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Work in pencil.
Do not be a hero. You will make mistakes. Big ones. You will write
entire pages of mathematics, only to realise that it is all wrong. Worse
yet, you will realise that it is "mostly right"; it only needs to be "slightly"
changed... in about 30 places (for example, changing all the subscripts
"i" to "i+1", or changing the elements in a column of a matrix...
and you've written the matrix about ten times.)
If you write in pen, you will end up crossing out so many things that
your assignment will look like an explosion at an ink factory. This doesn't
make it any easier to write, and it certainly doesn't make it any easier
to read.
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Do not be afraid to waste paper.
Use lots and lots of paper. Double space. Triple space. Write each
question on a separate page. You will not regret it. Invariably, you will
realise, belatedly, that changes, additions, or extensions need to be made
to your answers. That extra space will come in useful. I use the
backs of previously-used pieces of paper for everything, which has the advantage of also being green.
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Put one equals sign per line.
Why? It makes it easier for everyone to read a long solution. It makes it easier for everyone (including you) to find any mistakes in your long solution. To really help yourself, align the signs.
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Do not write down the questions first, and "leave space'' to fill in
the answers later.
The answer will always, always, always take more space than
you think it will. Always. "Guessing" how much room you will need is sheer
folly. You will guess wrong.
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When in doubt, draw a picture.
Try to make it to scale.
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Do not wait until the last minute to get help with a difficult problem.
You are not expected to know how to solve every problem immediately,
otherwise we would not bother to have math classes. However,
leaving an assignment or studying for a test until the last minute will
only cause you suffering and heartache. Remember the mantra: You
can't cram math. The day before the test is too late to
start learning a complicated concept.
Having said that...
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Do not let difficult concepts get by you.
Remember the other mantra: math is cumulative. Suppose you write
a test that covers concept A, but you never quite got
the hang of concept A. However, you figure that since you've already
written the test, you don't need to learn concept A. Unfortunately,
concept B depends on understanding concept A. You see where this
is heading.
The first best time to get help was as soon as difficulties arose.
The next best time is now. It might mean a little bit of extra work,
but it will be worth it in the end.
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Do not give up in frustration.
Sometimes, you just need a little time to let the material sink in.
Be patient. Take a break from the problem for an hour or so and return
to it with a fresh mind.
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Try the problem before asking for help.
You will not learn if you always wait for someone else to give you
the solution. If you don't know where to begin with a problem, ask
yourself: "What do I need to find out? What are my knowns? What are
my unknowns? What kinds of things do I know that relate my knowns
to my unknowns?" Often, you will see how to proceed once you have
asked these questions.
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Learn to complete the square and memorize the quadratic formula.
Again with the mantra: math is cumulative. Not just within a course, but from year to year. Review all that stuff you learned in earlier grades. It's useful. You want to have all the math tools at your fingertips; you don't want to have to go searching for them.
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Pay attention in class.
I often make comments about problems in class. I always show how I want the solutions written. Don't zone out. Stay engaged. It will save you much suffering and heartache.
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Do not be sloppy when doing your homework.
Typographical mistakes on math tests (e.g., changing signs, missing
parentheses, and various other sloppy math errors) are not merely the result
of the stress of writing quizzes and tests. These kinds of
errors stem from doing your homework in careless and sloppy manner. P Practice does not make perfect; practice makes permanent.
If you play sports or an instrument or act or do anything in public,
you know that the way you practice or rehearse is pretty much the way you
play in a game or in performance because when the pressure is on, instinct
takes over and your body performs in the way it is used to, which, if you've
been practicing badly (as in, acquiring bad habits), means you will play
or perform badly.
Doing math is no different. It is very easy to do your homework
sloppily and say "When I get to the test, I'll write it down properly,"
but tests are stress situations and your brain will do what it usually
does. Which in this case, might be not carrying equal signs, saying
that df/dx is equal to f(x), ignoring negative signs, losing brackets, etc...
The same holds for writing out the solutions properly (including justifications
and writing clearly). If you do it in your homework, every time,
you will be so used to doing it that it will come as second nature and
won't take any longer to do on the test. The added bonus is that
if you are presented with a question that you haven't seen before, you're
already used to thinking through the justifications and so new stuff won't
throw you for a loop. Also, if ever, at the end of term, you've gone
back through assignments you did at the beginning of term and wondered
how you could have been such a genius then and not have a clue how to do
those problems now, you won't have to spend as much time figuring out what
you were doing because you will have written down the justifications!
(See How to Avoid Losing Marks)
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Check over your work.
So simple, but so often overlooked. Get into the habit of checking
your solutions so you can catch any mistakes. If the answer in the
back of the book and your answer do not agree, check your work. I spend a lot of time going through solutions for students
who think they do not understand how to solve the problem when really they just
made simple mistakes that would have been caught by checking. This
wastes time that could be spent going through more difficult conceptual
problems.
It's not enough to just read over your work, either, becuase you will
see what you expect to see, not the errors. Use another method to make
sure your answer is right: sub your solutions back into the question if
you can. Get a homework buddy and check each other's work. Do the problem in a different (but correct) way.
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