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