Category Archives: Complex analysis

Zeros of random polynomials

Posted on 21/11/2017 by lamwk

Given a polynomial , where the coefficients are random, what can we say about the distribution of the roots (on )? Of course, it would depend on what “random” means. Here, “random” means that the sequence is an i.i.d. sequence … Continue reading →

Posted in Algebra, Complex analysis, Potential theory, Probability | Leave a comment

Euler’s formula e^ix = cos x + i sin x: a geometric approach

Posted on 08/11/2017 by KKK

Today I mentioned the famous Euler’s formula briefly in my calculus class (when discussing hyperbolic functions, lecture notes here): where is a solution to (usually denoted by “”, but indeed there is no single-valued square root for complex numbers, or … Continue reading →

Posted in Analysis, Calculus, Complex analysis, Geometry | Leave a comment

Complex analysis – Problem solving strategies.

Posted on 24/08/2012 by leonardwong

This post is written in spirit of Terrance Tao’s post on problem solving strategies in real analysis. Our emphasis will be on concrete techniques with plenty of examples (many are taken from past prelim questions in UW).

Posted in Complex analysis | Leave a comment

Principle of subordination

Posted on 04/03/2012 by leonardwong

First we recall the statement of Schwarz’s lemma, which is a basic result in complex analysis. Let be the unit disk in . Schwarz’s lemma. Let . If for all and , then , and for all . If or … Continue reading →

Posted in Complex analysis | 2 Comments