MAXIMUM PRINCIPLE -- Part 1 -- Core Theorems of Complex Analysis

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I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring.

Part 2:    • The Schwarz Lemma -- Complex Analysis  
Part 3:    • Liouville's theorem -- Complex Analysis  

In this video, we give a proof of the Maximum Principle, which is a monumental result in the subject of complex analysis. The maximum principle is also referred to as the maximum modulus principle, and states that the modulus of a holomorphic function cannot achieve an interior maximum. The proof we give here is elementary, albeit requiring the less-elementary open mapping theorem, and is due to the late Professor Alexander Isaev.

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