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I am already a grad student, but sadly I still have problems with careless computations. In my most recent mid-term (multivariable analysis), I lost 21 points out of 100 because of calculation errors and other cringe-worthy mistakes. If you ask me to explain proofs, I don't believe there will be a problem, but I have no "feels" for computing results. A lot of times, when I have an error, I just don't see it.

I admit too that sometimes I detest calculations and just want to get over with them. Unlike learning a proof, there is no understanding in calculating a result. I still remember learning Taylor series in Calculus -- hated it. After tons of calculations, I had no idea if I was right or wrong, did not know how to check it, nor understand why I was doing a series expansion in the first place. (I got every question in my homework wrong because I could not keep count on the index. The grader gave me 1 point for turning in something ....)

Anyway, there is no use whining; a wrong answer is a wrong answer. Also, I cannot afford to lose 20 points on each exam. What self-check mechanism do other MSE users have?

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    $\begingroup$ use wolframalpha $\endgroup$ – janmarqz Apr 19 '16 at 5:13
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    $\begingroup$ I am confused when you say you are a graduate student. What is your discipline? If it is mathematics or applied math, you should know by now you cannot decouple computation from proof, and you cannot really claim to be able to construct proofs without significant skill in the yoga of computations. If you are in a non-mathematical scientific field, intuition matters even more than rigorous demonstration, and there is no way to get a feel for an object without significant computations. As a graduate student, I feel you need to do much more than find a 'self-check mechanism'. $\endgroup$ – guest Apr 19 '16 at 6:03
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I have one method for you.But this is only to check if multiplications(that you do by hand) are correct.I mean, it will only help a quick check whether or not you have done the simple additions and products in a long multiplication correctly.Say, you have

$$a_1a_2\dots a_n\\\times b_1b_2\dots b_m \\ -----\\c_1c_2\dots c_p$$

$a_i,b_j \ \&\ c_k$ represent the digits of the multiplicand, multiplier and the answer respectively.

The rule is :

Define $A = \Sigma a_i$. If $A\ge10$, redefine $A=\Sigma$ Digits of previous $A$ ; and continue redefining $A$ until $A$ is some number below $10$.

Similarly define and (if necessary) redefine $B$ to a number below $10$. And same for $C$.

Now let $D=A\times B$. Redefine $D$ (similarly) as above to a number below $10$.

If $D=C$ , your answer is correct.

Please don't ask for a proof or reference. It's a method I gathered from a primary teacher and has worked well for me.

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