Dr. Katharine Long
Professor
Department of Mathematics and Statistics
Texas Tech University
Contact: katharine DOT long AT ttu DOT edu
Phone: I don't have an office phone. This is the 21st century. Use email.
My
teaching
and research are in applied mathematics, with research focused
on numerical solution of partial differential equations applied to problems in
physics and biology.
I work with a lot of graduate and undergraduate research students.
A university education should expose you to surprising, uncomfortable ideas
In elementary school we learn two plus two is four, and that the states of matter are solid, liquid, and gas. Those are two obvious and intuitive statements, but
only one of them is true.
A university
education
involves learning things that are neither obvious nor intuitive, and are often
disconcerting.
There exist curves that are continuous everywhere yet smooth nowhere. Triangles are two dimensional, bricks three dimensional, but some shapes have fractional dimension.
There are many, many states of matter, some of which behave in
ways that defy all intuition.
Electrons are neither particles nor waves,
yet can behave like either particles or waves depending on how you set up the experiment.
There are numbers that can be defined precisely but whose value can never be computed to any accuracy.
There exist mathematical propositions that can never be
proved true or false, and we can't know in advance which ones they are.
Mathematics and physics and biology are strange and endlessly surprising,
and as you learn more they get more strange and surprising, not less. And that's
ok. Accepting our ignorance and confusion is the first step to understanding.
Unfortunately, governments past and present sometimes try to keep university
students from being taught the strange, confusing, uncertain parts of
science, and try to enforce teaching comfortable simplicity rather than uncomfortable complexity.
But reality persists whether we teach it or not.
E pur si muove.