Teaching & Mentoring

M. Chertkov Teaching & Mentoring Vision (11/2023)

Journey from Los Alamos to Leadership in Academic Mentorship

I relocated to Tucson in 2019, drawn by the exceptional opportunities in teaching and mentoring. During my two decades at Los Alamos prior to this move, I had the privilege of mentoring numerous postdocs. Many of these individuals have since become esteemed professors and staff members in universities, national labs, and companies worldwide. This mentoring aspect was a highlight of my time at Los Alamos, and though I cherished it, I found myself missing the classroom environment. Witnessing the remarkable achievements of my Graduate Research Assistants at Los Alamos, especially during the brief but intense summer months, was inspiring. Notably, many of these initial collaborations evolved into lasting professional relationships. This experience fueled my desire to engage more deeply with student development. Seizing the opportunity, I wholeheartedly embraced the role of chairing the Graduate Inter-Disciplinary Program (GIDP) in Applied Mathematics (AM) at UArizona.

Achievements in Graduate Program Development

Tasked with elevating this already prestigious program with 48 years of history, my goal was to redefine Applied Mathematics for the 21st century. This vision included integrating traditional methodologies with cutting-edge approaches and tools from information theory, control theory, computer science, operations research, machine learning, and Artificial Intelligence (AI). The past five years have been a remarkable journey, marked by significant achievements. Highlights of our progress include [see this recently written report for a comprehensive review]:

1. Curriculum Overhaul: We successfully updated six core courses to modern standards, involving key members, establishing a program-linked postdoctoral position for innovative teaching methods and student integration workshops.

2. Streamlined Qualification Process: The qualification process was simplified and aligned with core courses, managed by three committees (“theory”, “methods” and “algorithms”), enhancing the student pathway and allowing early involvement in internships and research.

3. Diverse Recruitment Strategy: We broadened our recruitment to attract students from various disciplines such as physics, engineering, and computer science, enriching our program's intellectual diversity.

4. Strong Collaborations with Laboratories: We established significant partnerships with National and Industrial Laboratories, integrating real-world applications and approaching a dedicated PhD program status for our partners.

5. Thriving Student Community: A range of social and academic activities, including seminars, hikes, and trips, were implemented to foster a supportive and engaging student community.

6. Pioneering in AI for Sciences: We positioned ourselves as leaders in "AI for Sciences," leading numerous AI-related collaborative proposals and securing significant funding, enhancing our program's national reputation in this emerging field.

Innovative Course Development and Living Textbooks

In addition to spearheading the comprehensive redesign of the six-course curriculum, I have dedicated my efforts to creating and teaching the two-semester core course "Principles and Methods in Applied Mathematics". This endeavor has culminated in a dynamic, continuously updated resource, a 'living book'. Moreover, I have developed and instructed two specialized courses: "Inference, Learning, and Optimization (INFERLO) with Graphs and Networks" in the Fall of 2022, and "Stochastic Control and Learning (SCL)" in the Fall of 2023. The INFERLO course draws from another evolving living book, a project I have been passionately developing for over 15 years. My intention is to transform the course material from the SCL course into my third living book, an endeavor I plan to undertake in a year or two while teaching this or similar course second time.

Expanding Horizons in Applied Mathematics and Statistical Mechanics Education

As I approach the next chapter in my academic career, I am enthusiastic about broadening the scope of Contemporary Applied Mathematics and Statistical Mechanics for our graduate students. My commitment is to refine and innovate our curriculum, introducing courses that not only enhance their academic breadth but also their practical skills, particularly in AI and its applications in physical and other sciences. I advocate for an educational model where teaching and research synergize, benefiting students, faculty, and the field alike. In this spirit, I am considering novel courses that bridge classical physics, applied mathematics, and modern domains such as AI. A potential course offering, "Introduction to Classical and Statistical Mechanics Foundations of AI," could serve as an interdisciplinary gateway, acquainting STEM undergraduates with the burgeoning opportunities at the intersection of these fields.

Cultivating Interdisciplinary Excellence in STEM Education

In my tenure as an educator, I've noted that the most academically successful students often have a strong mathematical foundation enriched by a deep understanding of physics and engineering. Interdisciplinary fluency, particularly the synergy between mathematics, physics, and other scientific and engineering fields, is beneficial. This cross-disciplinary integration can be fostered through programs like accelerated master's in applied mathematics, which are immensely attractive to students from diverse STEM backgrounds. Such master's programs, especially when aligned with corresponding PhD programs, enhance the depth and breadth of a student's expertise. At UArizona, we are pioneering an accelerated MSc in Applied Mathematics, a model I am eager to expand to professional degrees in other STEM disciplines. This could potentially include physics, various engineering fields, and innovative hybrid programs like "Physics of AI".

Strategic Collaborations to Shape Future STEM Education

I envision significant educational opportunities emerging from collaborations with national and industrial Laboratories. I firmly believe that STEM graduate programs at our leading research universities should forge enduring partnerships with government agencies like the DOE and DOD, as well as private companies at the forefront of the AI revolution. Such collaborations can offer a coordinated "pipeline" experience for our students in physics, applied mathematics, and other science and engineering fields, both at the graduate and undergraduate levels. My vision is being shaped and refined, particularly in light of the recent NSF funding my team received for the 'Innovation in Graduate Education (IGE)' proposal, titled "IGE: Integrating Data Science into the Applied Mathematics PhD: Generalized Skills for Non-Academic Careers". This project aims to transform the Applied Mathematics program by embedding AI and data science into its PhD curriculum. This initiative, developed in collaboration with national and industrial labs, strives to nurture a new cadre of researchers adept in non-academic STEM careers. It emphasizes interdisciplinary skills and caters to national security concerns. Beyond attracting a diverse student population, this project aspires to set a precedent for other STEM programs, extending its influence beyond Applied Mathematics into fields like Physics and Engineering. It aims to seamlessly integrate traditional STEM skills with modern AI expertise, responding to the growing need for PhDs skilled in navigating both academic and non-academic environments.

Advancing Undergraduate Education for the AI Era

I am eager to engage more deeply in the teaching and transformation of undergraduate programs in physics, applied mathematics, and related science and engineering fields. My ambition is to play a key role in developing innovative undergraduate curricula that not only enhance students' knowledge but also strategically orient them towards STEM careers, especially in national and industrial labs and the evolving academic landscape. It is crucial to introduce talented undergraduates to these opportunities as early as possible. These students are entering the very pipeline that our nation urgently needs to thrive in the Age of AI. This need is underscored by the recent initiatives of the Biden administration (April 2023), which focus on creating new pathways for the STEM workforce in response to the AI revolution, climate change, and related areas. Key initiatives include "Educational Programs in STEM," "Public-Private Partnerships," and "Funding for Research and Development". These efforts reflect a comprehensive strategy that encompasses educational advancement, workforce training, research investment, and policy innovation. This holistic approach aims to ensure that the U.S. continues to lead in technological innovation and is fully equipped to address global challenges, such as climate change, with advanced knowledge and expertise.

Commitment to Diversity and Inclusivity

To advance a diverse STEM workforce at undergraduate and graduate levels, I advocate for an integrated strategy to enhance graduate and undegraduate programs. Drawing from my experience with the AM GIDP at UArizona, I propose updating curricula to reflect current demands, simplifying student qualification processes, diversifying recruitment, and strengthening ties with industry and national labs as key to fostering diversity. Experience has shown that nurturing a student community engaged in AI innovation and providing varied educational and research opportunities are effective in attracting a diverse cohort, including first-generation, female, and minority students. A steadfast commitment to inclusivity not only enriches the intellectual landscape but also equips students for diverse careers in academia and beyond.

Forward-Looking Education in the Age of AI

Understanding the necessity of a collaborative approach to achieve our educational goals, I recognize that faculty members, university leaders, and an array of institutional, and national and industrial lab resources are vital to this endeavor. The urgency brought by the AI revolution underscores the need to establish innovative educational pathways that prepare students for advanced science and engineering roles in AI-driven fields. The development of such curricula presents an exhilarating chance for educators, researchers, and students to not only contribute to the AI landscape but also to meet the growing demands of national and industrial laboratories. This alignment with industry and government trends opens new avenues for research universities to engage in lucrative partnerships. Motivated by these prospects, I am actively seeking and forging new paths to champion these educational reforms at both the undergraduate and graduate levels, ensuring our institution remains at the forefront of this transformative era.