Tricks Of The Trade In Undergraduate Mathematics — Introduction

While Undergraduate mathematics seems to be a taught differently to it’s High School counterpart, it does not imply that the underlying mathematics is different. All that happens is that in High School we are taught repetitive drills and mnemonics (like FOIL for opening brackets) for memorizing formulas which are used to solve ‘exercises’.

“The best teaching can be done only when there is a direct individual relationship between a student and a good teacher — a situation in which the student discusses the ideas, thinks about the things,and talks about the things. It’s impossible to learn very much by simply sitting in a lecture or even by simply doing problems that are assigned"

-Richard Feynman

I deliberately use the word ‘exercises’ rather than problems used by Richard Feynman simply because most of the work is done for us and very little (if at all any) problem-solving is being done. If you are lucky enough to have a good teacher like Feynman to guide you on your mathematical journey then you’re good to go. If not you got to do most of the work actually restructuring your idea about mathematics, emphasizing more on abstract cases and when say, you discover a property that holds in 3-dimensions, try to generalize to n-dimensions. In effect, learn how to think like a mathematician. Easier said than done I know but I’ll try to make the journey smoother for you. First we dive into the philosophy of undergraduate mathematics, stay tuned!