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Math 416
Complex variables. This is a course that explores the theory and applications of complex analysis as extension of Real analysis.
The course is taught by Professor. John E. McCarthy mccarthy@math.wustl.edu
Some interesting fact is that he cover the lecture terribly quick. At least for me. I need to preview and review the lecture after the course ended. The only thing that I can take granted of is that many theorem in real analysis still holds in the complex. By elegant definition designing, we build a wonderful math with complex variables and extended theorems, which is more helpful when solving questions that cannot be solved in real numbers.
McCarthy like to write \zeta for z and his writing for \zeta is almost identical with z, I decided to use the traditional notation system I've learned to avoid confusion in my notes.
I will use B_r(z_0) to denote a disk in \mathbb{C} such that B_r(z_0) = \{ z \in \mathbb{C} : |z - z_0| < r \}
I will use z to replace the strange notation of \zeta. If that makes sense.