Math Explained
Clear explanations from algebra to calculus and beyond.
Algebra
Equations, functions and graphs.
How the Quadratic Formula Works and Why It Always Solves
Understand where the quadratic formula comes from, how the discriminant predicts the type of roots, and how to apply it to any quadratic equation.
AlgebraHow to Solve Linear Equations Step by Step
Learn how to solve linear equations by keeping both sides balanced, undoing operations in the right order, and checking your answer.
Geometry & Trigonometry
Shapes, angles and trig functions.
How the Pythagorean Theorem Works, with Proofs and Examples
See why a squared plus b squared equals c squared for right triangles, with a clear area proof, common triples, and practical examples.
GeometryHow Sine, Cosine and Tangent Work in Right Triangles
Learn sine, cosine and tangent as ratios of triangle sides, see the exact values for common angles, and understand how they extend to the unit circle.
Calculus
Limits, derivatives and integrals.
What a Derivative Means: Rates of Change Explained
Understand the derivative as an instantaneous rate of change, built from the limit of the difference quotient, with worked examples and standard rules.
CalculusWhat an Integral Measures: Area, Accumulation and the Fundamental Theorem
Learn how integrals add up tiny pieces to measure area and totals, how Riemann sums build them, and how the fundamental theorem evaluates them.
Probability & Statistics
Chance, distributions and data.
How Standard Deviation Is Calculated, Step by Step
Learn how standard deviation measures spread, why deviations are squared, when to divide by n or n-1, and how to compute it on a small dataset.
StatsHow the Central Limit Theorem Works
Learn why sample averages tend toward a bell curve even when the raw data is skewed, with the logic, the standard error rule, and worked examples.
Linear Algebra
Vectors, matrices and transformations.
How Matrix Multiplication Works, With Worked Examples
Learn the row-by-column rule for multiplying matrices, why the dimensions must match, why order matters, and what the product means geometrically.
Linear AlgWhat Is a Determinant? A Plain Guide With Examples
Understand the determinant as the area or volume scaling factor of a matrix, learn the 2x2 and 3x3 formulas, and see why zero means no inverse.
Number Theory
Primes, modular arithmetic and famous problems.
How Modular Arithmetic Works: Clocks, Remainders and Inverses
Learn modular arithmetic through clock examples, the congruence notation, modular inverses, Fermat's little theorem, and everyday uses like check digits.
NumbersHow the Sieve of Eratosthenes Finds Prime Numbers
Learn how the sieve of Eratosthenes lists all primes up to a limit by crossing out multiples, why it stops at the square root, and how fast it runs.