Tuesday, November 30, 2010

Three Opinions and Two Facts

Partial credit is great. But there's no need to complain if partial credit isn't given. Why? Well, one day, it just might happen that partial credit won't be given and you won't be in a position to complain, so get used to it.

Example: You are working on a project, everybody does their part. Perhaps people check your work over. In any case, your project gets designed and then for some reason or another it fails. Well... you don't get partial credit. I suppose in this case, you wouldn't want to take any credit! (for the blame)

The previous example also lends itself to waiting for other people to check your work for you. Just because someone might check your work, doesn't mean you can skip checking your own work. Sometimes the wait is too late. Also it can just reflect badly. Granted, you don't always have to do such a thorough job, especially when you're tired, but when you can, check your work.

Speaking of checking your work, what about showing your work? Ideally, you should have a sufficient amount of work that will allow the reader (keeping your audience in mind, that is how familiar will the reader be in your work) to follow relatively easy and also, highlight (meaning to emphasize or summarize in some form) the answer. Sometimes clear and concise is better than showing an excessive amount of work, and sometimes being descriptive is better than being brief.

Example (in math):
Writing $\tan (x)+\sec ^2 (x)$ is a better alternative to writing $\frac{\sin(x)}{\cos(x)}+1/{\cos^2(x)}$

Example (in life):
Your boss requests a summary of the work you've been doing. Your write-up is long and will probably include a cover letter summarizing the contents. He or she will probably just read the cover letter, but it's possible he or she will glance inside or pass it on to someone who does understand. Alternatively, what's written inside should be understandable to the audience, in this case your boss.

And unrelated to the above, when integrating, area that is below the x-axis is negative! (This is of course for Calculus I)

Be consistent with your variable.
Example: $G(x)=\int _2^x \sqrt{3t}+\sin(t)dt$
Then $G^{\prime}(x)=\sqrt{3x}+\sin(x)$ for $x>0$
Don't write $G^{\prime}(x)=\sqrt{3t}+\sin(t)$ for $t>0$
You could if you want write $G^{\prime}(t)=\sqrt{3t}+\sin(t)$ for $t>0$
Or $G^{\prime}(u)=\sqrt{3u}+\sin(u)$ for $u>0$
Or $G^{\prime}(v)=\sqrt{3v}+\sin(v)$ for $v>0$
Or $G^{\prime}(%)=\sqrt{3%}+\sin(%)$ for $%>0$
And so on...

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