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In my self study of calculus, I've found that there are examples in the books i read where the author rewrites an equation or expression either as part of a logical step in a proof, or to simplify it so that he can perform other desired operations on it.

But when it comes time for me to try practice questions, i look at the expression/equation and have no intuition or idea as to how to meaningfully simplify or rewrite it to suit my purpose. I also have a tendency of looking at expressions and initially getting intimidated by their complexity

Thus I'm interested in studying a field which will help me become comfortable with working with, manipulating and rewriting expressions/equations including basic operators, exponents, log and trig functions.

From my limited understanding basic algebra would be a good starting place, but which more advanced fields should i study to get an even stronger/more advanced ability to be comfortable with/manipulate expressions and equations?

user1299028
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    Well, calculus. – k.stm Mar 18 '14 at 17:44
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    Algebra is the main one. Toss in a little trig for identities. Which subject in calculus were you struggling with? – Mike Mar 18 '14 at 17:57
  • I agree with @Mike. Trigonometry is a fantastic place to learn manipulative algebra. But most the books I learnt from were local and I can safely say you won't get your hands on them. Maybe someone else can suggest a decent book. – Ishfaaq Mar 18 '14 at 18:13
  • I felt i struggled in general. I worked my way through derivatives and integrals, but not without my share of confusion- i.e. times where i looked at questions i ought to be able to solve and had no idea where to start. Then again it could just be that i dont have enough experience with different approaches of integration. – user1299028 Mar 18 '14 at 19:29

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In my opinion one learns those kind of manipulation by experience and i don't think that there is any area which do not uses such things. Consider for example that you need to prove $|x-y|\leq |x-z|+|z-y|\ \forall\ x,y,z\in \mathbb{R}$. The standard trick is to write $x-y=x-z+z-y$ in LHS and then proceed using the properties of modulus. Now a person who sees it for the first time may wonder that how one manipulates such thing but slowly while doing similar kind of operations one gets accustomed to it.

wanderer
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