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Tips for math (and science).
You may have noticed in your math education that each new rule or theory can be used to solve some sort of problem. Try to figure out what that problem is - that is, what is being solved by the new theory- and you will find math and science more interesting and fun.
That being said, sometimes things are done for the sake of saving time, and then 'saving time' becomes the new problem being solved, the original problem being the one of ultimate interest.
Mechanical math is a sin, but it also has its advantages at times. It can be a tool to gain more interesting results, and you let someone else prove the details. We see this in engineering math, or math that is more practical minded. but as you do more advanced math, there is an expectation that you can follow proofs.
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