Lead Author: Abhishek Divekar
Mastering GenAI begins with mastering the math. "GenAI Math From Scratch" provides you the necessary mathematical foundation you need to succeed, without paywalls. This free online book begins with high-school level set theory and probability, then advance through linear algebra, calculus, real analysis and beyond, until you can read graduate-level GenAI papers with confidence.
Think of the journey as a spiral staircase wrapped around sturdy pillars, like in the image below. With each turn you ascend, the pillars expand outwards, revealing how these mathematical foundations power NLP, computer vision, reinforcement learning, and a wide space of emerging GenAI paradigms. Along the way, you'll also master modern tooling - NumPy, PyTorch, and parallel-programming patterns...math that lives in real code, not just symbols on your screen.
Ready to level up? 🚀 Start reading here: https://adivekar.quarto.pub/gen-ai-math-from-scratch
"GenAI Math From Scratch" was initially contributed by winners of the Indian AI Olympiad 2025. Since then, it has evolved into a community-driven resource dedicated to advancing rigorous GenAI education for both leaders and learners worldwide.
Please help us by starring this repository!
If this textbook helps you, inspires you, or simply sounds interesting, please hit that ⭐️ button in the top-right corner.
Every star is a vote for open and inclusive GenAI education 🎉
| What your star does | Why it matters |
|---|---|
| Boosts visibility | More educators, students, and potential contributors discover the project. |
| Unlocks resources | High star counts help us secure free compute credits & tooling grants for contributors. |
| Proves demand | Signals to mentors, reviewers, and future partner orgs that free AI math is worth backing. |
| Motivates the team | A tiny dopamine hit keeps volunteers refining examples, diagrams, and proofs. |
- Share the repo on social media or with your study group.
- Open an issue with suggestions, typos, or tricky sections that need love.
- Submit a Pull-Request – new examples, clearer wording, or fresh diagrams are always welcome! See the CONTRIBUTING section below.
- Students in low-income or under-resourced regions – they get a high-school to graduate-level AI math roadmap at zero cost.
- Self-taught AI engineers – clear, open-source explanations beat paywalled courses.
- The research community – a common reference lowers the barrier to entry and raises the floor of understanding.
If you are interested in contributing to the project, welcome! Please go through the following steps:
cd ~
git clone https://github.com/adivekar-utexas/gen-ai-math-from-scratch.git
cd gen-ai-math-from-scratch/cd book/
conda create --prefix env python=3.12 --yes
conda activate ./env
pip install uv
uv pip install pandas numpy s3fs tqdm pydantic urllib3 ipython ipykernel jupyterlab jupyter jupyter_contrib_nbextensions ipywidgets statsmodels scikit-learn nltk plotly plotly-express bokeh seaborn hvplot holoviews matplotlib
conda install jupyter --yes
python3 -m ipykernel install --user --name quarto-amfs-book
quarto check jupyter(Needs Step 1 to be completed)
- Download the "Quarto" extension.
- Clone this repo locally.
- File > New Window
- (In new window) File > Open folder > open repo folder
- Cmd + Shift + P > Python > Select Interpreter
- Select ./book/env/bin/python
After you have made a contribution to your local copy, commit it and raise a pull-request.