Multiplication

Multiplication is the Addition of like terms:

We could say that “five times four” is the same “five, added four times”.

Often the word Multiplication is simply referring to the multiplication of two scalars, but the word Multiplication extends to work with things other than scalars (people usually say “numbers” rather than “scalars”).

Multiplication is a Binary Operation.

Appendix A

From looking at an inexpensive calculator, it’s easy to say “there are four operations: +,-,*,/ but in math if you go far enough, you reduce this to two, with Subtraction become a type of Addition and Division becoming a type of Multiplication:

• 
• 

Appendix B

Quite a bit of work deals with two operations, Addition and Multiplication. You will deal with Algebraic Structures that start with sets and then include rules (often called axioms) that explain what must be true regarding Addition or true regarding Addition and Multiplication.

Appendix C

The multiplication of real Integers gives multiplication the feeling that it is “repeated counting”. However, when you work with the multiplication of complex numbers, multiplication will seem to be more about rotation.

Multiplication by rotates by 90 degrees, multiplication by rotates by 180 degrees, changing the direction, and this is why the sign changes.

Appendix D

The word multiplication gets used in Group Theory when you are working with Symmetry Elements such as rotations and reflections. We multiply a four hour rotation by another four hour rotation and get an eight hour rotation, which is equal to a negative four hour rotation. You might find it strange to say “multiply” since we use addition get from “4 and 4” to 8.

• Addition