## Homotopy

Homotopies are studied in a branch of mathematics known as Algebraic Topology. A homotopy is a deformation of one thing into another without cutting it. For example, if we imagine a stretchy object, then all the shapes we can stretch or twist it ...

## Idempotence

Idempotence is a property that an operation in mathematics or computer science may have. It roughly means that the operation can be carried out again and again without changing the result. The word idempotence was made by Benjamin Pierce because ...

## Identity (mathematics)

For other senses of this word, see identity. In mathematics, the term identity has several important uses: An identity is an equality that remains true even if you change all the variables that are used in that equality. An equality in mathematic ...

## Identity Property

In math, the identity property is made up of two parts: the additive identity property and the multiplicative identity property. The additive identity property says that the sum of adding any number and zero 0 is just the original number. For tha ...

## Imaginary unit

In math, imaginary unit or i {\displaystyle i}, is a number value that only exists outside of real numbers and is used in algebra. Though imaginary numbers can be used to solve a lot of mathematical problems, they cannot be represented by an amou ...

## Inequality

Inequality is when one object is: Smaller than the other a &lt; b {\displaystyle a &gt; b {\displaystyle a&gt; b} means that a is bigger than b Not bigger than the other a ≤ b {\displaystyle a\leq b} means that a is not bigger than b, or it is sm ...

## Infinite monkey theorem

The infinite monkey theorem says that a monkey randomly hitting keys on a typewriter will eventually type out one of William Shakespeares works. When people talk about the infinite monkey theorem, the "monkey" is not always a real monkey. Instead ...

## Infinity

Infinity is about things which never end. Sometimes, it is also written ∞ {\displaystyle \infty }. Infinity means many different things, depending on when it is used. The word is from Latin origin, meaning "without end". Infinity goes on forever, ...

## Integer

In mathematics, integers are the natural numbers and their negatives. Integers can also be shown on a number line as follows: . − 4, − 3, − 2, − 1, 0, + 1, + 2, + 3, + 4. {\displaystyle { 4 3 2 1.0,+1,+2,+3,+4.}\,\!} In particular, zero is also a ...

## Intermediate value theorem

The intermediate value theorem says that if a function, f {\displaystyle f}, is continuous over a closed interval }, and is equal to f {\displaystyle f} and f {\displaystyle f} at either end of the interval, for any number, c, between f {\display ...

## International Congress of Mathematicians

The International Congress of Mathematicians is the largest conference for mathematics. It meets once every four years. The organizer is the International Mathematical Union.

## International Congress on Industrial and Applied Mathematics

The International Congress on Industrial and Applied Mathematics is an international conference about applied mathematics. It is organized by the International Council on Industrial and Applied Mathematics.

## Interval (mathematics)

In mathematics, an interval is a group of numbers that includes all numbers between the beginning and the end. Numbers that are larger than the beginning number and smaller than the end number are inside the interval, and numbers that are smaller ...

## Inverse function

An inverse function is a concept of mathematics. A function will calculate some output y {\displaystyle y}, given some input x {\displaystyle x}. This is usually written f = y {\displaystyle f=y}. The inverse function does the reverse. Lets say g ...

## Japan Society for Industrial and Applied Mathematics

Japan Society for Industrial and Applied Mathematics is a Japanese non-profit organization for the field of applied mathematics. JSIAM is not a branch but a Japanese counterpart of the Society for Industrial and Applied Mathematics based in the U ...

## Kepler conjecture

The Kepler conjecture is a problem in math. It wants to know the best way to put spheres together so there will be only a little bit of room between the spheres. That means the spheres are put together very tightly, meaning they are dense.

## Lambda calculus

In mathematical logic and computer science, lambda calculus, also λ-calculus, is a formal system. It was designed to investigate the definition of functions, and how to apply them. It is also a tool for analysing recursion. It was introduced by A ...

## Law of sines

The sine rule or law of sines, is a theorem in mathematics. It says that, if you have a triangle like the one in the picture, the equation below is true. a sin ⁡ A = b sin ⁡ B = c sin ⁡ C = D {\displaystyle {\frac {a}{\sin A}}\,=\,{\frac {b}{\sin ...

## Least common multiple

The least common multiple of two integers is the smallest positive integer between all the multiples of both. It is usually written as LCM. Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of ...

## Lemma (mathematics)

A good small thing can lead to many big things. Some powerful results in mathematics are known as lemmas, such as Bezouts lemma, Dehns lemma, Euclids lemma, Farkas lemma, Fatous lemma, Gausss lemma, Greendlingers lemma, Itōs lemma, Jordans lemma, ...

## Limit (mathematics)

In mathematics, a limit is an anticipated value of a function or sequence based on the points around it. As a function performs operations on different inputs, this can cause strange results with certain numbers, especially if we try to plot them ...

## Limit of a function

In calculus, a branch of mathematics, the limit of a function is the behavior of a certain function near a selected input value for that function. Limits are one of the main calculus topics, along with derivatives, integration, and differential e ...

## Limit of a sequence

In mathematics, a sequence is an ordered set of mathematical objects. In some cases, the sequence tends towards a limit, in which case the limit is denoted using the symbol lim {\displaystyle \lim }, and the sequence is said to be convergent, oth ...

## Linear equation

In mathematics, a linear equation is a type of equation. In a linear equation, both terms have to be constant. A linear equation is the equation of a straight line. This type of equation is written in the form: y = mx + b or y - y1 = mx - x1 wher ...

## Logarithm

Logarithms or logs are a part of mathematics. They are related to exponential functions. A logarithm tells what exponent is needed to make a certain number, so logarithms are the inverse of exponentiation. Historically, they were useful in multip ...

## Long division

Long division is a method of dividing two numbers, using repeated multiplications and subtractions in a tableau. Because it is easy to do, it is usually taught in schools. There are other methods which are faster, or easier to program with a comp ...

## Lorenz attractor

The Lorenz attractor is a system of equations. Edward N. Lorenz formulated the equations as a simplified mathematical model for atmospheric convection. The equations are ordinary differential equations, called Lorenz equations. They are notable f ...

## Magnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind. In mathematical language one would say: It is an ordering of the class of objects to which it belongs. The An ...

## Manifold

A manifold is a concept from mathematics. Making a manifold is like making a flat map of a sphere. The Earth is a sphere, a three dimensional object of geometry. Yet, maps two-dimensional representations can be made of the Earth. At the edges of ...

## Markov chain

A Markov chain is a model of some random process that happens over time. Markov chains are called that because they follow a rule called the Markov property. The Markov property says that whatever happens next in a process only depends on how it ...

## Mathematical constant

A mathematical constant is a number, which has a special meaning for calculations. For example, the constant π means the ratio of a circles circumference to its diameter. This value is always the same for any circle. A mathematical constant is of ...

## Mathematical induction

Mathematical induction is a special way of proving a mathematical truth. It can be used to prove that something is true for all the natural numbers. The idea is that if: Whenever that same thing is true for a case, it will be true for the next ca ...

## Mathematical logic

Mathematical logic is a field of mathematics that tries to formalize logic so that it can be used for mathematics more easily. Logic is about reasoning, and mathematical logic shows this with symbols. Most of mathematical logic was developed in t ...

## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of building a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering discipl ...

## Mathematical proof

A mathematical proof is a way to show that a mathematical theorem is true. To prove a theorem is to show that theorem holds in all cases. To prove a statement, one can either use axioms, or theorems which have already been shown to be true. Many ...

## Mathematics Subject Classification

The Mathematics Subject Classification system is an alphanumeric ordering system for categorizing or arranging mathematical topics, similar to how a library arranges or orders their books on the shelves. The system was invented by the American Ma ...

## Matrix analysis

Matrix analysis is a subfield of linear algebra. It focuses on analytical properties of matrices. In this subject, vector norms and matrix norms are introduced. The goal of this area is deepen understanding to matrix eigenvalues and system of lin ...

## Maximum and minimum

So, in mathematics, the maximum and minimum of a set A is the largest and smallest element of A. They are written as max {\displaystyle \max} and min {\displaystyle \min}, respectively. Similarly, the maximum and minimum of a function are the lar ...

## Mediant (mathematics)

In mathematics, the mediant of two fractions a c and b d {\displaystyle {\frac {a}{c}}{\text{ and }}{\frac {b}{d}}} is a + b c + d {\displaystyle {\frac {a+b}{c+d}}}. It is commonly referred to as the freshman sum, due to it being a common mistak ...

## Mental calculation

Mental calculation or mental maths is doing arithmetic without using any tools such as a computer or a calculator. and without writing anything down. Mental calculation uses only the human brain. People who use mental arithmetic use shortcuts to ...

## Methods of computing square roots

There are a numbers of ways to calculate square roots of numbers, and even more ways to estimate them. The mathematical operation of finding a root is the opposite operation of exponentiation, and therefore involves a similar but reverse thought ...

## Monster group

In math, there are many subjects. One of these is group theory. In group theory, the Monster group is important. It is also called the Fischer-Griess Monster, or the Friendly Giant. It is a group of finite order, which is equal to: 2 46 3 20 5 9 ...

## Monty Hall problem

The Monty Hall problem is a famous problem in probability. The problem is based on a television game show from the United States, Lets Make a Deal. It is named for this shows host, Monty Hall. In the problem, there are three doors. A car prize of ...

## Multiplication table

A multiplication table is a tool used to learn how to multiply two numbers. The oldest known multiplication tables were written by the Babylonians about 4000 years ago. Many people think it is important to know how to multiply two numbers by hear ...

## Mutual information

Mutual information measures how much more is known about one random value when given another. For example, knowing the temperature of a random day of the year will not reveal what month it is, but it will give some hint. In the same way, knowing ...

## Navier–Stokes equations

The Navier–Stokes equations are mathematical equations that describe the motion of fluids. The equations are named after Claude-Louis Navier and George Gabriel Stokes. The equations happen when you apply Newtons second law to fluid dynamics with ...

## Norm (mathematics)

In mathematics, the norm of a vector is its length. A vector is a mathematical object that has a size, called the magnitude, and a direction. For the real numbers, the only norm is the absolute value. For spaces with more dimensions, the norm can ...

## Nth root

An n -th root of a number r is a number which, if n copies are multiplied together, makes r. It is also called a radical or a radical expression. It is a number k for which the following equation is true: k n = r {\displaystyle k^{n}=r} for the m ...

## Number line

A number line is a line with integers on it extending forever in both directions. Usually, zero is placed in the middle of the line. The numbers have an equal space from each other. Other numbers in between the numbers on the line represent ratio ...

## Numerical digit

Numerical digits are the number text characters used to show numerals. For example, the numeral "56" has two digits: 5 and 6. In the decimal system, each digit is how many of a certain power of 10 are needed to get the value. The rightmost, or un ...