The Notebook
İstanbul, Turkey


Jensen's Inequality
May 17, 2018

This blog post is aimed to explain proof of Jensen's Inequality.

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On Lagrange Multipliers
December 9, 2014

This blog post is aimed to explain proof of Lagrange Multipliers.

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Notes on Cryptology
September 11, 2014

This blog post is aimed to explain basic cryptology concepts and math behind RSA algorithm.

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Proof on Infinity of Prime Numbers
September 11, 2014

In this post, I show that we have infinitely many prime numbers. To do so, I use a proof from 300 BC which provided by Greek Mathematician.

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Fermat’s Little Theorem
September 9, 2014

A French lawyer at the Parlement of Toulouse, and amateur (means lover of) Mathematician in 17th century, called Pierre de Fermat proposed the following statement:

If p is a prime number, then for any integer n, the number n^{p} - n is an integer multiple of p

This post is dedicated to provide the proof of the statement

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Euler's Totient Function
September 4, 2014

A Swiss mathematician from 18th century, called Leonhard Euler formulated the following proposition.

If n is a positive integer, than totient function of n gives the amount of integers, that are less than n and relatively prime to n .

This post is dedicated to express the formula and elaborate the proof of it.

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