A few mathematical study skills... Reading Theorems

by Ashley Reiter Ahlin

In almost any advanced math text, theorems, their proofs, and motivation for them make up a significant portion of the text. The question then arises, how does one read and understand a theorem properly? What is important to know and remember about a theorem?

A few questions to consider are:

We might ask more questions about the proof of theorem:
Note that, in some ways, the easiest way to read a proof is to check that each step follows from the previous ones. This is a bit like following a game of chess by checking to see that each move was legal, or like running a spell-checker on an essay. It's important, and necessary, but it's not really the point. It's tempting to read only in this step by step manner, and never put together what actually happened. The problem with this is that you are unlikely to remember anything about how to prove the theorem, if you've only read in this manner. Once you're read a theorem and its proof, you can go back and ask some questions to help synthesize your understanding. For example:

Reading Mathematical Definitions

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