# Study Notes A reference for the ideas behind computer science. Written and illustrated by [Amittai Siavava](https://amittai.studio). --- Computer science is a single connected structure of ideas, each one resting on the ones beneath it. Understood that way, a hard result can be **rederived** from first principles the moment you need it, rather than recalled on cue. _Figure 001 — The abstraction stack — every layer rests on the one beneath it, from silicon up to the programs you write. _ _Figure 002 — Algorithms, theory, architecture — one connected map. _ The same ideas recur across subjects: the cost analysis that decides which algorithm scales, the automaton that fixes what a regular expression can match, the cache that explains why one loop outruns another. A small set of ideas appears again and again at different levels of the same machine. Rigor is what makes an idea portable. A claim you have only seen asserted you can only repeat; a claim you have watched _derived_ you can bend, combine, and trust in a case nobody showed you. A proof is the part of a result you get to keep. _Figure 003 — Theory of computation: formal, and checkable. _ An algorithm comes with an argument for why it is correct, not just code that passes its tests; a bound comes with the derivation that forces it. The reasoning is what tells you when a result will still hold. Intuition and rigor work together. An idea appears in a concrete case first — a table filling in, a search frontier fanning out, a flow saturating its bottleneck — and then takes its precise form in symbols. The picture shows what is true; the symbols show why. _Figure 004 — Why cost matters: n, n·log n, n², 2ⁿ. _ Cost recurs through all of it. The gap between a linear pass and a quadratic one is invisible on ten items and decisive on ten million; learning to see that gap before writing code is much of what separates a program that works from one that scales. _Figure 005 — Computer architecture: from gates up to programs. _ Follow any abstraction far enough and it ends in something physical — a logic gate settling, a clock ticking, a cache miss going out to main memory. Knowing that bottom layer is what keeps the machine from surprising you. None of this makes a hard subject easy. The aim is to make it **legible** — its parts and the reasons behind them laid out in plain view — because a subject whose structure you can see is one you can actually learn. --- ## Subjects 23 available. ### [Algorithms](/algorithms) How to solve problems efficiently — and prove that you have. From measuring cost and choosing the right data structure, through divide & conquer, graphs, greedy, and dynamic programming, to problems that are provably intractable. ### [Theory of Computation](/theory-of-computation) _(coming soon)_ Automata, formal languages, computability, and complexity — what can be computed, and how hard it is. ### [Computer Architecture](/computer-architecture) From logic gates to pipelines, caches, and memory hierarchies — how a machine actually runs your code. ### [Physical Computing](/physical-computing) _(coming soon)_ Computational methods for physical systems — simulating cloth, hair, fluids, and structures in code. ### [Databases](/databases) _(coming soon)_ The relational model, query languages, and what keeps data correct under concurrency and failure. ### [Deep Learning](/deep-learning) Neural networks, gradient descent, and how machines learn patterns too subtle to program by hand. ### [Reinforcement Learning](/reinforcement-learning) Learning to act from reward alone — agents that try, fail, and improve by trial and error, from bandits to AlphaZero. ### [Artificial Intelligence](/artificial-intelligence) The classical science of intelligent agents — search, logic, planning, probability, and decision-making, from the Russell & Norvig canon. ### [Natural Language Processing](/natural-language-processing) How machines read, represent, and generate human language — from regular expressions and n-grams to embeddings, transformers, and LLMs. ### [Calculus](/calculus) Limits, derivatives, and integrals — the mathematics of change and accumulation, from the tangent-line problem through infinite series to Stokes' theorem in three dimensions. ### [Linear Algebra](/linear-algebra) Vectors, matrices, and the geometry of linear maps — solving systems, factoring matrices, and finding the eigenvectors and singular values that reveal what a transformation really does. ### [Differential Equations](/differential-equations) Equations whose unknowns are functions — solving them exactly when possible, qualitatively when not, and numerically when all else fails; from first-order models to chaos and Fourier series. ### [Real Analysis](/real-analysis) Calculus rebuilt on proof — the completeness of the reals, metric spaces, and the theorems that say exactly when limits, derivatives, and integrals do what calculus assumed they would. ### [Abstract Algebra](/abstract-algebra) Groups, rings, and fields — the axioms behind symmetry and arithmetic, from permutations and Sylow theorems to Galois theory and why the quintic has no formula. ### [Category Theory](/category-theory) Mathematics organized by arrows — universal properties, functors, the Yoneda lemma, limits, adjunctions, and the monads and closed categories that connect it all to programming. ### [Logic](/logic) The mathematics of proof itself — propositional and first-order logic, what can be expressed, what can be deduced, and the completeness and incompleteness theorems that mark the boundary. ### [Mechanics & Dynamics](/mechanics) How forces change motion, how conservation laws simplify many-body systems, and how the same mechanics extends from projectiles and rotation to fluids, waves, and thermal processes. ### [Electricity & Magnetism](/electricity-and-magnetism) How charge produces fields and potential, how circuits store and transfer energy, and how coupled electric and magnetic fields propagate as light. ### [Relativity](/relativity) Special and general relativity from the two postulates to curved spacetime — the Lorentz group, relativistic dynamics, the Schwarzschild solution, black holes, and gravitational waves. ### [Quantum Mechanics](/quantum-mechanics) From the old quantum theory to the full Hilbert-space formalism — matter waves, the Schrödinger equation, angular momentum and spin, and the approximation methods that make real atoms and molecules tractable. ### [Atomic Physics](/atomic-physics) How quantum mechanics builds real atoms — the hydrogen spectrum and its fine and hyperfine structure, many-electron shells, atoms in external fields, radiative transitions, lasers, and the cold-atom clocks at the frontier. ### [Statistical Mechanics](/statistical-mechanics) How the laws of thermodynamics emerge from counting microstates — the ensembles, the partition function, quantum statistics, Bose and Fermi gases, phase transitions, and the fluctuation–response relations that tie them together. ### [Condensed Matter Physics](/condensed-matter) How atoms assemble into solids and where their electrons go — bonding and crystal structure, phonons, the free-electron gas and band theory, semiconductors, magnetism, and superconductivity. ### [Nuclear Physics](/nuclear-physics) What holds the nucleus together and how it comes apart — sizes and masses, the nuclear force, the shell and collective models, every decay mode, reactions, and fission and fusion. ### [Particle Physics](/particle-physics) The Standard Model, derived — natural units and relativistic kinematics, symmetries, the quark model, QED, the weak interaction, QCD, electroweak unification and the Higgs, neutrinos, and what lies beyond. ### [Astrophysics & Cosmology](/astrophysics-cosmology) From starlight to the Big Bang — how we measure the sky, the structure and evolution of stars, their violent deaths, gravitational waves, galaxies and dark matter, and the expanding, cooling universe.