Complex Analysis – Cantor's Archive

Complex Analysis

Beyond Infinity

Analytic Continuation and its Applications in Quantum Physics

Complex Analysis

The Beautiful World of Complex Functions

Exploring Hidden Structure in Higher Dimensions

Riemann Hypothesis

A Fun Proof of the Riemann Hypothesis

Real math about a fictional object.

Euler

The Most Beautiful Equation in the World

And the Geometry of Numbers

Complex Analysis

Euler’s Fabulous Formula

Here we investigate and understand the brilliant formula which unlocks the power of complex numbers.

Complex Analysis

There is no such thing as √-1

What are complex numbers, after all?

Hilbert

The Hardy-Hilbert Space of the Unit Disc and Composition Operators

The Hardy space has three equivalent definitions. Each of them emphasizes a different aspect of the space and all three of these aspects…

Analysis

An Elementary Proof of the Fundamental Theorem of Algebra

Using only elementary methods we will prove the Fundamental Theorem of Algebra. Along the way, we’ll befriend some key ideas from…

Complex Analysis

Proving The Cauchy-Goursat Theorem

Let’s prove a beautiful Theorem from complex analysis!! For the determined amateur with some knowledge of 12th grade math and calculus.

Number Theory

Faltings’s Theorem and the Mordell Conjecture

On the number of rational solutions to polynomials.

Complex Analysis

A Gentle Introduction to Analytic Continuation

How to Extend the Domain of Analytic Functions

Analysis

Mighty Ruler Conquers Quadratic Equations

The methods of finding roots of a quadratic equations are quite easy and are very well understood. There are all kinds of approaches…