Monthly Archives: December 2014

An imaginary tale by Paul Nahin

Posted on December 30, 2014 by Sumant Sumant

I first encountered this book in 2009 at Morris library and I still remember at that time I was trying to read it and dozzed off. Over the years Paul Nahin has become my favorite author. He is a very … Continue reading →

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Prime Obsession: Notes

Posted on December 30, 2014 by Sumant Sumant

    Chapter 1 Chapter 20: The Riemann Operator and Other Approaches   Chaos Theory development began with Poincare with his three body problem. However the real progress started in 1960s with the availability of fast computers. Ed Lorentz is … Continue reading →

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Dirichlet’s Discontinuous Integral

Posted on December 30, 2014 by Sumant Sumant
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Prime reciprocal series is diverging

Posted on December 30, 2014 by Sumant Sumant

We know that Harmonic series is diverging. The proof is very simple by grouping the terms. Whereas for geometric sequence is converging. Our question is what happens when we have . We will prove this by contradiction. Assuming that the … Continue reading →

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Relation between Gamma Function and Zeta Function

Posted on December 30, 2014 by Sumant Sumant

We know that Let   Which means Taking sum on both the sides we get  

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Arithmetic Geometric Inequality

Posted on December 30, 2014 by Sumant Sumant

This is a famous inequality that one should know. The case for two numbers is really easy The case for 4 variables is also pretty straight forward The case for 3 variables is a little bit tricky but can be … Continue reading →

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ABC conjecture

Posted on December 24, 2014 by Sumant Sumant

It’s one of the most sought after solution in Mathematics. Currently Shinichi Mochizuiki is the front runner to have given the solution. However solution is complicated over 500 pages long and it is still being verified. Shinichi did his schooling … Continue reading →

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