Multiplication

In simple algebra, multiplication is the process of calculating the result when a number  is taken  times. The result of a multiplication is called the product of  and , and each of the numbers  and  is called a factor of the product . Multiplication is denoted , , , or simply . The symbol  is known as the multiplication sign. Normal multiplication is associative, commutative, and distributive.

More generally, multiplication can also be defined for other mathematical objects such as groups, matrices, sets, and tensors.

Karatsuba and Ofman (1962) discovered that multiplication of two  digit numbers can be done with a bit complexity of less than  using an algorithm now known as Karatsuba multiplication.

Eddy Grant's pop song "Electric Avenue" (Electric Avenue, 2001) includes the commentary: "Who is to blame in one country; Never can get to the one; Dealin' in multiplication; And they still can't feed everyone, oh no."

REFERENCES:
Cundy, H. M. "What Is ?" Math. Gaz. 43, 101, 1959.

Karatsuba, A. and Ofman, Yu. "Multiplication of Many-Digital Numbers by Automatic Computers." Doklady Akad. Nauk SSSR 145, 293-294, 1962. Translation in Physics-Doklady 7, 595-596, 1963.