Is It Normal to Spend Hours on a Few Math Problems?

[zooxanthellae]

I've recently started working through Spivak's Calculus on my own (after the BC Calculus curriculum) and am making progress, albeit slowly. For example, yesterday I spent a couple of hours doing just 2 problems (1 and 3 in Chapter 2, if anyone's interested). I understand that these problems aren't supposed to be easy "plug and chug", and making the transition from cookbook math to more rigorous work can be rocky, but I'm also wondering if this is abnormal, and my efforts might be better spent elsewhere.

I, frankly, kind of enjoy it (in a frustrating way) but...how slow is this?

 

[Maybe_Memorie]

I don't know what BC Calculus is, but I've looked at the two problems, and they shouldn't be taking that long. A few minutes, 20 max, perhaps. Although after saying that, I've seen both of the those problems as preparation for final exams in the Ireland version of high school, which doesn't go into as much detail as other countries.

 

[Angry Citizen]

How Long Should This Be Taking?

As long as is necessary. Don't hurry through problems. Mathematics is not a race. With understanding comes speed, but the understanding comes first.

 

[Klockan3]

I looked at the problems and problem 3 seems like it could take a while if you aren't used to the stuff. It is quite common for people to sit for really long times working through just a few simple problems, it can take a while to understand the concepts.

 

[zooxanthellae]

I looked at the problems and problem 3 seems like it could take a while if you aren't used to the stuff. It is quite common for people to sit for really long times working through just a few simple problems, it can take a while to understand the concepts.

This is basically how it broke down. Problem 1 took maybe a half hour (because I actually expanded the polynomials and wrote out a lot of apparently unnecessary steps.) Problem 3 took considerably longer.

 

[Dembadon]

... I, frankly, kind of enjoy it (in a frustrating way) but...how slow is this?

emphasis added

I don't see the issue.

If you are enjoying it, who cares how long it takes? Are you trying to learn something, or meet a deadline? Mathematics books, when read for one's own interest, are not meant to be finished in a certain amount of time.

When you understand the material, then you've spent the appropriate amount of time on whatever problem you happen to be working.

 

[gretun]

I think that is what is so weird about math. If you don't get it, it can haunt you, if you get it, it's like you are on top of the world.

 

[zooxanthellae]

emphasis added

I don't see the issue.

If you are enjoying it, who cares how long it takes? Are you trying to learn something, or meet a deadline? Mathematics books, when read for one's own interest, are not meant to be finished in a certain amount of time.

When you understand the material, then you've spent the appropriate amount of time on whatever problem you happen to be working.

Well, I'd analogize it to basketball. I like playing basketball, but I'm pretty bad at it, and physically would probably max out at a high-school level. I like it, but at the same time I realize that trying to make a career out of playing basketball would probably not end well.

 

[sEsposito]

I don't know what the exact problems you're referring to entail, but I don't see anything wrong with taking all the time you need to work through a problem. Personally, I often spend a great deal of time on a handful of problems, especially when I'm not familiar with he subject matter. I'd much rather understand and complete a small amount of problems than rush through a large amount.

Take your time, and enjoy yourself! That's what makes learning easier.