Category Archives: Uncategorized

Improper integrals and periodic functions

The idea for this post came from a question I saw in a math help forum about improper integrals. While this problem has a very simple solution using basic tools in integral calculus, I want to show a more geometric … Continue reading

Posted in Uncategorized | Leave a comment

Radars and the Chinese Remainder Theorem

The radar is a detection system that was developed before and during World War II for military uses, though by today it has many other applications including, for example, astronomical and geological research. The name radar is an acronym for … Continue reading

Posted in Uncategorized | Tagged , | 2 Comments

Billiard tables – and what is mathematical research

Mathematical research is something that most people don’t really understand. They can imagine someone in a lab mixing chemicals or doing experiments with some scientific machinery, but mathematical research? The goal of this post is to share with you a … Continue reading

Posted in Uncategorized | Leave a comment

Lattice parametrization

We came to the point where we have already seen how lattices appear naturally in problems arising from number theory. In this post we construct a nice space which parametrize the set of all lattices of a certain dimension, with … Continue reading

Posted in Uncategorized | Tagged , , , | Leave a comment

The rise of algebraic extensions

In the post about number theory and lattices,¬†we tried to determine when is the Euclidean distance in is actually a Euclidean norm and we were led to study the embeddings of rings such as as lattices in . As mentioned … Continue reading

Posted in Algebraic number theory and dynamics, Uncategorized | Tagged , , | Leave a comment

A wild lattice appears

A couple of years ago I began doing some research in a new mathematical area (at least new for me) and suddenly lattices began to appear everywhere. The thing that makes these lattices interesting is how they are connected to … Continue reading

Posted in Uncategorized | Tagged | Leave a comment