Nibcode Solutions Blog

Nowadays information is at hand. Just open your browser, type some words about what you want to know, and thousands of pages will arise to satisfy your information needs; and surprisingly, you will find the most relevant information in the first proposed pages. It’s not a mystery the way the search engines work to make their magic, it’s just mathematics. Behind their complex algorithms is hidden the linear algebra and other mathematical theories.

Every search engine needs three basic elements: a web crawler, a database to save the data it finds, and an algorithm to determine the order of pages returned by any search inquiry. The two first elements can be automated easily, the main problem lies on the third one, and here is where the mathematical tools are the key to the solution.

Since humans invented the written language, they have tried to share information secretly. This is basically, the objective of Cryptography, the study of the techniques to protect sensitive communications by means of data encryption and its posterior decryption. Encryption is the transformation of data into some unreadable form, so, even those who can see the encrypted data cannot understand the hidden information. Decryption is the reverse of encryption; it is the transformation of encrypted data back into some intelligible form.

Although there are different methods to encrypt and decrypt messages, we'll focus on a linear algebra based cipher, the Hill cipher, which uses a matrix as a cipher to encode a message, and it's extremely difficult to break when a large matrix is used. The receiver of the message decodes it using the inverse of the matrix.

Linear Algebra is not what it seems at first thought. Behind all the matrices, polynomials, vectors and spaces, there is a fascinating subject which tools can help you to solve many practical problems. Linear Algebra is a topic connected to different fields inside and outside mathematics like functional analysis, differential equations, engineering, graph theory, statistics, linear programming, and computer graphics.

There are hundreds of books with the aim of teaching Linear Algebra, your choice will depend, basically, on the kind of course you are taking, and on the approach, prose and rigor of the text you prefer to study. Here I propose a brief list of books, based on my personal experience, from famous books I have read or consulted.

Many people find in the lottery the chance to change their life, but the reality is that the odds are so low that most people can be playing for hundreds of years without ever get closer to the prize. A thought usually goes through the mind of the players is: "If there are people who won the price, why cannot I win it too?", which I do not doubt, but let us look at the numbers and see how lucky we would be if we won the lottery.

Let's explain how to calculate the chance to win the lottery based on 49 possible numbers, where 6 numbers are randomly selected in each drawn.