Injective. $f(a_1)=f(a_2)\rightarrow a_1=a_2.$ This kind of functions are called an injection or one-to-one function.
Surjective. Every element in the codomain has at least one element in the domain mapping to it; the range equals the codomain. This kind of functions are called a surjection or onto function.
Bijective. A function is bijective if it is both injective and surjective. This kind of functions are called a bijection.
Algebraic structure. operations(e.g., $+,\cdot$), relations(e.g., order), laws(e.g., associativity, commutativity)
Automorphism. A map on a set which preserves its algebraic structure.
Power. $(\text{base})^{(\text{exponent})}=(\text{power})$; “$2$ to the power of $6$ is equal to $64$.”
Root. $\sqrt[{(\text{index})}]{(\text{radicand})}$; “$\sqrt[6]{64}$, the positive $6$-th root of $64$ is equal to $2$”.
Composition. $(f\circ g)(x)$ is read out loud as “$f$ of $g$ at $x$,” or “$f$ of $g$ evaluated at $x$.”
Derivative. $((Df)\circ g)(Dg)$ is read out loud as “the derivative of $f$ composed with $g$, multiplied by the derivative of $g$,” or “the product of the derivative of $f$ composed with $g$ and the derivative of $g$.”