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Measure Theory and the Lebesgue Integral

Written by: Karthik Prasad   Calculus is one of the greatest inventions in Mathematics. Its two primary tools—the derivative and integral—allow us to calculate the rates of change and work done respectively,and are used throughout the world. However, it doesn’t always do things the way

The Isoperimetric Inequality

Written by Karthik Prasad   Introduction  Perimeter and area are two fundamental values associated with any 2D figure, but how are they related? It seems simple, but it turns out that this question is much more complicated than most have previously thought—it took mathematicians thousands

Explaining the Properties of the Real Numbers

Written by: Karthik Prasad   The real numbers are something every math student is familiar with—after all, they are the numbers that make up the real world itself. However, we often take the existence and structure of these numbers for granted. We will discuss the

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The Yang-Mills Problem

Written by: Karthik Prasad Seven Problems. 1 million dollars for each one solved. The Yang-Mills Mass Gap problem is one of the fabled Millenium Problems and is of great interest in mathematical physics. Its statement is…incomprehensible for most, filled with abstract terms: prove that for

A Brief History of Modern Physics

Written by: Karthik Prasad     The 19th and 20th centuries gave physicists a glimpse into the true underpinnings of the universe itself: modern physics. Three major theories emerged in this time period–special relativity, quantum mechanics, and general relativity. This article aims to overview the