Mathematical Foundations
Build the number sense, notation, logic, units, and checking habits that make every later topic easier.
From school maths to LLMs
See the maths.
Then make it work.
A complete, visual path through algebra, calculus, probability, statistics, optimization, stochastic calculus, and the mathematics inside machine learning, deep learning, and language models.
17 chapters123 guided lessons1,700 practice questions
Every difficult idea begins with a picture, then becomes a formula.
01
Picture first
Animations build the mental model before symbols appear.
02
Use it for real
Every chapter connects to ML, LLMs, trading, physics, and daily decisions.
03
Earn the answer
Each chapter has 100 questions from easy to advanced. Answers stay hidden until you ask.
Saved on this device
Your progress starts here.
Small steps count. Finish one picture, one example, and one check at a time.
The learning path
One idea prepares the next.
Follow the path in order if you are starting fresh. If you already know a topic, open it directly and use the mastery list to test yourself.
Foundations
Build the language
Numbers, functions, counting, and algebra become pictures you can reason with.Algebra and Functions
Learn to express changing quantities, solve constraints, and see a function as a reusable input-output rule.
Permutations and Combinations
Count complex choices without listing every case, while keeping order, repetition, and restrictions straight.
The Binomial Theorem
Expand powers of two-term expressions, understand Pascal's triangle, and connect coefficients to counting and probability.
Core tools
Describe change and space
Vectors, matrices, and calculus explain how models represent and learn patterns.Vectors and Analytic Geometry
Turn directions, distances, lines, planes, angles, and projections into coordinates you can calculate with.
Linear Algebra
Understand matrices as transformations, solve systems, and learn the structures behind rank, basis, eigenvectors, and modern ML.
Single-Variable Calculus
Learn how one changing quantity behaves: approach with limits, measure instant change with derivatives, total small pieces with integrals, and replace hard functions with useful series.
Multivariable & Matrix Calculus
Move from curves to surfaces and tensors: partial derivatives, gradients, Jacobians, Hessians, matrix derivatives, and the chain rule behind backpropagation.
Uncertainty
Reason with incomplete information
Probability and statistics turn noisy observations into careful conclusions.Probability Foundations
Build probability from outcomes and events, then learn conditional probability, independence, counting, and Bayes' rule.
Random Variables and Distributions
Build probability measures, turn outcomes into random variables, compare convergence modes, and learn the distributions and limit theorems used throughout data science.
Statistics and Inference
Learn how study design and samples become honest estimates, robust comparisons, intervals, tests, and simple predictive relationships.
Advanced Probability and Bayesian Reasoning
Study joint laws, transformations, bounds, Bayesian updating, hierarchical pooling, decisions, Monte Carlo, MCMC, and variational inference.
Learning systems
Put the machinery together
Optimization, computation, information, randomness, and model mathematics connect.Optimization
Turn goals into objective functions, then solve unconstrained, constrained, convex, nonconvex, and noisy optimization problems with methods you can reason about.
Numerical Methods & Computational Math
Understand how finite computers approximate real mathematics: floating-point error, conditioning, stable algorithms, numerical calculus, linear solves, and iterative root finding.
Information Theory
Measure discrete and continuous uncertainty, shared information, maximum-entropy models, compression limits, and the losses used to train probabilistic models.
Stochastic Processes and Stochastic Calculus
Follow random quantities through time, from walks and martingales through multidimensional calculus, SDE simulation, density PDEs, and measure changes.
ML, Deep Learning, and LLM Math Integration
Connect probability, statistics, vectors, calculus, optimization, and information theory inside real learning systems.
Your finish line
You will read equations as stories about shape, change, and uncertainty.
By the final chapter, embeddings, gradients, attention, cross-entropy, stochastic updates, and sampling will connect to ideas you built yourself.
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