Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$

Number : A number $x$ is a mathematical symbol representing a quantity.

Product : A product is the result of a multiplication.

Scalar : A scalar is a number. The word scalar is often used to distinguish a number from a vector.

Vector : Most commonly vector refers to a matrix with one column $\begin{pmatrix}x_1\\ \vdots \\x_n\\\end{pmatrix}.$ In general a vector is an element of a vector space.

Boundary : The boundary of a 2-dimensional shape is the 1-dimensional shape that separates the 2-dimensional shape from the rest of the 2-dimensional space.

Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.

Constant : Constant is another word for a fixed number that is mainly used in the context of expressions or functions like $f(x)=c$ that are equal to the same number irrespective of any variable.

Ellipse : An ellipse is a two-dimensional shape with a boundary that is a set of points for which the combined distance from two points is constant. Circles are special cases of ellipses. The boundary of an ellipse can also written as the set of points $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$

Point : A point is an element in a space. Shapes are made of sets of points.

Set : A set is a collection of objects.

Scalar product : The scalar product of two vectors $\begin{pmatrix}a_1\\a_2\\ \vdots \\a_n\\\end{pmatrix}$ and $\begin{pmatrix}b_1\\b_2\\ \vdots \\b_n\\\end{pmatrix}$ is defined by $\begin{pmatrix}a_1\\a_2\\ \vdots \\a_n\\\end{pmatrix}\cdot\begin{pmatrix}b_1\\b_2\\ \vdots \\b_n\\\end{pmatrix}=a_1b_1+a_2b_2\ldots+a_nb_n.$ The scalar product is equal to the product of the norms of the two vectors times the cosine of the angle between the two vectors.