Personal notes on Mathematics and Physics

These are the personal notes that I takes during my research in

symmetries of differential equations,

Cartan geometry,

gauge theory,

distributions of vector fields...

But also other topics that interests me like Galois theory or category theory. And even my personal ideas.

Also, basic material from:

• Linear Algebra,

• Abstract Algebra,

• Analysis,

• Discrete Differential Geometry,

• Physics,...

• Basic geometry,

• Noncommutative Geometry

• Logic

I started to write them in September 2021.

Disclaimer:

• The html files are generated by using a python script, so Mathjax could be failing in some formulas. Please let me know in order to correct them.

• Some pieces are written in Spanish (I will translate them little by little), or refers to personal notes written in other formats. Let me know if you are interested in any clarification.

• There can be mistakes, since this notes reflects my own learning process.

Some of these notes (the ones with more quality) are also being published in this blog.

The main reason for doing this is learning. So please, feel free to send any questions, comment or mistakes that you can find while reading these notes. I will be very grateful.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es