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Related to this question.

This problem is the root reason why I was never good at math - I am horrible at all forms of simplification in mathematics, hence I am bad at proofs.

The problem is that there is no way I can "work through" a simplification problem - I either know the steps in advance or I can't do it at all. There is no "working it out", no fixed technique, no guarantees - that the technique you used for the first problem works in simplifying and proving an identity in the second problem. The best example of such problems are proving trig identities but there are numerous other examples.

A lot of people say practice is the answer, but I just end up hitting a wall and looking at the solution which does not add to my skill. The solution tells me nothing about how a person might arrive to the solution - it likes magic. There is only one and only one way to solve the problem and you have to find it among all other infinite wrong ways. There is nothing in the problem to "work out" - either you know it or you don't.

So is there a logical/deterministic way one can do and get better at simplification?

I am good at understanding logic, but I can't see patterns. Hence I am a good coder since that mostly involves breaking problem into sub-parts and combining the solutions.

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  • $\begingroup$ Can you give an example of something you found difficult to simplify? $\endgroup$ – littleO Apr 16 '18 at 13:03
  • $\begingroup$ Any trigonometry identity of intermediate difficulty or any proof by mathematical induction. Integration, the list goes on. $\endgroup$ – ng.newbie Apr 16 '18 at 13:27
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Yes, there is! Many people these days are down on memorization of basic facts, because, quite rightly, they recognize that high-level thinking and problem-solving are more than rote memorization. However, if you ask a mathematician what $9\times 7$ is, they will immediately, without thinking about it, tell you that it's $63$. This is across the board for experts in general. One trait characteristic of experts, and this is well-documented in the book Why Don't Students Like School, by Daniel T. Willingham (highly recommended!), is that the expert is a master of the basic facts of the discipline.

The bottom line is this: being good at math is more than rote memory, but it includes memorizing the basic facts solidly. Once you've got those down, you don't have to use brain resources simply recalling those whenever you need them, you can use your brain resources on the higher-level thinking skills.

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  • $\begingroup$ So simplification is more of just memorization correct rather than working through it. $\endgroup$ – ng.newbie Apr 16 '18 at 16:12
  • $\begingroup$ No, definitely not. I never said that. What I said was that the memorization of basic facts is a necessary supporting activity to solving higher-level problems. There is no one-size-fits-all approach to any kind of problem-solving. But a solid memory of basic facts gives you quite a few patterns against which you can compare your problem to problems you've seen before. $\endgroup$ – Adrian Keister Apr 16 '18 at 16:14
  • $\begingroup$ Yeah but this is my experience has been I get stuck at a new problem and I have no other option but to look at the solution. This does not contribute in enriching my skills all I know now is one new problem that I have memorized. $\endgroup$ – ng.newbie Apr 16 '18 at 16:18
  • $\begingroup$ This is why memorizing the core basic facts is important: the core basic facts apply to MANY more situations than a single problem does. $\endgroup$ – Adrian Keister Apr 16 '18 at 16:21
  • $\begingroup$ Any book you recommend for algebraic simplification practice? Please tell me a book where the solutions are also given because I will be getting stuck. $\endgroup$ – ng.newbie Apr 17 '18 at 4:12

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