May 25, 2018
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On Bertrand's Postulate and how we prove it using discrete functions related to prime numbers as well as the Gamma Function |
Dec 26, 2017: FLOOD OF PAPERS FROM PAST 2 YEARS
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Random thing from MIT PRIMES; I tried doing some of the problems and gave up by the end of the third one...hehe. I did make some nice tables/pictures/colors there at the end though. |
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On Cubic Polynomials: here, we find the cubic formula and how to use it and roots of unity to find roots of a cubic polynomial. |
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The Gamma Function: we introduce the gamma function, and explain how to evaluate 0.5 factorial, using lots of integration and series and some advanced cosine integrals, 2nd edition. |
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Extra tidbit on the Gaussian integral. |
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On Stirling's approximation for the factorial, found using the infinite product form of the gamma function, creative telescoping, and Legendre's duplication formula, all proven within the paper. Reading the first gamma function paper is recommended. |
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Here, we prove that the sum of the reciprocals of the primes is infinite, by using the sum of the reciprocals of the natural numbers and the sum of the reciprocals of the squared numbers |
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We discuss how matrices work in Page Rank Algorithms, and how we can use the power of Linear Algebra to understand how Google works. |
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We explore the world of matrices and the special things you can do with matrices, like finding a formula for Fibonacci numbers and recursive formulas in general |
