When I read a mathematical textbook at graduate level to learn and master a particular subject that I am unfamiliar with, I always struggle with the strategy on the exercises. Sometimes I spent one hour on one exercise problem without making any progress. Sometimes I skip exercise problems with guilt and worried that I may not have learnt the material well. I can think of the following possible strategies on exercises:
- Ignore all of them. Just focus on reading the main body of the textbook.
- Set a time limit. Say for every hour I spent on reading the main body, I spent twice much time on solving exercise problems. I try to solve whatever I can within two hours and skip the rest.
- Never move on to a new session unless I have solved all exercise problems in the previous session. If I get stuck, spend hours working on it and if still no success, look it up or ask somebody until I understand the solution.
- Spend a reasonable amount of time on each problem and if I could not solve it, read the solution from a solution manual. This strategy seldom works as for most books on graduate level, solution manuals are unavailable.
What strategy do you recommend? I personal feel that Strategy 3 is the most time-consuming but it is also the only one that does not bother my conscience. But because it consumes a huge amount of time, I am not sure if it is wise to adopt it.