Teaching

Mathematical understanding. A regression, a numerical solver, or a neural network is a set of assumptions and a piece of mathematical structure before it is a line of code. I teach students to state those assumptions, follow the reasoning that justifies the method, and recognize the conditions under which it fails. In proof based courses this means walking through the reasoning that produces a finished argument rather than only the argument itself; in applied courses it means that every computational technique is preceded by the result that justifies it. A student who understands the mathematics can judge whether a familiar tool fits an unfamiliar problem.

From theory to computation to interpretation. My courses follow a consistent progression: a scientific question leads to a mathematical formulation, the formulation is carried out in computation, and the computation is interpreted in the language of the original question. Python, R, and MATLAB are integrated into mathematics courses for this reason, not as a separate skill. Students derive before they implement, validate before they trust, and interpret before they report, so that computation extends their mathematics rather than replacing it.

An inclusive and demanding classroom. I have taught students with widely varying preparation, from lecture halls in Khartoum to the calculus sequence and tutoring center at Auburn University to data science majors at Jacksonville University and graduate courses at Delaware State University. That experience shaped a simple practice: diagnose where a student actually is, adjust pacing and examples to meet them there, and keep the standard they are working toward fixed. Assignments build skill in a graduated sequence, office hours are structured so that asking a hard question is the expected behavior, and rigorous questions are welcomed from everyone. Supporting students from groups historically underrepresented in the mathematical sciences is a responsibility I hold with conviction; in my experience rigor and accessibility are complementary rather than competing goals.

Active learning and independent thinking. Class time is for thinking rather than transcription. Interactive modules, developed with the support of a Scholarship of Teaching and Learning grant, let students test ideas before they are formalized, and assessment rewards a correct formulation and a well argued interpretation over a memorized procedure. The long term goal is a student who can formulate a problem, reason from assumptions, use computation intelligently, evaluate results critically, and explain the conclusions to someone else. Support decreases as a course proceeds so that independence is practiced rather than merely expected.

Mentoring and responsible tools. Research mentoring extends the classroom: students move from a well posed question to a validated computational solution and a presentation of the result, and several undergraduate projects have led to conference papers and preprints. Generative AI is now part of how students learn and code, so I integrate its responsible and transparent use into my courses through a student guide built on three questions, described below, rather than leaving students to guess where the line lies.