Categories
Mathipedia covers more than theory. Alongside the mathematics itself there are proof walkthroughs, calculator references, and a look at where math turns up in pop culture.
Concepts
The ideas themselves — what a thing is, why it works, and where it shows up.
- AdditionThe arithmetic operation of combining quantities, including its commutative and associative properties and its extension to matrices and complex numbers.
- Differential EquationsEquations that relate a function to its own derivative, the main families they are sorted into, and how separation of variables solves the simplest of them.
- DivisibilityWhat it means for one number to divide another, defined through multiplication rather than division, with worked proofs of the basic properties.
- Euler's ConstantThe irrational number e, defined as a limit, notable for being the base of the natural logarithm and its own derivative.
- FractalsAn introduction to fractals, self-similar shapes with finite area but infinite perimeter.
- FunctionsHow functions map inputs to outputs, from notation and the formal set-theoretic definition through inverse, injective, surjective, and bijective functions.
- InductionProving a statement for every natural number by establishing a base case and a step that carries each case to the next, with the well-ordering property behind it and a worked example.
- IntegralsThe operator representing the area or volume bounded by a function, covering definite and indefinite integrals and the notation for both.
- LogarithmsThe inverse exponential operator
- PEMDAS & BODMASMnemonic devices to help remember elemtary order of operations.
- Proof by ContradictionThe proof technique of assuming the negation of what you want to prove and following it until something breaks, with a worked example showing there is no largest integer.
- Pythagorean TheoremThe relationship between the legs and the hypotenuse of a right triangle, and the integer triples that satisfy it.
- Set TheoryUnderstanding how to group things and the properties that follow.
- Sets of NumbersExploring different sets of numbers and introductory set theory.
- Sigma NotationExploring different sets of numbers and introductory set theory.
- The Quadratic FormulaThe formula for finding the x-intercepts of a second-degree polynomial (quadratic equation).
Proofs
Famous arguments, taken apart line by line.
- Euclid's TheoremThe proof that the prime numbers never run out, and the flawed retelling of it that circulates widely.
- Euler's IdentityWhy $e^{i\pi}+1=0$ holds, worked from the power series definition of the exponential function.
- Self-Solving Card TrickA simple card trick that uses algebra to look like magic
- The Gaussian IntegralEvaluating the definite integral of a non-integratable function
Calculators
Hardware and software: what the buttons do, and what the machine cannot tell you.
- Four-Function CalculatorsThe simplest class of calculator, limited to the four arithmetic operations, and why some courses insist on one.
- Graphing CalculatorsCalculators with a screen that can plot functions, covering both handhelds like the TI-84 and browser tools like Desmos.
Pop culture
Mathematics in television, film, music, and fiction — and whether it checks out.
- Pi in bbno$'s "in my zone"A line in bbno$'s Valorant collaboration "in my zone" quotes pi as 3.1459
- The Collatz Conjecture in Black Panther: Wakanda ForeverHow a joke about the unsolved Collatz conjecture ended up on a sign in Black Panther: Wakanda Forever, and what the conjecture actually says.
History
Who worked it out, when, and what they were actually trying to solve.
- Leonhard EulerA biography of the Swiss mathematician known for Euler's Constant, Euler's Identity, and his extensive contributions across mathematics.
Reference
Tables, identities, and notation you came here to look up.
- Derivative TricksA collection of derivatives with convenient answers.