Leading Undergraduate Research Projects in Mathematical Modeling

Abstract

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived from calculus, but can be suitably modified to solve more complex problems; and finally provide pointers on how to train students through the UR process that can help to impact student’s future academic and non-academic careers.     

Snippets of physics

Variational principles play a central role in theoretical physics in many guises. We will discuss, in this instalment, some curious features associated with a couple of variational problems.     

Snippets of physics

The fact that an accelerated charge radiates energy is considered an elementary textbook result in electromagnetism. Nevertheless, this process of radiation (and its reaction on the charged particle) raises several conundrums about which technical papers are written even today. In this installment, we will try to understand why an accelerated charge radiates in a simple, yet rigorous, manner.     

Snippets of physics

We continue our exploration of random walks with some more curious results. We discuss the dimension dependence of some of the features of the random walk, describe an unexpected connection between random walks and electrical networks and finally discuss some remarkable features of random walk with geometrically decreasing step-length.     

Dawn of science

It was traders who tilted the scale in favour of the new number system in the Arab world.     

Snippets of physics

Some of the curious effects in quantum theory and statistical mechanics can be interpreted by analytically continuing the time coordinate to purely inaginary values. We explore some of these issues in this instalment.