These are notes I typed up during my attempts to understand mathematical concepts. It could contain as little as a single theorem or as much as a whole subject, depending on the reason I read them. As the time progressed, I noticed I had so many notes, and I thought it might be useful for someone out there. That is why I decided to post these notes.

The first disclaimer is that these notes are initially for myself, so some tedious calculations or proofs might be included/omitted. Secondly, it certainly contains some (indeliberate) mistakes, so if you find any mistakes or have any suggestions, feel free to contact me via my email. I would be happy to update these notes.

Calculator

• WolframAlpha 

• Symbolab 

• Pi-Base - database of topological spaces and their properties (very powerful for providing counterexamples)

• minimal polynomial of a matrix https://www.123calculus.com/en/matrix-minimal-polynomial-page-1-35-320.html

• GCD of polynomials over finite fields https://planetcalc.com/8355/

• continued fraction https://r-knott.surrey.ac.uk/Fibonacci/cfCALC.html

• integral https://www.integral-calculator.com 

• Six degree of freedom

• Sudoku checker

Teaching Material

• Lean Game - interactive game for learning Lean

• Texnique - LaTeX practicing game

• Project Euler - Mathematical problems suitable for practicing computer programming

• Can human generate a truly random sequence of H and T?

• 100 Debates in mathematics

Visualization

• Desmos.com - graphing calculator

• Cayley graphs of semidirect product groups https://juliapoo.github.io/mathematics/2023/07/15/plotting-cayley-graphs.html

• Interactive matrix visualization https://shad.io/MatVis/

• 2D vector field https://www.geogebra.org/m/QPE4PaDZ

• 3D vector field https://www.geogebra.org/m/u3xregNW