
Problems versus Exercises - tokenadult
http://www.epsiloncamp.org/ProblemsversusExercises.php
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jcutrell
I'm writing a book currently - I've got another view on problem versus
exercise.

A problem - a real problem - is something that doesn't yet have a solution. An
exercise already has a solution.

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qianyilong
This is why I hated math until Calculus. I enjoyed my calculus class and Loved
Linear algebra. The course work started to consist or more problems and less
exercises.

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avn2109
The other articles on this site are pretty interesting, too. Especially the
one about "Courage and Stupidity."

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billjings
I imagine a lot of people will take away from this article the idea that
problems are important, and that exercises are not, that exercises can be
discarded. That's an easy lesson to take away because, if you're like me, you
like problems and hate exercises.

Unfortunately it's not true, though. Without exercises, most of us would not
know as much vocabulary as we do. We would probably not know how to add,
subtract, or multiply efficiently. We would not know how to write.

Exercise work isn't fun, but it serves a real purpose - it makes knowledge
readily accessible. By rehearsing the act of recalling the technique, it makes
that technique ready to use. It might be an interesting problem figuring out
how to field strip a weapon, but a competent soldier needs to exercise that
capability until it's second nature.

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eatitraw
> We would probably not know how to add, subtract, or multiply efficiently.

Why do we need to do simple arithmetic efficiently in our minds? We already
have readily accessible computers for this, let's focus on something computers
can't do for us yet.

> but a competent soldier needs to exercise that capability until it's second
> nature

I'd prefer a robot to fight in a war(instead of me).

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Dewie
I guess these correspond to what mathematicians and the like call "trivial"
and "non-trivial".

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carlob
Not exactly.

Trivial usually denotes solutions that are obvious and not very interesting
such as 0, 1 or the empty set. It's more of a property of the solution than
the difficulty of the problem.

By extension sometimes you can say a proof is trivial, when it's very easy,
but I think the primary use is the one I mentioned above.

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ByronT
Feynman on "trivial":

[http://books.google.com/books?id=7papZR4oVssC&lpg=PA84&ots=e...](http://books.google.com/books?id=7papZR4oVssC&lpg=PA84&ots=esWVgdoKZZ&pg=PA84#v=onepage&q&f=false)

