This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

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.” ...

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play ...

Trigonometric identities are powerful tools for simplifying complex equations in math and science. Three core groups—reciprocal, quotient, and Pythagorean—form the foundation. Effective strategies ...

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. The points could be an infinite collection of electrons ...

Alan Veliz-Cuba has received funding from the Simons Foundation and the American Mathematical Society for some of his research. You can probably think of a time when you’ve used math to solve an ...