About

Short Biography

I have been a professor of mathematics at the University of Tennessee, Knoxville, since 2007. Before that I was a postdoc at UC, Irvine, in Orange County California, where I worked with John Lowengrub and Vittorio Cristini on complex fluids, crystal microstructure, and cancer progression. I received my PhD in 2003 from the University of Virginia, where I studied engineering physics, working with the nicest person in the world, Dr. William C. Johnson.

I teach courses in PDE, analysis, applied mathematics, and numerical analysis. With Abner Salgado, I wrote a graduate-level textbook entitled Classical Numerical Analysis: A Comprehensive Course, published by Cambridge University Press in 2023. You can check it out on Amazon or on Cambridge Core. We have another book coming soon on the topic of multigrid methods, focusing on basic theory and implementation in Matlab.

I have a YouTube channel, WiseAppliedMaths, where I post lectures from some of the courses that I teach. My latest playlists are courses on Asymptotic Analysis, Multigrid Methods, and Finite Element Methods.

Research

I work in the intersection of numerical analysis, partial differential equations, soft matter physics, and kinetic theory. I build models to study heat, mass, and ion flow and the formation of interfaces in complex fluids and materials, and I try to design efficient numerical methods to get approximate solutions.

Citations

My citation information can be found in the Google Scholar, Scopus, and other links below, and my UTK Faculty Profile can be found here. I was recognized by Web of Science as a highly cited researcher in 2020 and 2022.

Favorite (Mostly Maths) Quotes

“All science is either physics or stamp collecting.” –Ernest Rutherford

“The currency of approximation is derivatives.” – (I learned of this quote from Ohannes Karakashian. I am still working to find the originator.)

“The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn’s lemma?” – Jerry Bona

“There is nothing more practical than a good theory.” – Ludwig Boltzmann.

“[D]emocracy is the worst form of Government except for all those other forms that have been tried.” – Winston Churchill

“No self-respecting architect leaves the scaffolding in place after completing his building.” – Carl Friedrich Gauss

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” – John von Neumann

“‘Obvious’ is the most dangerous word in mathematics.” – Eric Temple Bell

“Nothing takes place in the world whose meaning is not that of some maximum or minimum.” – Leonhard Euler

“A mathematician is a machine for turning coffee into theorems.” – Alfréd Rényi

“Some ideas are so stupid that only intellectuals (professors) believe them.” – George Orwell

“One of the principal objects of theoretical research is to find the point of view from which the subject appears in the greatest simplicity.” – Josiah Willard Gibbs

“If your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” – Sir Arthur Eddington