How Many Homework Problems Should You Do When Self-Studying?

[deluks917]

On this forum a great deal of advice is available on which books are best used to teach oneself almost any subject. Everyone also suggests doing the problems in the book. My question is how many problems do you suggest doing? On this boards recommendation I taught myself most of Spivaks Calculus. I did maybe 75% of the problems in the text. I really enjoyed the text but doing so many problems took an extremely long time (I found many of the problems quite difficult.

In general I would like to teach myself more subjects (right now Algebra from Artin and ODE's from V.I. Arnold). However I have nowhere near enough time to do every question in those books even I don't sleep (and I plan on sleeping). In general I guess my question is when you learned a subject (either on your own or in class) and felt like you learned it well how many problems did you do? I have tried to find good problem sets on MIT opencourseware (they have one for Artin) but it seems like the courses only list around 10 problem sets of 3-6 questions per semester. This seems far too few (even though the questions do appear difficult.) Thanks for any advice.

 

[╔(σ_σ)╝]

I haven't fully finished teaching myself a course but i recently started learning analysis 1 from Marsden's Elementary Classical Analysis 2ed. I usually try to do the problem that i can't figure out right away( that's almost all the questions lol). I look at the question and if i can see a clear way of going about it i skip it. I try to pick out problems that look puzzling and interesting as they always summarize all the main ideas from the chapter. I mean the point of doing the exercises is to get familiar with the topic and I do not need to do 75% of the problems for this. I usually like to pick questions that require "everything" i have learnt.

That is my strategy. That's my two cents.

 

[diazona]

What ╔(σ_σ)╝ said makes sense, you do the problems that allow you to understand the material. For self-study, a reasonable cycle might go like this: pick a problem at random, read it, and see if you understand the topics involved and can immediately figure out how to solve it. If so, skip it (or if you're in the mood, just do it anyway for the heck of it). If not, do the problem, referencing the text as necessary. When you finish, repeat with a different randomly chosen problem, for as long as you have time.

By the way, 30-40 homework problems for a semester is quite reasonable for college classes. Many of these problems can take hours, or even days. You could easily occupy all your free time for a week working on a 3-question homework assignment. The reason most textbooks include a lot more questions than that is to give a wide selection of different problems to do. Nobody seriously expects that you will do all of them in a one-semester course (or the equivalent amount of self-study).