Give a Counterexample
Have you noticed that disputes are often unconstructive, and the winner is the one who shouted louder or expressed themselves more assertively? But if we apply the laws of logic to our arguments, any disagreement can be resolved smoothly and elegantly. In mathematics, this technique has been honed to perfection.
Everyday Combinatorics
Some claim that mathematics is merely an abstract science needed only in school. Arithmetic is seen as sufficient for everyday life — for counting money. What about the branch of mathematics known as combinatorics? It’s barely a part of the school curriculum, merely perceived as gymnastics for the mind, but it can be found everywhere — from the analysis of popular games, such as poker, to the creation of drugs.
Fractals
In everyday life, we rarely hear the mysterious word “fractal,” but we encounter them on a daily basis. Trees, mountains, smoke, plants, and even the circulatory system have fractal structures. Fractals can be applied in various areas: from image compression algorithms to the study of blood vessels of living organisms. So what is a fractal?