Antonio Lupetti

Mathematics is not something distant. It is a structure that quietly shapes reality.

I’ve been working on a new video for algebrica.org

Over the past two weeks, I've thoroughly revised and updated all the articles in Algebrica's chapter on complex numbers. Here is the complete list of updated articles:

1. Complex Numbers
2. Operations with Complex Numbers
3. Complex Numbers in Trigonometric Form
4. Euler’s Formula
5. Complex Numbers in Exponential Form
6. De Moivre’s Theorem
7. Roots of Unity
8. Fundamental Inequalities for Complex Numbers
9. Triangle Inequality
10. Cauchy–Schwarz Inequality
11. Complex Powers
12. Complex Logarithm

All content is freely available on Algebrica, with no ads or paywalls. You can also download the Markdown source files for free from the GitHub repository.

algebrica.org/complex-number…

Our universe is not described by mathematics.
It is mathematics.

algebrica.org

"Game Theory" is a free university-level textbook that offers a comprehensive introduction to the mathematical foundations of game theory.

This edition has over 630 pages and covers strategic-form games, dominant strategies, Nash equilibrium, mixed strategies, dynamic games, backward induction, expected utility theory, Bayesian games, incomplete information, sequential equilibrium, and more.

The book combines mathematical theory, proofs, examples, and exercises with detailed solutions. I think it's an excellent resource for anyone interested in the mathematics of strategic decision-making.

faculty.econ.ucdavis.edu/faculty/bonann…

"Understanding Linear Algebra" is another interesting university-level textbook that offers a clear, accessible introduction to the fundamental concepts of linear algebra, particularly suitable for first-year university students.

The book is freely available and covers systems of linear equations, vectors, matrices, linear combinations, linear independence, matrix transformations, bases and coordinate systems, determinants, eigenvalues and eigenvectors, diagonalization, orthogonality, least squares, numerical methods, and much more.

I think it's a useful resource for anyone approaching linear algebra for the first time or looking for a reference to review the foundamentals.

scholarworks.gvsu.edu/cgi/viewconten…