Zeta Explained #01: Intro and the Basel Problem

This is the first video in a series explaining the Riemann zeta function. The idea of the series is to start with basics and eventually work our way to the Riemann-Von Mangoldt equation estimating the number of zeros in the critical strip between 0 and T as O(T log T). The viewer is expected to understand calculus and complex numbers, whereas I will try to explain concepts from complex analysis as needed. This particular video covers an introduction of the zeta function and an explanation of the Basel problem. 00:00 - Intro 03:12 - Scope of the video series 05:17 - Definition of the Riemann zeta function 08:15 - 1+2+3+4+... = -1/12? 09:47 - Start of the Basel Problem 13:02 - Proof sketch of the Basel Problem 15:50 - Factorizing a general function 22:28 - Factorizing the sine function 25:28 - Multiplying out the infinite product 28:03 - Solving the Basel Problem