Introduction
We propose a novel cyclic process (as depicted above) by which we start in one of three computational domains: programming, math, or algorithms; and cycles through them in that order, so as to make each pass enhance the next, until a certain discovery is made. The value of such an approach is two-fold. First, it integrates different elements of computational thinking that are essential for computer scientists and problem solvers in general. Second, it mimics to a great extent a natural process of learning, where people move from concrete observations (output of a PRogram), to conceptualization and hypotheses (Math), to active experimentation based on hypotheses and what has been learned (ALgorithms); new algorithms in turn can yield better programs and close the cycle. Read more below:

• Idea of PRiMAL.
• This REU is now funded by MAA (Mathematical Association of America) in collaboration with NSF (the National Science Foundation).

Some example research problems and ideas
In general, the research problems will be fun and attractive to someone with a decent background in programming and/or has genuine interest in math, algorithms, and computation, and who would seek the mathematics or theoretical computer science as a graduate or career choice. Here are some examples:

• Infinite Skolem sequences (a pilot REU in Summer 2024 using PRiMAL),
• Three points make a right triangle,
• Blindsort,
• Other towers of Hanoi,
• Living on a random torus,
• Musical scales,
• The intimidated chickens.

Watch a talk called Fibonacci-ish at Math Encounters (sponsored by MoMath and the Simons Foundations) about some of these problems. Here's a summary of the problems with their relevant research topics and a possible starting point.

Mentoring team
The team will consists of Saad Mneimneh (Mentor) and a graduate student (helper), in addition to possible other faculty who are colleagues of prof. Mneimneh:

• Faculty mentors,
• PhD students (who will help mentoring)

Prerequisites
Experience in discrete math, proofs, algorithms, and programming (not necessarily all at once).

What to expect as a participant
If you like mathematics and theoretical CS themes, this is for you... Research questions span discrete math, computational geometry, probability, combinatorics, proofs, sequences, recurrences, and algorithms.