Chapter 4 Algebraic Structure
To many, algebra is jokingly referred to as the advanced study of the last three letters of the alphabet. But what is it really? The answer might be different to different people (even mathematicians who study advanced topics). If we look at commonalities among varying people’s perspectives, we will likely see that algebra deals with the relationships among quantities or mathematical objects. We see an underlying structure whether we are dealing with numbers, or matrices, or functions, or geometric movements on objects, or, .... In this chapter we will look at this structure and try to understand why Poincaré said:
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. — Henri Poincaré.
