should you be able to tackle any problem Algebra 1 thru calculus 3?
Are you talking about an undergraduate degree in maths? Then, yes, one should be able to tackle algebra and calculus problems, as these are the foundations of a maths degree! That said, there's almost certainly some calculus questions you could ask me that I, for one, wouldnt be able to answer straight away, so I hope this thread won't turn into a "challenge!"
I was referring to a bachelors. But the question could apply to masters as well.
It depends on two things really, one is the manner in which you ask the question and the other is the depth of the question. There are many things about elementary topics that you'd never be taught in any class that was required for your undergrad math degree. Math has existed for a long time and people haven't gotten exponentially smarter to keep up with the advances. Some pretty smart people were looking at problems one might consider elementary today; if they had trouble there why wouldn't you? There are some not so subtle nuances here: the fact is that you can look at a problem with hindsight, that makes it easier, but I think you get my point.
My guess is that if you've truly learned something from your undergrad work you should at the least be able to do any problem in any widely used introductory text book of calculus or linear algebra. I say this as an undergrad myself, so perhaps you should wait for someone wiser to post.
Hm I wouldn't say you should be able to solve every problem you see, but you should at least have a very good idea on how to solve it and be able to understand the solution and have a general idea of what the solution will be.
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