Using competitive math question books for learning math?

[member 624364]

Hi, I have seen that their are competitive math books like Moems, Mathcounts, Mandelbrot and AMC. Are these useful for learning and practicing math, or are they only useful for doing competitions and would be mostly a waste of time instead of learning from textbooks or just learning more new topics and advancing quicker?If it’s of any help. I think I’d like to become a mathematician or at least a computer scientist using a lot of advanced mathematics in my research. Thanks.

 

[fresh_42]

So many questions in one thread to answer!

Hi, I have seen that their are competitive math books like Moems, Mathcounts, Mandelbrot and AMC. Are these useful for learning and practicing math ...

Yes and no, but more no. You can practice your capability to associate unusual ways to solve problems and depending on how successful you are, provide you with positive confirmation. However, this is the risk at the same time: what if you are not successful? It is a different skill that doesn't necessarily relate to mathematical skills. In any case, they can't substitute a textbook. It is entertainment, not math. Most proofs in mathematics are straight forward, although some require a few good ideas. But this is better practiced by learning real proofs.

... or are they only useful for doing competitions...

IMO yes, although you can learn from everything, even from those books. The question is whether it will help you with math or not. And the answer is: probably not.

... and would be mostly a waste of time instead of learning from textbooks or just learning more new topics and advancing quicker?

It's a different purpose: textbooks are for learning, riddles are to relax and have some fun. However, I assume sports will be more effective.

If it’s of any help.

Yes, namely to practice to think about many ways to a solution instead of just the few which are associated to a certain method, resp. area.

I think I’d like to become a mathematician or at least a computer scientist using a lot of advanced mathematics in my research.Thanks.

For programming it's definitely of help, as there are usually more than one way to solve a software problem.

You should have a look on the problems we post here for our members (in the general mathematics forum), which are of mathematical nature, i.e. they can mostly (not all) only be solved if one has already some mathematical foundation.