Mathematical operations include addition, subtraction, multiplication, division, square roots, and powers. The document provides examples of how to write out each operation in words and symbols, such as "one plus one equals two" for addition, "five minus two equals three" for subtraction, "three times four is twelve" for multiplication, "twenty divided by five is four" for division, "the square root of nine is three" for square roots, and "five squared" or "two cubed" for powers.