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Seeing the forest for the trees

As you go on in a math career, at times it's difficult to tell what the point of it all is. For instance, why in the world should we study polynomials? One reason is that it's practice thinking mathematically about abstract ideas. When we learn arithmetic, we start with numbers we can hold and see. Correspondingly, we learn how polynomials can be in the forms of lines or parabolas and that those describe shapes. We deal with larger and larger degree polynomials, giving us practice understanding properties of functions. Later on, polynomials become the basis on which we model all analytic functions. In other words if we want to create a function or model with certain properties, we construct them out of polynomials the same way we make large models out of Legos. This all requires a fluency in working with polynomials gained throughout your math studies. Today I relearned this lesson, to be able to relate specific topics to the big picture, the practical application.

David