AI Foundations

The mathematical foundation every AI practitioner needs — vectors, matrices, probability, and the calculus behind learning — explained with intuition and everyday examples, not just equations.

How machines learn patterns from data instead of following hand-written rules — the three families of learning, why models overfit, and how to tell a good model from a lucky one. Plain language, real examples.

What neural networks really are, why stacking layers lets them learn features on their own, and how CNNs and RNNs see images and read sequences — explained with everyday analogies and real use cases.

The single idea — letting a model decide what to pay attention to — that fixed the memory problem in older networks and became the architecture behind every modern AI. Explained from scratch, in plain words.

What an LLM really is, how 'predict the next word' produces something that feels like reasoning, how these models are trained and made helpful, and where they quietly fail — in plain language.

How to connect a language model to real knowledge and real actions — so it answers from your documents instead of guessing, and can search, calculate, and call APIs. The leap from 'chatbot' to 'useful system'.

The craft that decides whether an AI system is reliable or flaky: giving the model exactly the right information, in the right shape, at the right moment. Far more than writing clever prompts.

The model is one small part; the system around it does the real work. Tools, memory, permissions, runtime safety, evaluations, and observability — the 'harness' that turns a clever model into a dependable product.

An agent isn't one answer — it's a cycle: plan, act, observe, check, repeat. Designing that loop so it converges on a result instead of spinning forever is where AI agents become genuinely dependable.

The difference between a demo and a product that survives real users: monitoring, cost control, security, guardrails, and rollback. The operational layer that keeps AI systems safe, affordable, and trustworthy in production.

How computers came to understand human language — from counting words, to capturing meaning with embeddings, to the modern era of LLMs. The story and the still-useful fundamentals, in plain language.

How computers turn a grid of pixels into understanding — detecting features, recognising objects, and tracking motion. The ideas behind face unlock, medical imaging, and self-driving, explained simply with real use cases.

How machines store what they *know* — facts, rules, and meaning encoded so a computer can reason over them, not just pattern-match. The symbolic half of AI, from Aristotle's syllogisms to ontologies and today's neuro-symbolic systems.

How to give machines structured, connected knowledge they can reason over — facts as a web of relationships rather than loose text. The idea behind Google's panels, recommendations, and grounding LLMs in real facts.

When a problem has more possible answers than atoms in the universe, you can't check them all. Nature-inspired search — evolution, ant trails, swarms — finds excellent answers fast. The elegant maths behind scheduling, routing, and tuning.

Two ways to give an AI your knowledge — organise it as a folder (Google's Open Knowledge Format) or embed it as vectors (RAG). What a folder and a vector really are, how they compare, and how to combine them into one architecture. Built from scratch, for beginner to advanced.

The single idea underneath every modern AI — turning words into numbers you can measure and do maths on. From an eight-year-old's picture to the billions of numbers inside ChatGPT and Claude, with a spinnable 3D model and the real facts on scale, compute, and cost.