Abstract Algebra is my favorite Math categories; it totally opened a new world for me. 2+2 is not necessarily equal to 4 anymore; we could not take a+b = b+ a for grant ; logos or pictures have mathematical meaning presentations…..

The foundation of Contemporary Algebra is built on the concept of **Group**. Some math genius got so bored so they started to look at the *algebraic structures* in different Set, and they found some interesting facts:

For **Integers, Z **under** addition**, we have

- for in

e.g. … - For every in Z, there is a , such that,

e.g. …

e.g. ….

But some of these properties will **not** hold if it is integers under **minus**, e.g. is not equal to

After the studying of the algebriac structure of numbers, mathematicians reached the definition of **Group**.

A **Group** is a **set** of elements closed under a **binary** operation with 3 conditions:

- Every group contains a unique
**identity**.

n+e=n - Every element in the group has an
**inverse**.

a+ (-a) = e - The operation is
**associative**.

a+(b+c)= (a+b)+c

Next time, we will give some example of **Group** ….