This book was written first as a gift.
To my girls — Allyana, Emalina, and Milana — I want you to grow up with the confidence that the world is knowable. Not “easy,” not “obvious,” but understandable if you’re willing to stay curious, ask good questions, and keep going when something feels hard. Mathematics is one of the clearest languages we have for that kind of understanding: it teaches you how to separate signal from noise, how to reason from first principles, and how to build truth step by step.
In the years ahead, intelligence — both human and machine — will shape nearly everything. My hope is that this book helps you see how intelligence is built: how patterns become models, how models become decisions, and how decisions can be made with humility and care. If you can learn to read the equations behind the world, you won’t just use the future — you’ll help create it.
Thank you to my wife, for believing in me, for holding our family together through the long stretches of work, and for reminding me what matters most. And thank you to my mom, for her steady love and support — for the sacrifices that made my education possible, and for the strength that taught me to finish what I start.
And thank you to my dad, for never once doubting me — for the quiet confidence that made me feel brave enough to try, and the steady presence that reminded me I could.
And to my mom, again — thank you for helping us day and night with the kids so I could do this work. Your love shows up in every page, even when your name isn’t on the cover.
If you’re reading this years from now: I love you. Always.
How this book is meant to be used
This book is a practical reference for rebuilding mathematical intuition across calculus, linear algebra, and probability/statistics — and then connecting those ideas to modern machine learning. The goal is not memorization; it’s developing the ability to read equations in technical papers and understand what they are doing, why they work, and how to implement them.
If you’re skimming, read each chapter’s opening sections and the Key Takeaways at the end. If you’re studying, follow the code examples and re-run them with variations (different parameters, initial conditions, and datasets). For reference use, rely on the PDF’s built-in table of contents to jump directly to the concept you need.
A note on the 2026 revision
This is the 2026 revision of a book first written in 2024. Chapters 1–8 are unchanged — the math there is genuinely timeless, and the explanations have not needed rewriting. Chapter 9 has been refreshed: the original sections on PPO, DPO, and attention are still there, and five new sections have been added to cover the ideas the field moved to between 2023 and 2025 — rotary position encodings (RoPE), grouped-query attention, flash attention, scaling laws, GRPO, and diffusion / flow matching. Chapter 10 has been rewritten from scratch as a reading walkthrough of a single 2025 paper (DeepSeek-R1), so that the book closes with a worked example of using its own math to follow current research.
The earlier Chapter 10 — a broader "mathematical mastery across domains" capstone — has been archived. Everything it contained is still covered in the relevant earlier chapters.