This course will develop the ideas of complex numbers, complexvalued functions of a single complex variable, and the basic calculus of these functions. It is interesting to note that one of the earliest applications of this material was developed by Steinmetz while he was here at Union College. Because complex numbers include what are called "imaginary numbers", many mistakenly feel that they have no bearing on the "real" world. This is not the case, and the mathematics of complex numbers is a powerful tool for engineers and physical scientists in general.
They also form a beautiful and important field in pure mathematics, with surprisingly rich connections to a variety of unexpected areas. For example, many of you will have heard of fractals, but you probably don't know that one of the most famous examples, the Mandelbrot set, is based on complex numbers. In this course, you should gain some sense of the elegance and mystery associated with this important field of mathematics.

