COVID 19 Regression analysis Update

Posted on Tue 19 May 2020 in Mathematics • Tagged with Mathematics, COVID 19

The Previous COVID regression analysis was fairly accurate. However, the opening of lockdown offset the statistics a bit and now there are more number of projected cases. Here is a recomputation of the statistics, which projects an average of 172,000 cases by June 1 and 520,000 cases overall …

Continue reading

No square ends in 3

Posted on Fri 15 May 2020 in Mathematics • Tagged with Mathematics

This is an interesting number theory fact that seems strange when taken at face value. Here's a small proof of it:

Continue reading

COVID 19 regression analysis

Posted on Wed 06 May 2020 in Mathematics • Tagged with Mathematics, COVID 19

regression This is a regression analysis attempt for the COVID-19 spread data. The graphs represent total cases per day. The Orange graph is USA, the smaller graph on the left is China and the graph on the right is India. A Standard gaussian curve of the form $Ae^{-b(x-c)^2 …

Continue reading

Roots of $f(f(..f(x)..))$, where $ f(x) = ax^2 + bx + c $, are symmetric about $ \frac{-b}{2a} $

Posted on Thu 30 April 2020 in Mathematics

Define $ f(x) = ax^2 + bx + c , a,b,c \in \mathbb{R}$ and $ f^n(x) = f(f^{n-1}(x)), n>1 $. Prove that the real roots of $ f^n(x) $ are symmetric about the vertical line passing through vertex i.e. $ x = \frac{-b}{2a} $

This seems like …

Continue reading

An integral involving ζ(2) (And Euler's first proof for the Basel Problem)

Posted on Wed 29 April 2020 in Mathematics

Evaluate the integral $$\int_0^1 \frac{\log(x)}{x-1}dx$$

There are a few methods of doing this: the first one uses the taylor series expansion of \( \log(1-x) \): $$I = -\int_0^1 \frac{\log(1-x)}{x}dx$$ $$I = \int_0^1 \frac 1x \left( x + \frac{x^2}{2} + \frac{x …

Continue reading

ICSE Mathematics - Last 23 years analysis and 2018 forecast

Posted on Tue 09 January 2018 in Mathematics

A speculative format for the 2018 ICSE Mathematics paper, created by analysis of the mathematics question papers of the past 23 years. Analysis results

Continue reading