Extractable patterns

"You are number of languages that you know" said one of the quotes attributed to Al-Farabi, which my school teacher used to tell us. Indeed almost all languages describe the same objects: humans, animals, nature and universe in general. However, the way each language does so might differ from another one. This difference makes learning new languages fun. A somewhat similar statement can be said about programming languages. Almost all of them perform some kind of logical and computational transformations on given data, however the ways they do so might significantly differ. Having learnt some Python to play with Machine Learning (ML) algorithms, I wanted to explore other programming languages. The first language which came to mind was C++. It is one of the languages used to code massive and complex software systems. So did I explored using a website  https://www.programiz.com/cpp-programming . How it went The installation part went easy. The application XCode does a solid ...

When one reads about Machine Learning (ML) or Artificial Intelligence (AI) it is common to come across a list of approaches to AI such as: symbolic reasoning, Bayesian learning, artificial neural networks and so on. Seeing this list I was puzzled with a notion of Bayesian Learning. The only thing I knew with a name Bayes in its name was a famous Bayes's theorem which states that \[ P(H\mid E) = \frac{P(E\mid H)P(H)}{P(E)} \] where $P(H)$ and $P(H\mid E)$ denote prior and posterior probabilities of hypothesis $H$, respectively. What puzzled me is the application of such a simple looking formula to draw patterns from data. In order to learn basic principles of Bayesian learning, I decided to consult Wikipedia and few online tutorials. This post is about results of this exploration. Wikipedia says Bayesian learning (inference?) is a method of statistical inference in which Bayes's theorem is used to update the probability for a hypothesis as more evidence or informatio...

A subject of Algebraic Geometry (AG) is one of central branches of Mathematics, yet I have almost no knowledge of objects and spaces that algebraic geometers study. The mere look at the name suggests some kind of relationship between algebra and geometry. So does algebra lends its hand to solve geometric problems, or is it other way around. I did not know. Realising my ignorance of the matter, I decided to rectify situation I decided to read some Wikipedia articles along with some introductory books on the subject matter. In this post I intend to share fruits of my explorations. How AG was born? AG was born out of desire to solve systems of polynomial equations. Suppose we have a system \[ f_i(X_1,\ldots,X_n) = 0, \quad i=1,\ldots, m \] where each $f_i$ is a polynomial of $n$ variables with coefficients drawn from some field $k$, which can succinctly be written as $f_i\in k[X_1,\ldots,X_n]$. What to do next? Mostly it is pretty difficult to solve such systems. However, i...