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Maths, CS & AI Compendium

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bury good ideas under dense notation, skip the intuition, assume you already know half the material, and quickly get outdated in fast-moving fields like AI.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

Citation

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