science and Other Applications, presented by Rick Cleary, Babson College and Chris Malone, Winona State University; Part A, Wednesday, 1:00–3:00 pm, and Part B, Saturday, 1:00–3:00 pm. This PEP will provide an opportunity for individuals and departments to think in a big picture way about how to create a more modern and inclusive curriculum. Based on our own experience and recommendations in a report from Rutgers Education and Employment Research Center (EERC Curriculum Report) commissioned by www.tpsemath.org, we will ask participants to think broadly about what constitutes a program in mathematics that prepares students for careers in data science or other applications areas such as public policy, health care or business.

Our expected takeaways for participants are:

1. Consideration of updated mathematics curricula that can be taught without the usual three semesters of calculus as a pre-requisite, and how this might encourage a more diverse set of students.
2. How to structure courses and programs that have sophisticated mathematical content but are simultaneously useful for students preparing for careers rather than graduate school.
3. Ideas for structuring a new major or program in a mathematics department that involves stakeholders from outside mathematics, particularly employers and other academic departments.
4. Careful evaluation of courses and pre-requisite structures that will encourage broader participation in new programs.

Workshop participants will be asked to respond to a pre-course questionnaire. Responses from this questionnaire will be used by the presenters to form small groups for discussion during the course. Rick Cleary will lead discussion for the first two points. He has over 15 years of experience building non-standard mathematics curricula for students interested in engineering and business. Chris Malone will lead discussion on points three and four. He helped build the successful data science major at Winona State University. Details can be found here.

Evidence-based Practices for More Effective Mentoring Relationships, presented by Pamela E. Harris, Williams College and Abbe Herzig, American Mathematical Society; Part A, Friday, 1:00–3:00 pm, and Part B, Saturday, 1:00–3:00 pm. This interactive and evidence-based mini-course will be based on the curriculum Entering Mentoring, developed by the Center for the Improvement for Mentored Experiences in Research (CIMER) at the Wisconsin Center for Education Research. Both Dr. Harris and Dr. Herzig are CIMER-trained facilitators for this curriculum series.

CIMER is leading a nationwide initiative to improve mentoring relationships for mentees and mentors at all career stages through the development, implementation, and study of evidence-based and culturally-responsive mentoring practices. Culturally responsive relationships between mentors and mentees can help mathematicians of underrepresented groups successfully progress in their careers, becoming effective mentors, scientific leaders, and research team members of the future.

The Entering Mentoring curriculum was developed for mentors across science, technology, engineering, mathematics, and medicine (STEMM) disciplines at different career stages, working with undergraduate and graduate students, postdoctoral fellows, and junior faculty. The curriculum has been shown to be effective in increasing mentoring knowledge, skills, and behavior. The PEP will use curriculum materials developed specifically for mentoring in the mathematical sciences.

Participants will learn the importance of three dimensions of mentoring relationships: building research skills, participating in professional practices, and developing a mathematical identity. The goal is to accelerate the process of becoming an effective mentor by providing mentors with an intellectual framework, an opportunity to experiment with various methods, and a forum in which to solve mentoring dilemmas in collaboration with their peers. By the end of the training, mentors will have articulated their personal approach to and philosophy of mentoring and have a toolbox of strategies they can use to help their mentees develop in all three dimensions of professional success. Co-sponsored by the American Mathematical Society, The Center for Minorities in the Mathematical Sciences, and Lathisms.

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)

Glimpses of mathematics from robotics: simple kinematic problems for the planar robot arms, presented by Lydia Novozhilova, Western Connecticut State University, Hasib Rahmiyar, Stony Brook University, and Hieu Nguyen, University of Connecticut; Part A, Thursday, 9:00–11:00 am, and Part B, Thursday, 1:00–3:00 pm. Mathematical approach to the specific class of models introduced in this PEP is one of many topics in a book manuscript “Exploring mathematics with CAS assistance”. (The manuscript is currently under consideration by the editorial board at MAA Press). This PEP has three segments: (1) A brief introduction to the basic terminology, mathematical tools needed for modeling kinematics of robot manipulators (RMs), or robot arms, and two approaches to the kinematic modeling. (2) Analysis and solutions of the kinematic problems for a simple class of RMs and exploration of these solutions using a SageMath code (the code will be provided). (3) Working with a Jupyter notebook. The notebook includes (i) formulation of the lab “Solving the inverse kinematic problem for three-link open, planar robotic arms” and an algorithm for solving this problem; (ii) a SageMath code template for implementing the algorithm. With help of the moderators, participants will work through the code filling in the blank command lines and then run the code on test problems to obtain and visualize the configurations of the RMs of interest. This PEP touches upon very diverse mathematical concepts, like matrices, special orthogonal groups, circle group, matrix exponential, and the Jacobian of a mapping between multidimensional spaces. For the best impact of this interactive course, participants should bring a laptop with wireless internet accessibility. Every participant will also need an account with CoCalc (it is free) to get access to SageMath for using it in the course but no prior experience with this software system is expected.

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.

Using Your Voice for Influence and Impact: Incorporating Mathematics into Public Discourse, presented by Kira Hamman, Penn State Mont Alto, Scott Hershberger, American Mathematical Society, Karen Saxe, American Mathematical Society, Francis Su, Harvey Mudd College, and Scott Turner, American Mathematical Society; Part A, Wednesday, 8:00 – 10:00 am and Part B, Friday, 8:00 – 10:00 am. Polarized politics and misinformation—often amplified by social media—are of great concern to people who value facts and evidence-based decision making. Mathematical scientists are in a unique position to combat the erosion of public discourse with quantitative information. But to be effective they need to reach a general audience. One way to do this is by preparing opinion pieces for popular media. Indeed, media outlets regularly seek clear, concise, evidence-based opinions from experts on pressing issues. This PEP will cover:

• Choosing compelling topics and angles
• Writing for a general audience
• Structuring an opinion piece
• Distilling complex ideas and relevant quantitative information
• Harnessing the power of storytelling to share science with a general public
• Getting a piece into the hands of people who will publish it

Participants will be asked to come to the PEP with topic ideas for an opinion piece. Before the program, they will also receive published samples in which authors successfully incorporated scientific information and/or shared viewpoints, as well as a list of best practices.

After instruction and small-group brainstorming in the first session, participants will be asked to return on day two with a first draft of around 800 words. These will be discussed in a session that will include a panel of established writers, who will describe their experiences writing and publishing math-infused opinion pieces.

Besides receiving resources and guidance to reach the wider world, participants will leave the PEP with drafts that can be polished for publication. They will also belong to a newly minted collection of like-minded colleagues—mathematicians using their expertise to contribute to the public discourse.

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.

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