Introduction - Maths, CS & AI Compendium

Overview

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bury good ideas under dense notation, skip the intuition, assume you already know half the material, and quickly get outdated in fast-moving fields like AI.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.

Background

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.

Outline

#	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	Coming
09	Audio & Speech	DSP, ASR, TTS, voice & acoustic activity detection, diarization, source separation, active noise cancelation, wavenet, conformer	Coming
10	Multimodal Learning	fusion strategies, contrastive learning, VLMs, image tokenizer, video audio co-generation	Coming
11	Autonomous Systems	perception, robot learning, VLAs, self-driving cars, space robots	Coming
12	Computing & OS	discreet maths, computer architecture, operating systems, RAM, concurrency, parallelism, programming languages	Coming
13	Data Structures & Algorithms	arrays, trees, graph, search, sorting, hashmaps	Coming
14	SIMD & GPU Programming	ARM & NEON, X86 chips, RISC ships, GPUs, TPUs, triton, CUDA, Vulkan	Coming
15	Systems Design	systems design fundamentals, cloud computing, large scale infra, ML systems design examples	Coming
16	Inference	quantisation, streamingLLMs, continuous batching, edge inference,	Coming
17	Intersecting Fields	quantum ML, neuromorphic ML, AI for finace, AI for bio	Coming
18	Research Blog	share small-scale experimental finding, 1 per md file with your name & affiliation, I have a lot	Coming

Citation

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

Contributions

Star & watch to get content as they drop.
Suggest topics via GitHub issues.
PR corrections and better intuition.
Create SVG images in ../images/ for all diagrams.
For equations, use ```math fenced code blocks (NOT $$)
For display math — GitHub escapes \\ inside $$, breaking matrices.
Inline math $...$ is fine for simple expressions but move anything with \\ into a ```math block.
Use \ast instead of * for conjugate/adjoint in inline math.