Pfeffer, Douglas

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Education

2014 Florida Atlantic University, B.S.
2016 University of Florida, M.S.
2019 University of Florida, Ph.D.

Courses Taught

College Algebra
Calculus for Business
Precalculus
Discrete Mathematics

View CV

Career Specialties

Douglas Pfeffer is a mathematician specializing in operator theory, real/complex analysis and linear algebra. Additionally, he is interested in math history, mathematical pedagogy and mathematical outreach.

Professional and Community Activities

Pfeffer's mathematical research program lies at the intersection of operator theory and complex analysis, where he investigates function algebras generated by imposing algebraic constraints on the classic disc algebra – functions holomorphic on the complex unit disc that extend to be continuous on the unit circle. For example, one can ask such functions have their first derivative vanish at zero – this constrained algebra is known as the Neil Algebra. Pfeffer's current work aims to develop the theory behind Toeplitz operators associated to these algebras. This has led to two recent co-authored publications: “Szego and Widom theorems for finite codimensional subalgebras of a class of uniform algebra” in Complex Analysis and Operator Theory (2021) and “Spectra for Toeplitz Operators Associated with a Constrained Subalgebra” in Integral Equations and Operator Theory (2022). Since 2020, Pfeffer has also co-founded and co-organized the Operator Theory Talks for Early Researchers (OTTER) community, where early career researchers gather virtually to help one another navigate academia and make strides in their research. This involvement complements his yearly involvement in the Southeastern Analysis Meetings (SEAM).

Pfeffer's research extends to the history of mathematics as well, where he is active in the History of Mathematics Special Interest Group of the Mathematical Association of America (HOM SIGMAA). His program in this vein looks at the development of applied coursework in the 20th-century American undergraduate mathematics curriculum. Active in undergraduate research as well, Pfeffer regularly has students join him in the study of nomographs. This object is a two-dimensional diagram designed to allow the approximate solving of a given equation. In the modern age of computers, such objects still find use in professions where such conveniences are inaccessible. His undergraduate researchers have even included precalculus students, where we’ve worked to both develop new nomographs for various workforces as well as detail their theoretical underpinning.

Since being an MAA Project NExT fellow (Silver ’19), he has also been involved in online communities centered on innovating the classroom using research-backed, equitable teaching techniques such as Inquiry-Based Learning, Standards-Based Grading, the Flipped Classroom, and more. This has led to the recent publication of the co-authored book chapter “Double Integrals and the Human Condition” in Cross-Curricular Pure Math Applications (to appear in 2023 as a MAA Notes volume).He is also an ardent believer in outreach, where he organizes and teaches the virtual Tucson Math Circle for elementary school kids. These interests have led to the recent co-authored publication “From Mirrors to Wallpapers: A Virtual Math Circle Series on Symmetry” in the Journal of Math Circles (2022).

Honors and Awards

MAA Project NExT fellow (Silver ‘19)