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 Marian – Mathematics

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 Marian – Mathematics

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 Marian – Mathematics

The ‘day of the week boy or girl’ paradox explained
There is a wellknown result in probability theory that seems to defy common sense. Note that in the problem statement we assume that the (...)
July 25, 2016 – Jakub Marian – Mathematics

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 Marian – Mathematics

By the way, have you already seen my brand new web app for nonnative speakers of English? It's based on reading texts and learning by having all meanings, pronunciations, grammar forms etc. easily accessible. It looks like this:
What does it mean for a function to be welldefined?
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 Marian – Mathematics

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 counterintuitive (...)
October 16, 2014 – Jakub Marian – Mathematics

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 Marian – Mathematics

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 Marian – Mathematics

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 Marian – Mathematics
