Mathematics
From algebra through AI systems.
I — Core Mathematics
II — Calculus
Calculus I — Differential & Integral Calculus
Limits, derivatives, and integrals -- built on the algebra and trigonometry you already have, with a live widget for every idea that can be dragged instead of just described.
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Calculus II — Integral Calculus & Infinite Series
Integration built into a toolkit, then turned loose on volumes, curves, differential equations, and the infinite series that let a polynomial stand in for any function you like.
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Calculus III — Multivariable Calculus
Functions of several variables, in 3D: gradients, tangent planes, double and triple integrals, and the vector calculus that ties circulation, flux, and divergence into one family of theorems -- built on surfaces you can actually rotate, not just read about.
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Advanced Multivariable Calculus
A second pass on multivariable calculus with real machinery -- the derivative as a linear map, curvilinear coordinates and tensors, differential forms and the generalized Stokes theorem, potential theory, and the calculus of variations -- for everything Calculus III's classical vector calculus didn't have room to prove.
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III — Linear Algebra
Linear Algebra — Vectors, Matrices, and the Geometry of Data
Vectors, systems, matrices, and the transformations they represent, built toward the eigenvalues, least squares, and data-science tools that make this the most-used branch of math outside calculus itself.
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Advanced Linear Algebra
A second pass on linear algebra with real machinery -- duality, forms, spectral theory over the complex numbers, canonical forms, matrix factorizations, the singular value decomposition, and multilinear algebra -- for everything Linear Algebra I promised it would hand off.
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IV — Discrete Mathematics
Discrete Mathematics I — Logic, Proof, and Structure
The language mathematics is actually written in: propositions, quantifiers, and proof, then the sets, functions, relations, graphs, and counting arguments that every algorithm and probability model is built out of.
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Discrete Mathematics II — Combinatorics
Counting arguments, arrangements, and distributions — the strategy layer above the formulas Discrete Mathematics I introduced, on the way to generating functions and graph enumeration.
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Graph Theory
Vertices, edges, and the structural questions every network, algorithm, and optimization problem reduces to.
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V — Probability & Statistics
Probability
Random variables, distributions, and the language of uncertainty -- built on counting and calculus, in service of the statistics and machine-learning courses ahead.
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Statistics
Estimation, inference, regression, and statistical model evaluation -- built on probability, in service of reasoning carefully about data.
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VII — Differential Equations
Ordinary Differential Equations
First- and higher-order ODEs, systems, dynamical-systems classification, and the Laplace transform -- built on the calculus and linear algebra that came before, in service of the numerical analysis and PDE courses ahead.
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Partial Differential Equations
Heat, wave, and Laplace equations; separation of variables; Green's functions; and the Bessel/Legendre special functions it produces.
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VI — Advanced Mathematics
Complex Analysis
Functions of a complex variable -- where differentiability becomes a much stronger, more geometric idea, and a single theorem (Cauchy's) unlocks results no real-variable argument can reach.
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Fourier Analysis
Decomposing periodic and non-periodic signals into simple oscillatory pieces — Fourier series, the Fourier transform, convolution, sampling, and the DFT — built on Calculus II and Linear Algebra.
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Information Theory
What can be compressed, what can be transmitted reliably, and why -- built on probability and linear algebra, from Shannon's entropy through channel capacity to today's machine-learning applications.
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Group Theory
Symmetry made algebraic -- groups, subgroups, and the homomorphisms between them, built from first principles up through the classification of finite groups and the Sylow theorems.
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VIII — Computational Mathematics
Numerical Analysis
Error, root-finding, interpolation, and numerical linear algebra/ODEs -- the practical algorithms behind approximate solutions, and why they work.
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Optimization
Unconstrained to constrained, linear to nonlinear, exact to stochastic -- the algorithms that search for the best answer, and the theory that certifies one has actually been found.
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IX — Applied Mathematics & Engineering
Digital Signal Processing
Discrete-time signals and systems, the z-transform, sampling, the DFT and FFT, and digital filter design -- built on Fourier Analysis and Probability, with every technique answering "what does this do to a real signal?"
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Digital Image Processing
Applied mathematics for real images -- pixels, convolution, transformations, frequency analysis, and restoration, built on Linear Algebra, Fourier Analysis, and Calculus III, with every technique answering "what does this do to an image?"
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Computer Vision
From pixels to perception -- classical geometric vision (features, cameras, stereo, motion) through modern learned vision (detection, segmentation, embeddings, vision-language models), built on Digital Image Processing and Linear Algebra.
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X — Artificial Intelligence & Machine Learning
Modern Machine Learning
Supervised and unsupervised learning, from linear models to ensembles -- building, evaluating, and trusting a real predictive pipeline.
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Deep Learning / Neural Networks
Neurons to transformers -- building, training, debugging, and understanding modern networks.
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XI — Language Models & Generative AI
Wiring Language Models
From tokens and Transformers to RAG, tools, agents, fine-tuning, and production LLM systems -- how to wire a language model into a reliable, useful, secure piece of software.
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Generative AI
Autoregressive, VAE, GAN, and diffusion approaches to generative modeling.
Not yet published
Reinforcement Learning
MDPs, value/policy methods, and modern deep-RL algorithms.
Not yet published
AI Systems / MLOps
Training and serving pipelines, deployment, monitoring, and AI security.
Not yet published
Natural Language Processing
Applied text and sequence tasks -- classification, tagging, translation, speech, and time series -- with RNNs and transformers.
Not yet published
Mathematics dependency map
Mathematics dependency map
Click to expand
Solid boxes are published courses (click to open); dashed boxes are planned. A dashed grey box outside the border is a prerequisite from another subject -- click it to jump to that subject's page. An arrow points from a prerequisite up into the course that builds on it.