Personal notes on Mathematics and Physics

These are the personal notes that I takes during my research. The starting points of the tree of notes are:

• symmetries of differential equations,
• Cartan geometry,
• gauge theory,
• distributions of vector fields...
• Galois theory,
• Machine Learning
• category theory.
• stochastic calculus
• Linear Algebra,
• Abstract Algebra,
• Analysis,
• Discrete Differential Geometry,
• Physics
• Basic geometry,
• Noncommutative Geometry
• Logic
• Maple cheat-sheet

I also wrote about my personal research, and some lecture notes of the courses I teach.

I started compiling these notes in September 2021.

Disclaimer:

• The html files are generated by using the Digital Garden Plugin in obsidian. Please let me know if you find not rendered formulas, in order to correct them.
• Some pieces are (still) 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. I also annotate my daily 2025 milestones.
The main reason for doing this is learning. So please, feel free to send any questions, comment or mistakes that you find while reading these notes. I will be very grateful.

Antonio J. Pan-Collantes.
antonio.pan@uca.es
Personal website.