I've gotten all A's in math so far, and always a 95% or better on tests, but am wondering how well I actually need to understand why what I do works the way it does. I've memorized the formulas thoroughly, but really don't understand why they work.
If I have A's in calculus 1 + 2 , does it matter whether or not I understand the work thoroughly, or just that I do well, for Computer Science?
If I have A's in calculus 1 + 2 , does it matter whether or not I understand the work thoroughly, or just that I do well, for Computer Science?
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For Computer Science, an understanding of how to apply and use the formulas should suffice. You don't need to know how to prove them. However, you should be sure to have a good understanding of the limitations of the rules, so you don't find yourself using them in situations where they don't really apply. That would mean knowing all the assumptions that go into a formula.
If it says, "if conditions A, B, and C are met, then formula D can be used," you can get into trouble by just blindly using D without being aware of whether A, B and C are actually met.
For example if the theorem says, "if p is prime and p doesn't divide a, then a^p = p mod p," you have two conditions you always have to check before you can go ahead and use the result.
If it says, "if conditions A, B, and C are met, then formula D can be used," you can get into trouble by just blindly using D without being aware of whether A, B and C are actually met.
For example if the theorem says, "if p is prime and p doesn't divide a, then a^p = p mod p," you have two conditions you always have to check before you can go ahead and use the result.