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Euler Product Formula - A Beautiful Equation in Number Theory

Offered By: Dr Trefor Bazett via YouTube

Tags

Number Theory Courses Riemann Hypothesis Courses Riemann Zeta Function Courses Analytic Number Theory Courses

Course Description

Overview

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Dive into a fascinating 17-minute video exploring the Euler Product Formula, a groundbreaking mathematical equation proven by Euler in 1737. Learn how this formula connects a sum over natural numbers with a product over all prime numbers. Follow along as the proof is demonstrated using the Sieve of Eratosthenes, discover how the Basel problem emerges from this formula, and explore its extension beyond proving the infinity of prime numbers to the sum of reciprocal primes. Gain insights into the Riemann-Zeta function and its connection to the Riemann Hypothesis, one of the million-dollar Millennium Problems. Enhance your understanding of analytic number theory and appreciate the beauty of mathematical equations through this engaging and informative presentation.

Syllabus

Euler Product Formula
Proof of the Formula
s=1 and Reciprocal Primes
Reimann-zeta function and Riemann Hypothesis
Brilliant.org/TreforBazett


Taught by

Dr. Trefor Bazett

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