Richard Hummel Math
Clear math lessons built around concepts.
Start with a single idea, see why it works, then practice with guided examples and solutions.
Learning paths
Not sure where to start? Follow a curated sequence.
Prep for Calculus
9 topics
Build the algebra and pre-calc foundation you need before derivatives click.
Grade 12 Mathematics
10 topics
Core topics from a typical Grade 12 pre-calculus or advanced mathematics course.
Topics
Follow a concept sequence from start to finish.
Core Calculus
The essential sequence from limits through integration — the ideas that power all of modern science and engineering.
Differential Equations
From derivatives to equations that model change — the mathematics of everything that moves, grows, or decays.
Linear Algebra
Vectors, matrices, and the geometry of high-dimensional space — the language of machine learning and modern data science.
Probability & Inference
How to reason under uncertainty — from counting outcomes to drawing conclusions from data.
ML Foundations
The core ideas every machine learning practitioner needs — understanding what makes a model good, bad, or overfit.
Supervised Classification
The main toolkit for predicting categories — from probabilistic classifiers to geometric decision boundaries.
Core topics
Jump straight to a subject.
𝑥Algebra
See all →Linear Equations
Equations where the unknown appears only to the first power.
AlgebraFunctions
Rules that assign exactly one output to each input.
AlgebraQuadratic Equations
Equations involving a squared variable, solved by factoring or the quadratic formula.
AlgebraSlope
A measure of how quickly a line rises or falls as x changes.
AlgebraSystems of Equations
Collections of equations solved by the same values at once.
∫Calculus
See all →Limits
The foundational idea of calculus — what a function approaches as its input gets arbitrarily close to a value.
CalculusDerivatives
The instantaneous rate of change of a function — defined as the limit of the difference quotient and interpreted as the slope of a tangent line.
CalculusIntegrals
The integral as accumulated area — Riemann sums, definite integrals, and the antiderivative as an operation that reverses differentiation.
CalculusFundamental Theorem of Calculus
The bridge connecting differentiation and integration — why antiderivatives compute areas and why the two operations are inverses of each other.
CalculusDifferential Equations
Equations that relate a function to its own derivatives — the mathematical language of physics, biology, finance, and engineering.
σStatistics
See all →Probability
A number between 0 and 1 measuring how likely an event is to occur.
StatisticsNormal Distribution
The symmetric bell-shaped distribution that arises naturally from sums of many small random effects.
StatisticsHypothesis Testing
A formal framework for deciding whether data provides enough evidence to reject a default assumption.
StatisticsLinear Regression
Fitting a straight line to data to model and predict the relationship between two variables.
StatisticsConfidence Intervals
A range of plausible values for an unknown population parameter, constructed from sample data.
△Geometry
See all →Triangles
Three-sided polygons with rich properties connecting angles, sides, area, and similarity.
GeometryPythagorean Theorem
In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
GeometryTrigonometric Ratios
Sine, cosine, and tangent as ratios of sides in right triangles — the bridge between angles and lengths.
GeometryCircles
The set of all points equidistant from a centre, with theorems about chords, tangents, arcs, and inscribed angles.
GeometryVectors
Quantities with both magnitude and direction — addition, scaling, dot products, and geometric interpretation.
🤖Machine Learning
See all →Bias-Variance Tradeoff
The fundamental tension between underfitting (high bias) and overfitting (high variance) — decomposing prediction error into its components.
Machine LearningLogistic Regression
Modelling the probability of a binary outcome using the sigmoid function — fitting by maximum likelihood or gradient descent.
Machine LearningK-Means Clustering
Partitioning data into k clusters by iteratively assigning points to the nearest centroid and re-computing centroids until convergence.
Machine LearningDecision Trees
Flowchart-like models that recursively partition the feature space by asking yes/no questions — interpretable but prone to overfitting.
Machine LearningModel Evaluation
Confusion matrices, accuracy, precision, recall, F1 score, ROC curves, and AUC — the toolkit for measuring classifier and regressor performance.
Ready to explore?
Browse the full library — over 100 concepts across Algebra, Calculus, Statistics, Geometry, and Machine Learning.