Hello,
I have a bit of a general question about math books. I get the feeling that in a lot of math books, the organization for the theorems and lemmas are not explained well (ex. Topics in Algebra Herstein, Linear Algebra Hoffman).
So I'm curious what you all think about the advantages/disadvantages of this. Because on the one hand, it forces one to create the connections for themselves. But on the other hand, it makes the presentation less clear and interesting.
In the classes that I have taken, I find that I have to constantly bother the Professors to motivate what is going on instead of just going along and providing the stripped down proofs.
Furthermore, I am wondering what you all do to rectify this problem. Last semester, I had a great opportunity to speak with a professor about the reading that I did each week but it makes it much harder to study things independently when there is nobody to give perspective on why we are doing what we are doing. Any thoughts would be appreciated!
–Alex
Best Answer
I think you are doing exactly the right thing in demanding that your professor motivate the theorems and lemmas, and to show the ideas for the proof and not just the proof itself. Too often, mathematical writing is stripped of the motivation, leaving bare the logical structure as if it arose out of nothing.