Alvaro-Manzo/DEMOSTRACIONES

DEMOSTRACIONES is a thoughtful and sincere LaTeX-based mathematics repository with a clear educational purpose: collecting step-by-step demonstrations for foundational arithmetic, algebra, geometry, number theory, inequalities, and introductory physics. The strongest part of the project is the author’s intent and progression. The README presents the repository as a learning resource for students, educators, and self-taught learners, and main.tex backs that up with a large, structured Spanish-language proof document using theorem/proposition/proof environments, chapters, sections, a table of contents, and professional LaTeX packages like amsmath, amssymb, amsthm, hyperref, microtype, and tocloft. The project also includes a generated PDF, which is useful for readers who want the material without compiling LaTeX locally. The scope is surprisingly broad for a compact repo: proofs range from 1 = 0.999..., parity arguments, irrationality of square roots, induction-style summations, AM-GM, prime infinitude, polynomial identities, the quadratic formula, and basic geometry/physics formulas. That makes the repo feel like a personal mathematical notebook growing into a public study guide, which is a good fit for open-source learning material.

The main improvement area is repository polish and reproducibility. The README says to compile main.tex with pdflatex, but the repository currently includes main (2).pdf rather than the documented main.pdf, and main.tex references image files such as logo_unam_negro (1).png and pitagoras.png that are not present in the repository. TESIS_FCIENCIAS.tex also appears to be a separate thesis-titlepage template and references external assets/packages that are not included, so it may confuse readers unless it is documented or moved into an examples/templates folder. The README references CONTRIBUTING.md, but that file is missing. Adding the missing assets, renaming the PDF consistently, including a short “how to compile from a fresh clone” section, and adding a simple contribution guide would make the project much easier to use. A small CI workflow that compiles the LaTeX document would also be a strong next step, because it would catch missing images or package issues automatically. Overall, this is a meaningful educational repository with clear effort, a solid LaTeX foundation, and a strong learner-focused spirit; with a bit more structure around compilation, assets, and contribution docs, it could become a much more reliable and welcoming reference for beginner proof writing.