HenryNdubuaku/maths-cs-ai-compendium

What it is

An open, unconventional textbook covering mathematics, computing, and artificial intelligence from the ground up. It's written for curious practitioners who want to deeply understand the material, not just survive an exam or interview.

Why it exists

The author spent years working in AI/ML, filling notebooks with intuition-first explanations, real-world context, and no hand-waving. In 2025, a few friends used these notes to prep for interviews at DeepMind, OpenAI, Nvidia, etc. — all got in and perform well in their roles. The author also got into Y Combinator. Now the notes are shared publicly.

Content

The compendium has 18 chapters, all marked "Available":

1. Vectors — spaces, magnitude, direction, norms, metrics, dot/cross/outer products, basis, duality
2. Matrices — properties, special types, operations, linear transformations, decompositions (LU, QR, SVD)
3. Calculus — derivatives, integrals, multivariate calculus, Taylor approximation, optimisation, gradient descent
4. Statistics — descriptive measures, sampling, central limit theorem, hypothesis testing, confidence intervals
5. Probability — counting, conditional probability, distributions, Bayesian methods, information theory
6. Machine Learning — classical ML, gradient methods, deep learning, reinforcement learning, distributed training
7. Computational Linguistics — syntax, semantics, pragmatics, NLP, language models, RNNs, CNNs, attention, transformers, text diffusion, OCR, MoE, SSMs, modern LLM architectures, NLP evaluation
8. Computer Vision — image processing, object detection, segmentation, video processing, SLAM, CNNs, vision transformers, diffusion, flow matching, VR/AR
9. Audio & Speech — DSP, ASR, TTS, voice/acoustic activity detection, diarisation, source separation, active noise cancellation, wavenet, conformer
10. Multimodal Learning — fusion strategies, contrastive learning, CLIP, VLMs, image/video tokenisation, cross-modal generation, unified architectures, world models
11. Autonomous Systems — perception, robot learning, VLAs, self-driving cars, space robots
12. Graph Neural Networks — geometric deep learning, graph theory, GNNs, graph attention, Graph Transformers, 3D equivariant networks
13. Computing & OS — discrete maths, computer architecture, operating systems, concurrency, parallelism, programming languages
14. Data Structures & Algorithms — Big O, recursion, backtracking, DP, arrays, hashing, linked lists, stacks, trees, graphs, sorting, binary search
15. Production Software Engineering — Linux, Git, codebase design, testing, CI/CD, Docker, model serving, MLOps, monitoring, using coding agents
16. SIMD & GPU Programming — C++ for ML, how frameworks work, hardware fundamentals, ARM NEON/I8MM/SME2, x86 AVX, GPU/CUDA, Triton, TPUs, RISC-V, Vulkan, WebGPU
17. AI Inference — quantisation, efficient architectures, serving and batching, edge inference, speculative decoding, cost optimisation
18. ML Systems Design — systems fundamentals, cloud computing, distributed systems, ML lifecycle, feature stores, A/B testing, recommendation/search/ads/fraud design examples

MCP server

The repo includes an MCP server that lets any AI assistant (Claude Code, Cursor, VS Code, etc.) use the compendium as a knowledge base. It requires a local clone of the repo and comes with tools for educational purposes and example implementations.

Learning philosophy

The foreword argues that great AI researchers and engineers come from quality knowledge consumption and rich experience — like a neural network trained on good data. It cites Kvashchev's experiment, a long-term Serbian study showing that intensive three-year training in creative problem-solving can significantly boost fluid intelligence by 10–15 IQ points. It uses Charles Darwin as an example: considered average by his teachers, he described himself as a "slow processor" who needed time to soak in data. The compendium is designed for "the Darwins of the world" — people who benefit from a well-connected flow of knowledge. Only elementary maths and basic Python are required; everything else is picked up along the way.

Study technique

The author shares a two-phase method:

• Phase 1 — Cumulative reading: After class, read each material before bed. At the next lecture, start over from the beginning and read up to the current point, filling knowledge gaps with additional research. This helps the brain connect patterns.
• Phase 2 — Shadow reading before exams: Read each subtitle, close the book, then visualise and write an explanation for that concept. Only re-read what you missed (similar to masked-language modelling in machine learning). After re-reading, implement the concept in code to develop muscle memory.

Author

Henry Ndubuaku. The README points to his GitHub profile for more information.

Citation

A BibTeX entry is provided for citing the book:

@book{ndubuaku2025compendium,
  title     = {Maths, CS & AI Compendium},
  author    = {Henry Ndubuaku},
  year      = {2026},
  publisher = {GitHub},
  url       = {https://github.com/HenryNdubuaku/maths-cs-ai-compendium}
}

Access

Readable online at henryndubuaku.github.io/maths-cs-ai-compendium. The repo also displays a Trendshift badge (a popularity metric).