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.” ...

Earlier this year, Mathematician Ian Stewart came out with an excellent and deeply researched book titled "In Pursuit of the Unknown: 17 Equations That Changed the World" that takes a look at the most ...

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 ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

This chaotic-looking "double pendulum" follows a large number of rules that govern its motion. Researchers have trained AI to take data from its movements to uncover simple equations that successfully ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

Complex Hessian equations extend the classical framework of the complex Monge–Ampère equation by involving the m-th elementary symmetric function of the eigenvalues of the complex Hessian. This ...

In theory, almost any aspect of the physical world can be modeled and analyzed mathematically. In practice though, performing the mathematical manipulations required to perform an analysis can rapidly ...