Last year my math professor taught me a very important skill - how to read a math textbook. This is literally all she taught me. The rest of my limited knowledge of multivariable calculus was derived (pun intended) from my math book. But I digress. . .
Reading a math book is very different from reading any other book where the words all come together and form sentences that make sense. . . a math textbook is designed to confuse you. And once you understand this very important principle, reading it becomes so much easier.
For example, in my differential equations book we see the following:
The function x(t) = 1/(1 - t) is a solution of this equation, so long as t ≠ 1, because the derivative x’ = 1/(1 - t)2 is identical to x2 for t ≠ 1.
What?! Now, at this point, some of you may be making the mistake of trying to understand what all of that means. And possibly you succeeded. Congratulations! But it was all just a waste of time, because after that sentence, is another math sentence, and another. . . the book is just full of them!
So this is what I learned last year - it is okay if you don’t understand anything in your math book. You just keep reading until a) you see bold font or b) you see the word “theorem”. All of the other nonsense in a math book is just confusing gibberish. So you highlight the theorems and 9 times out of 10 that will be enough to get you through that chapter/quiz/test.
So, no, math books are not teachers. But teachers aren’t teachers either, so it’s the best thing we’ve got.
