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# Making sense out of the abstract...

"When we see it for the first time, it looks so abstract that it seems impossible something like this could have any real-world applications" - Edward Frenkel

As the under-graduation curtains close, confronting and comprehending the ideas of abstract algebra seem barbaric to my mind. Right from high school, one can view the negligence or rather the amount of incompetence people exhibit while teaching this area. As a consequence, leaving students, like myself, blindsided to the essence and worth of the field. This, and the following few post are meant to encapsulate my thoughts on this area of the subject and it's significance in human civilization.

In general, when a = qn + r, where a is the quotient and r is the remainder upon dividing a by n, we get, a mod n = r. As A consequence, 6 mod 2 = 0, since 6= 3.2 + 0.

If a and b are integers and n is a positive integer, then, a mod n = b mod n, if n divided a-b. This very modular arithmetic is often used in assigning an extra digit to identification numbers for the purpose of detecting forgery or errors. In the next post, we‘ll discuss a few examples and delve deeper into abstract algebra in general.