I cannot read a textbook to save my life

Question

I am a 2nd year undergraduate (going into 3rd year) in a CS & math program.

I have tried reading multiple textbooks (principles of analysis by rudin, algebra by artin, dummit and foote etc...), however I never seem to get much out of them. I find I am able to learn much more from lecture notes where I spend more time trying to figure how things work than reading text.

With textbooks, I feel like most of the reading I do goes through one ear out the other. Furthermore, with lecture notes, I am able to quickly get through the material which gives me more time to do problems.

Is this something I should be concerned about?

Answer 1

The problem is that most math books are not meant to be read. They have two problems:

1. They introduce ideas comically far in advance of them actually being used, so the reader has no clue what is essential to move forward, and what is just a passing example.
2. Most authors assume that you are going to work out every single example and comment for yourself to continually check that you understand what you are reading. If you are reading a math book correctly, you should be producing dozens of sheets of scratch paper, verifying all of the claims and examples. It's not enough to nod along, you really have to do it all yourself, because that's how you discover you missed some detail that the author omitted so that you could figure it out on your own.

On the one hand, if you know these two points, you know "how" to read the book. Flip through it and figure out what you want to learn, then work backwards, reading the material that builds up those ideas, and scribble out every related detail. If you get stuck, use math.stack or ask someone. Buy legal pads in bulk.

A lot of people say that mastering this process makes you a better mathematician, but it does not. The problem is that when you are really doing math, there's no book telling you the answer you should get or directing your mind towards results other people have already figured out. That's the problem with the writing style. It usually completely misses the creativity and ingenuity of problem solving in favor of a kind of intellectual weight-lifting.

So the problem is not necessarily with you, and once you learn to read a poorly written genre of books, well, you can read them. But you have to treat it not as a paperback novel or a genuine attempt to convey understanding, and instead as a provocation to work out the details for yourself. Slow down and work the examples out on your own, and don't fool yourself into thinking you understand something just because your brain doesn't raise an alarm. Feeling right and being correct are totally different things.