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bury good ideas under dense notation, skip the intuition, assume you already know half the material, and quickly get outdated in fast-moving fields like AI.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

This 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. Comes with tools for educational purposes and example implementations.

Table of contents:

🔢 Mathematical foundations

01 — Vectors: spaces, norms, metrics, dot/cross/outer products, basis, duality
02 — Matrices: properties, linear transformations, LU/QR/SVD decompositions
03 — Calculus: derivatives, integrals, Taylor approximation, optimisation, gradient descent
04 — Statistics: sampling, central limit theorem, hypothesis testing, confidence intervals
05 — Probability: counting, distributions, Bayesian methods, information theory

🧠 Machine learning by modality

06 — Machine Learning: classical ML, deep learning, RL, distributed training
07 — Computational Linguistics: NLP, RNNs, attention, transformers, MoE, SSMs, modern LLM architectures
08 — Computer Vision: detection, segmentation, SLAM, ViTs, diffusion, flow matching, VR/AR
09 — Audio & Speech: DSP, ASR, TTS, diarisation, source separation, WaveNet, Conformer
10 — Multimodal Learning: contrastive learning, CLIP, VLMs, video tokenisation, world models
11 — Autonomous Systems: perception, robot learning, VLAs, self-driving, space robots
12 — Graph Neural Networks: geometric deep learning, graph attention, 3D equivariant nets

⚙️ Engineering & systems

13 — Computing & OS: discrete maths, architecture, concurrency, parallelism
14 — Data Structures & Algorithms: Big O, recursion, DP, graphs, sorting, binary search
15 — Production Software Engineering: Linux, Git, CI/CD, Docker, MLOps, working with coding agents
16 — SIMD & GPU Programming: C++ for ML, ARM NEON, x86 AVX, CUDA, Triton, TPUs, WebGPU
17 — AI Inference: quantisation, serving and batching, edge, speculative decoding
18 — ML Systems Design: cloud, feature stores, A/B testing, recsys/search/fraud case studies

Link: GitHub

Navigational hashtags: #armknowledgesharing #armrepo
General hashtags: #math #mathematics #ml #machinelearning #engineering #mlsystemdesign

@data_science_weekly