Richard Gustavson

Dr. Gustavson received his Ph.D. in Mathematics from the City University of New York Graduate Center in 2017. His main area of research is the algebraic theory of differential and integral equations. This field lies both at the intersection of algebra and analysis, and also pure and applied mathematics. He is currently focused on developing algorithms to simplify systems of nonlinear integral equations using graph theory. His Ph.D. dissertation analyzed the complexity of various elimination algorithms for solving systems of differential equations. At Manhattan College, Dr. Gustavson is the advisor for the Concentration in Applied Mathematics and has co-organized the school's Putnam competition for the past four years.

Education

PHD, CUNY Graduate Center
MPHIL, CUNY Graduate Center
MA, CUNY Graduate Center
BA, Cornell University

Courses Taught

Fall 2023 Courses:

MATH 185: Calculus I
MATH 372: Linear Algebra I

Courses Taught in Past Semesters:

MATH 100: Pre-Calculus Mathematics
MATH 151: Topics in Modern Mathematics - Social Choice
MATH 154: Calculus for Business Decisions
MATH 185: Calculus I
MATH 186: Calculus II
MATH 187: Honors Calculus I
MATH 188: Honors Calculus II
MATH 243: Foundations for Higher Mathematics
MATH 285: Calculus III
MATH 286: Differential Equations
MATH 287: Honors Calculus III
MATH 372: Linear Algebra I
MATH 377: Algebra I
MATH 386: Partial Differential Equations
MATH 478: Algebra II
SCI 101: Science Orientation Seminar II

Research
- Algebraic theory of differential and integral equations
- Rota-Baxter algebras
- Symbolic computation

Publications and Scholarly Activities
Publications
- R. Gustavson and S. Rosen. "A reduction algorithm for Volterra integral equations." The PUMP Journal of Undergraduate Research, 6 (2023) 172-191. URL: https://journals.calstate.edu/pump/article/view/3631
- L. Guo, R. Gustavson, and Y. Li. "An algebraic study of Volterra integral equations and their operator linearity." Journal of Algebra, 595 (2022) 398-433. URL: https://doi.org/10.1016/j.jalgebra.2021.12.025
- R. Gustavson and O. León Sánchez. "Effective bounds for the consistency of differential equations." Journal of Symbolic Computation, 89 (2018) 41-72. URL: https://doi.org/10.1016/j.jsc.2017.11.003.
- R. Gustavson, A. Ovchinnikov, and G. Pogudin. "New order bounds in differential elimination algorithms." Journal of Symbolic Computation, 85 (2018) 128-147. URL: https://doi.org/10.1016/j.jsc.2017.07.006.
- R. Gustavson, M. Kondratieva, and A. Ovchinnikov. "New effective differential Nullstellensatz." Advances in Mathematics, 290 (2016) 1138-1158. URL: http://dx.doi.org/10.1016/j.aim.2015.12.021.
- R. Gustavson, A. Ovchinnikov, and G. Pogudin. "Bounds for orders of derivatives in differential elimination algorithms." ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation, pages 239-246. ACM Press, 2016. URL: http://dx.doi.org/10.1145/2930889.2930922.
- R. Gustavson and O. León Sánchez. "A new bound for the existence of differential field extensions." In I. Kotsireas, S. Rump, and C. Yap (eds), Mathematical Aspects of Computer and Information Sciences: MACIS 2015, Lecture Notes in Computer Science, vol. 9582, pages 358-361. Springer, Cham, 2016. URL: http://dx.doi.org/10.1007/978-3-319-32859-1_30.
- R. Gustavson. "Laplacians of covering complexes." Rose-Hulman Institute of Technology Undergraduate Mathematics Journal, 12(1) (2011) 1-18. URL: https://scholar.rose-hulman.edu/rhumj/vol12/iss1/1/

Professional Experience and Memberships
Experience
- Assistant Professor, Manhattan College, August 2018 - Present
- Visiting Assistant Professor, Manhattan College, August 2017 - August 2018
- Adjunct Lecturer, Hunter College, August 2016-May 2017
- Graduate Teaching Fellow, Hunter College, August 2013-May 2015
Memberships
- American Mathematical Society (AMS)
- Mathematical Association of America (MAA)
- Sigma Xi
- Phi Beta Kappa

Deposit Deadline Extension

The Deposit Deadline has been extended to May 15

Assistant Professor, Mathematics

Education

Courses Taught