Read online: henryndubuaku.github.io/maths-cs-ai-compendium
Most textbooks bury good ideas under dense notation, skip the intuition, assume you already know half the material, and quickly get outdated in fast-moving fields like AI. This is an open, unconventional textbook covering maths, computing, and artificial intelligence from the ground up. Written for curious practitioners looking to deeply understand the stuff, not just survive an exam/interview.
Over the past years working in AI/ML, I filled notebooks with intuition first, real-world context, no hand-waving explanations of maths, computing and AI concepts. In 2025, a few friends used these notes to prep for interviews at DeepMind, OpenAI, Nvidia etc. They all got in and currently perform well in their roles. So I'm sharing to everyone.
| # | Chapter | Summary | Status |
|---|---|---|---|
| 01 | Vectors | Spaces, magnitude, direction, norms, metrics, dot/cross/outer products, basis, duality | Available |
| 02 | Matrices | Properties, special types, operations, linear transformations, decompositions (LU, QR, SVD) | Available |
| 03 | Calculus | Derivatives, integrals, multivariate calculus, Taylor approximation, optimisation and gradient descent | Available |
| 04 | Statistics | Descriptive measures, sampling, central limit theorem, hypothesis testing, confidence intervals | Available |
| 05 | Probability | Counting, conditional probability, distributions, Bayesian methods, information theory | Available |
| 06 | Machine Learning | Classical ML, gradient methods, deep learning, reinforcement learning, distributed training | Available |
| 07 | Computational Linguistics | syntax, semantics, pragmatics, NLP, language models, RNNs, CNNs, attention, transformers, text diffusion, text OCR, MoE, SSMs, modern LLM architectures, NLP evaluation | Available |
| 08 | Computer Vision | image processing, object detection, segmentation, video processing, SLAM, CNNs, vision transformers, diffusion, flow matching, VR/AR | Available |
| 09 | Audio & Speech | DSP, ASR, TTS, voice & acoustic activity detection, diarisation, source separation, active noise cancellation, wavenet, conformer | Available |
| 10 | Multimodal Learning | fusion strategies, contrastive learning, CLIP, VLMs, image/video tokenisation, cross-modal generation, unified architectures, world models | Available |
| 11 | Autonomous Systems | perception, robot learning, VLAs, self-driving cars, space robots | Available |
| 12 | Graph Neural Networks | geometric deep learning, graph theory, GNNs, graph attention, Graph Transformers, 3D equivariant networks | Available |
| 13 | Computing & OS | discreet maths, computer architecture, operating systems, RAM, concurrency, parallelism, programming languages | Coming |
| 14 | Data Structures & Algorithms | arrays, trees, graph, search, sorting, hashmaps | Coming |
| 15 | SIMD & GPU Programming | ARM & NEON, X86 chips, RISC ships, GPUs, TPUs, triton, CUDA, Vulkan | Coming |
| 16 | ML Systems Design | systems design fundamentals, cloud computing, large scale infra, ML systems design examples | Coming |
| 17 | AI Inference | quantisation, streamingLLMs, continuous batching, edge inference, | Coming |
| 18 | Applied AI | Ai in finance, healthcare, protein, drug discovery | Coming |
| 19 | Bleeding Edge AI | quantum ML, neuromorphic ML, decentralised AI, datacenters in space, brain machine interfaces | Coming |
@book{ndubuaku2025compendium,
title = {Maths, CS & AI Compendium},
author = {Henry Ndubuaku},
year = {2026},
publisher = {GitHub},
url = {https://github.com/HenryNdubuaku/maths-cs-ai-compendium}
}