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Notices - August 1.

Welcome to Complex Variables!

You are currently signed up for MAT 515. I hope you are having a good summer. It is getting that time to begin thinking about the new year. You are going to want to come back eager to work and learn new things.  

In this course we will study functions of a complex variable, and differentiation and integration of complex functions. More information can be found at the course website - http://people.uncw.edu/hermanr/complex/index.htm, including the book we will use and other books of interest, including the Schaum’s Outline, which will be useful for studying for qualifying exams or looking at other examples.  

We will meet twice a week and you are expected to attend all of the classes and turn in your work on time. By now you should know that you cannot start homework the night before it is due. I expect that you will be able to find my office and feel comfortable enough to ask questions and work through any stumbling blocks you may have.  

Complex analysis is more than turning real analysis into complex by adding imaginary numbers. Complex analysis has a rich structure leading to an elegance and beauty not found in real analysis.   It encompasses much of what you have learned in real analysis, solving algebraic equations, analysis of periodicities, understanding singularities, studying convergence of solutions of differential equations, or the performing of difficult integrals. Beautiful structures have emerged such as Julia and Mandelbrot sets, air flow around wings, Riemann surfaces, stereographic projection, and conformal mappings. Interesting problems find their home in the complex plane, such as the Riemann hypothesis, the Riemann-Hilbert problems, Fermat’s Theorem, and many others in fields like modern algebra, number theory, geometry and topology.

Most years at UNCW, this has been a one-semester course. This year we are going to offer a second course, MAT 516, which I hope to see many of you and students from last year so that we can explore areas not typically covered around here.  However, for now, we have much to learn and I hope you are eager to get started. As a first homework, feel free to email me and let me know what you would like to learn in this course and anything else that would help the communication get started.

See you soon,

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