Jeffrey S. Mayer, CSU San Bernardino: Linear algebra permeates through and connects numerous aspects of my professional career. Linear algebra is central to modern mathematics and its applications within STEM. In the past few decades, there has been an explosion of important applications of linear algebra to other STEM disciplines including: network analysis, cryptography, machine learning, data science, and quantum computing. As such, linear algebra education plays an integral role in the future success of STEM students, both in academia and in industry, and this is a driving force in my work in linear algebra education. An open problem in linear algebra education is: what materials, content, and pedagogy are best suited to prepare linear algebra students to succeed in their courses and future STEM careers? My work on that problem has included creating and using new evidenced-based linear algebra curricula, mentoring other linear algebra instructors, researching student learning in linear algebra classrooms, and presenting at linear algebra math education conferences.
Linear algebra plays a central role in my mentoring of students and my pure math research. Linear algebra is an excellent source of problems and topics for mentoring students. I have advised students in masters theses that use linear algebra to study hyperbolic geometry, cryptography (via lattice reduction algorithms), and machine learning. Much of my pure mathematical research has used tools of linear algebraic groups (a highly generalized form of linear algebra) to study the geometry of hyperbolic manifolds and their generalizations. In this talk, I will discuss my work as a teacher, mentor, and researcher, woven together by linear algebra.