Courses
Every domain on the site is a skill tree. Open one to see its skills laid out by prerequisite — each links to its full page, and where a skill has interactive lessons you can solve your way to mastery. See how they all connect on the tech tree.
The Quantum Chemistry series
Six chained courses, from writing your first SCF to research practice. Each has a full syllabus; planned material is visible before it lands.
- I Quantum Chemistry I — Hartree-Fock from Nothing Variational principle → integrals → SCF, with 11 programs you write and a wasm SCF you can run.
- II Quantum Chemistry II — The Correlation Problem What the mean field misses and every strategy for buying it back: CI, MPn, coupled cluster, CASSCF.
- III Quantum Chemistry III — Density Functional Theory The workhorse of modern practice: Hohenberg-Kohn, Kohn-Sham, the functional zoo, and where it lies.
- IV Quantum Chemistry IV — The Machinery Angular momentum integrals, DIIS, gradients, geometry optimization, properties — what makes codes real.
- V Quantum Chemistry V — Research Practice Method selection, basis-set craft, benchmarking discipline, and a reproduce-a-paper capstone.
- VI Quantum Chemistry VI — Frontiers Electives: quantum Monte Carlo, periodic systems, relativistic effects, excited states beyond CIS.
All domains
- ∫ Explore
Calculus & Series →
Limits, derivatives, integrals, and the series expansions that approximate them.
- ⊞ Explore
Linear Algebra →
Vectors, matrices, eigenproblems — the language of nearly all numerics.
- {} Explore
Programming →
Control flow, types, functions — the bedrock every CS path stands on.
- C++ Lessons
Advanced C++ →
Value categories, move semantics, RAII — the modern C++ ownership model.
- ⤳ Explore
Algorithms & Data Structures →
Sorting, graphs, dynamic programming, and the complexity to reason about them.
- dy Explore
Differential Equations →
ODEs, the integrators that solve them, and the qualitative theory of flows.
- σ Explore
Statistics & Inference →
Probability, estimation, and how to reason from data to model.
- ⚙ Explore
Compilers →
Lexing, parsing, IR, and codegen — building a language end to end.
- ⟳ Explore
Control Theory →
Feedback, stability, and steering dynamical systems toward a target.
- ≈ Explore
Numerical Methods →
Root finding, quadrature, and the floating-point reality under every computation.
- ∂ Explore
Partial Differential Equations →
Heat, wave, and Laplace equations; characteristics, separation, Green’s functions.
- ⏱ Explore
Performance Engineering →
Caches, branches, vectorization — reading the machine under your code.
- ε Explore
Perturbation & Resummation →
Asymptotic series, Padé/Borel resummation, and when divergent series still work.
- ℏ Explore
Quantum Mechanics →
States, operators, and the eigenvalue problems that set energy levels.
- ⌁ Explore
Computational Neuroscience →
Spiking neurons as dynamical systems — from the LIF model upward.
- ◉ Explore
Machine Learning →
Regression to deep nets, viewed through the optimization that trains them.
- ⚛ Explore
Nuclear Physics →
Binding energy, decay, reactions, and the shell model.
- $ Explore
Quantitative Finance →
Pricing, Greeks, risk, and hedging with working code.
- ◇ Explore
Solid State Physics →
Bands, lattices, and the quantum mechanics of crystalline matter.
- ρ Explore
Density Functional Theory →
Trading the wavefunction for the density — the workhorse of electronic structure.