A bilingual, structured roadmap for self-studying mathematics through books, from foundational topics to advanced undergraduate and graduate-level mathematics.
This project was built based on my experience during my BSc and MSc in Mathematics. It focuses on books that are suitable for self-study, with a clear progression, study strategy, and transition criteria between phases.
- Portuguese: https://bertolucci-rl.github.io/math-self-study-roadmap/
- English: https://bertolucci-rl.github.io/math-self-study-roadmap/en/
The roadmap is divided into three tracks:
-
Basic Track
Foundations, precalculus, mathematical proofs, calculus, and real analysis. -
Undergraduate Track
Core areas of a mathematics degree: analysis, algebra, geometry, and topology. -
Complete Track
Advanced topics closer to graduate-level study and research.
I created this roadmap to help people who enjoy mathematics and want a long-term, book-based path for studying it seriously.
The goal is not to provide a shortcut, but to organize a realistic progression through books that are rigorous, coherent, and reasonably friendly for self-study.
Some references are Brazilian or Portuguese-language books. They are included intentionally, either because they are especially self-study friendly or because they played an important role in my own mathematical formation.
In future versions, I plan to include English-language alternatives for the main Portuguese references, making the roadmap more accessible to an international audience.
This roadmap may be useful for:
- self-learners who want to study mathematics through books;
- undergraduate students looking for a structured path;
- people coming from technical fields who want stronger mathematical foundations;
- anyone interested in learning mathematics with rigor and depth.
math-self-study-roadmap/
├── index.html # Portuguese version
├── en/
│ └── index.html # English version
├── assets/
│ └── covers/
├── README.md
└── LICENSE
I’m Ricardo Bertolucci, MSc in Mathematics, currently transitioning into Data Science and AI Engineering while maintaining a strong focus on mathematical thinking.
The written roadmap content is licensed under CC BY-NC 4.0.
Book cover images belong to their respective authors, publishers, or rights holders and are used only for identification, commentary, and educational reference.