My name is Sebastian Ferreira, and this is my math archive.
On 2024 I decided to reteach myself all the math I didn’t properly pay attention to since school, with the goal to genuinely understand it and being able to teach it.
This wiki is intended as a digital garden. Notes will evolve over time as my understanding and explanations improve.
Rather than a linear course, the content is organized into atomic entries. The idea is to let you learn what you need without forcing you to repeat what you already know.
Academic mathematics is often formal and highly abstract, which creates a steep learning curve for beginners. That abstraction is necessary, since mathematics is ultimately a language for abstraction.
I understand the need of mathematicians to keep math abstract, after all, is a language for abstraction.
Still, I aim to provide a bridge between everyday intuitions and the formal definitions.
This wiki is not meant to replace primary learning materials. Use it as a support when you feel stuck or when a definition feels opaque.
The focus here is pedagogical rather than fully rigorous. Examples are meant as stepping stones. The underlying mathematics usually goes further than what is shown.
Ultimately, to truly learn mathematics, you have to do it yourself.
See the Vector Space for how to get started.