Bernoulli distributed random variable : A random variable $X$ that can only take the values 0 and 1 has a Bernoulli distribution with parameter $p$ if $P[X=1]=p$ and $P[X=0]=1-p.$ A Bernoulli distributed random variable has an expected value $E[X]=p$ and a variance of $var(X)=p(1-p).$

Binomial coefficient : A binomial coefficient $\binom{n}{k}$ is defined as $\frac{n!}{k!(n-k)!}$ and equals the number of different sets of $k$ objects one can pick out of $n$ objects.

Binomially distributed random variable : A binomially distributed random variable $X$ with parameters $n,p$ is a random variable with $P[X=k]=\binom{n}{k}p^k(1-p)^{n-k}$ for $0\leq k\leq n.$ Its expected value is $E[X]=np$ and its variance is $var[X]=np(1-p).$ The sum of n independent Bernoulli random variables with parameter $p$ is binomially distributed with parameters $n,p.$

Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.

Equivalence : Equivalent fractions are fractions that represent the same number. Equivalent equations or inequalities are equations or inequalities that have the same set of solutions.

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Probability : A probability is a number between 0 and 1 that describes how likely an outcome is. For discrete events that are equally likely the probability can be calculated by dividing the number of favorable outcomes by the number of possible outcomes.

Set : A set is a collection of objects.

Sum : A sum is the result of an addition.

Variable : A letter in an expression or function that represents an arbitrary number.

Arctan : The arctangent function $\arctan x$ is the inverse function of the tangent function $\tan x$. If you are given the lengths $a$ and $b$ of the two legs in right triangle, you can calculate the angle between the hypotenuse and the leg with length $b$ as $\arctan \frac{a}{b}.$

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Derivative : A derivative of $f$ also written as $f^{\prime}$ or $\frac{d}{dx}f$ or $\frac{df}{dx}$ is defined by $f^{\prime}(x)=\lim \limits_{h\to 0}\frac{f(x+h)-f(x)}{h}.$ The derivative $f^{\prime}(x)$ can be interpreted as the speed at which the function value is changing or as the slope of the tangent in the graph of $f$ at $x$. For example the derivative of a constant function is 0, the derivative of $f(x)=x$ is 1 and the derivative of $x^2$ is $2x.$ All local extrema of differentiable functions $f$ are roots of the derivative of $f.$

Inverse function : The inverse function $f^{-1}$ of a function $f$ that does not map several value to the same value is defined by $f^{-1}(f(x))=x.$ In other words $f^{-1}(y)$ is the $x$ such that $f(x)=y.$ $f^{-1}$ is continuous if $f$ is continuous. If $f$ is differentiable we can calculate the derivative of an inverse function as $\frac{d}{dy}f^{-1}(y)=\frac{1}{f^{\prime}(f^-1(y))}.$ This can for example be used to calculate the derivatives of inverse trigonometric functions.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.

Tan : The tangent of an angle $0\leq\alpha\leq 180^{\circ}$ or $\tan \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the leg adjacent to $\alpha.$ For arbitrary angles the tangent function can be extended in a periodic way by inscribing the right triangle in a circle. The tangent function can be used to calculate unknown side lengths and angles in right triangles via its definition. We have $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

N-th root : The n-th root of a number $x\gt 0$ or $\sqrt[n]{x}$ is defined as the positive solution of the equation $(\sqrt[n]{x})^n=x.$ For example $\sqrt[4]{16}=2$ as $2^4=2 \cdot 2 \cdot 2 \cdot 2=16.$

Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$

Root : A root is a solution to an equation of the $f(x)=0$ where $f$ is a function or expression. For example the function $f(x)=x-1$ has the root $x=1.$

Square : A square is a quadrilateral with four right angles and four equal length sides. A square is a special case of a rectangle and a special case of a rhombus.

Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$