| > How do you actually read math, physics and programming books?
> Reading them the same way as you'd read a novel doesn't seem right. Indeed it doesn’t. As the author of the book in this post points out on his blog [1] in math you focus on learning the syntax first, just like in programming. Off the top of my head I can recommend pre-reading a chapter before reading it: go through theorems, bold/italic text, graphs, tables, conclusions, exercises. Also, try proving theorems yourself before reading proofs in a textbook. My general advice for you is to check out a book “How to Read a Book” by Mortimer J. Adler and Charles Van Doren. It’s a great manual for reading, which contains both general advice (in the form of 15 rules) applied to any reading material, and specific advices for math, philosophy, history, social science, etc. > I try to go chapter after chapter and make notes Notes are good, but only if they “active” notes. If you are able to formulate something in your own words it means you’ve done the work towards understanding, if you’re only able to express a thing in author’s words — you have not, and if you leave it at that the chances are you’ve wasted your time. In math you also have to do problems. Your ability to solve problems w/o the help of the textbook is the ultimate test of whether you’ve learned what you’ve read. Interleave: in your practice session work simultaneously on problems from different (usually sequential) chapters. IOW: don’t practice one topic during several study sessions until you’ve exhausted all exercises for that topic in a book — go read the next chapter (or chapters), and include its exerices in your next practice. Interleaving is harder, but more efficient. The reasons being that (1) our brain is bi-modal processing system, it needs time to process things both consciously and unconsciously, it does the latter while your attention is busy with other things; (2) it also needs time to consolidate memories, grow and strengthen new synaptic connections (which it primarily does in sleep) — so spreading a topic/exercises over time is generally a good idea. > but I often get bored because I don't see the usage in my real life coding
> Also after few chapters it often turns into a "job" of finishing the book. I don't have the pleasure of learning new stuff anymore. This is about psychology of study. Don’t turn it into a job, it’s not a competition, there are no bosses, no deadlines. Don’t push too hard, allow yourself time to integrate new knowledge by keeping yourself busy with other things and studying several subjects/books simultaneously — when you are tired of one thing, switch to another. It’s more efficient way of learning (as explained above), despite increase in absolute time for mastering a single subject. And work on your motivation. You can start by read what Paul Graham has to say on why study math [2]. Remember, math is hard; our brains are not wired for it. [1]
http://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-... [2]
http://www.paulgraham.com/college.html |
I would say the exact opposite of "our brains are not wired for [math]": mathematics is the simplest expression of our ultimate thought ("brain") processes.
It is only hard because it is so abstract and builds on a large corpus of what has already been constructed, but it was "designed" exactly after how our brains operate.
For a layperson, proving even the basic arithmetic might seem like magic, but once you go through the simple exercise of defining everything in terms of "One" and "Successor(One)" and compare that to how we teach our kids numbers, it's clear mathematics matches exactly how human brains operate.
Then again, I concede that not everybody's brain is "wired the same way," but I am sure there are plenty of us for whom mathematics is just natural: the only problem being the fact that majority of people have not been exposed to true mathematics.