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 CayleyHamilton Theorem
 Chinese remainder theorem
 Compression
 Diophantine approximation
 Dirichlet's approximation theorem
 Dirichlet's unit theorem
 Dynamics
 eigenvalues
 Entropy
 Generic Matrix
 Geometry
 Geometry of numbers
 Homogeneous spaces
 Hyperbolic space
 Lattices
 Minkowski's Theorem
 Number Theory
 Pell's equations
 radar
 random walk
 self similar sets
 Sierpinski carpet
 Sierpinski triangle
 SL_2(Z)
 stochastic matrices
 Weak Law of Large Numbers
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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
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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
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
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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
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Tagged Homogeneous spaces, Hyperbolic space, Lattices, SL_2(Z)
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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
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