Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...

Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...

Images of plants painted on pottery made up to 8,000 years ago may be the earliest example of humans’ mathematical thought, a ...

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

The world of math is complex … in more ways than one. Sure, it’s full of complex ideas that are all tied up and packaged within beautiful and often times complex wrapping paper that is adorned with ...

Kinetic theory and mathematical modeling have emerged as indispensable tools for elucidating the collective behaviour of complex systems. This discipline applies statistical mechanics to a diverse ...

In the Fall I'll be starting teaching again, after a semester away on sabbatical and then enjoying teaching relief during my first semester at Penn. I'll be teaching a course that I truly love, and ...