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.
• A proposal has been submitted to NSF, but it will not be shared here at the moment.

Some example research problems
In general, the research problems will be fun and attractive to someone with a decent background in programming who has genuine interest in math, algorithms, and computation, and who would seek the sub-field of 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:

• Faculty mentors,
• Two PhD students, and
• Two advanced undergraduate students.

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

What to expect as a participant
(under construction) For now, if you like theoretical CS themes, this is for you...

How to become a participant
Information on how to apply will become available if the REU is funded.