Derivative of $x^x$
Calculating the derivative of $x^x$ is a very simple task, but it may be hard to find the general idea on your own, so here it is. We will (...)
July 2, 2017 – Jakub MarianMathematics
Integral of $x^n$
How to calculate the indefinite integral of $x^n$? It’s quite simple. We are looking for a function $f(x)$ such that $f’(x) = x^n$. As you (...)
July 2, 2017 – Jakub MarianMathematics
Integral of $e^{-x^2}$ from $-\infty$ to $\infty$
In this article, I will give a detailed explanation of why the Gaussian integral is equal to $√\pi$, that is, why the following equality (...)
June 29, 2017 – Jakub MarianMathematics
The ‘day of the week boy or girl’ paradox explained
There is a well-known result in probability theory that seems to defy common sense. Note that in the problem statement we assume that the (...)
July 25, 2016 – Jakub MarianMathematics
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Labelling articles as “per capita” when the unit used is different
After I published my recent article about the Number of metal bands per capita in Europe, I got quite a few comments saying that my use of (...)
May 29, 2016 – Jakub MarianMathematics

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What does it mean for a function to be well-defined?
A common addendum to a formula defining a function in mathematical texts is, “it remains to be shown that the function is well defined.” (...)
March 3, 2015 – Jakub MarianMathematics
Is 0.999… (repeating) equal to 1?
The short answer is yes. $0.\bar 9$ (zero point 9 repeating) is exactly 1. However, a lot of people find this result counter-intuitive (...)
October 16, 2014 – Jakub MarianMathematics
Do certain numbers in a lottery have a higher probability of winning than others?
Does going for “nice” sequences of numbers, like 1 2 3 4 5 6, reduce the probability of winning in a lottery? Some people think so. “Have (...)
September 25, 2014 – Jakub MarianMathematics
Will computers ever be smarter than humans?
When I was a child, I was fascinated by the idea that some day we will be able to construct computers that will be smarter than us. Later, (...)
September 12, 2014 – Jakub MarianMathematics
Arithmetics in which you can divide by zero
When I was still in primary school, I was fascinated by things you “can’t do” in mathematics and developed a “theory” of division by zero. (...)
June 8, 2014 – Jakub MarianMathematics