Expression : An expression is a succession of constants, variables and mathematical operations that if evaluated for specific values of the variables represents a number.

Independence : Random variables $X,$ $Y$ are called independent if $P[X\in A, Y\in B]=P[X \in A]P[Y \in B].$ Independent identically distributed random variables feature prominently in the law of large numbers and the central limit theorem. Vectors $x_1,x_2\ldots, x_n$ are called linearly independent if $\lambda_1 x_1+\lambda_2 x_2+\ldots+\lambda_n x_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$

Integral : The integral of a function $f$ between $a$ and $b$ is defined as $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n}).$ For example $\int\limits_{a}^{b}xdx=\frac{b^2}{2}-\frac{a^2}{2}.$ The fundamental theorem of calculus provides a simple way to calculate integrals using antiderivatives.

Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$

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.

Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Integral : The integral of a function $f$ between $a$ and $b$ is defined as $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n}).$ For example $\int\limits_{a}^{b}xdx=\frac{b^2}{2}-\frac{a^2}{2}.$ The fundamental theorem of calculus provides a simple way to calculate integrals using antiderivatives.

Sum : A sum is the result of an addition.

Integral : The integral of a function $f$ between $a$ and $b$ is defined as $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n}).$ For example $\int\limits_{a}^{b}xdx=\frac{b^2}{2}-\frac{a^2}{2}.$ The fundamental theorem of calculus provides a simple way to calculate integrals using antiderivatives.

Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$

Riemann sum : Any of the terms $\frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n})$ appearing in the definition of the integral $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n})$ is called a Riemann sum.