1. May I write a computer program that solves a Test
problem? I would include the program with my answer.
A. A computer program that answers a question by
brute force is not welcome. For instance, a program that solves a
counting problem by listing every possibility and then counting the
total is brute force. On the other hand, it is unlikely that a test
question would allow a straightforward count. Thus the program would
have to have clever ideas about how to count. And once you discover
the clever ideas to make such a program work, you can almost surely
carry them out by hand anyway in a short amount of time, and thus
should do so.
Computers definitely have a role in mathematics -
many professional mathematicians use them for some calculations,
especially if even the best way they see to do a computation is
tedious. But we have chosen Qualifying Test questions for which
computers are not necessary if you think about the questions the
right way.
2. Should I sumit the answers printed or
handwritten?
A. You can submit it either way.
For
most students it is less time-consuming to submit handwritten answers
than to format mathematical symbolism on a computer. (The exception
is if you already know a math-formatting language such as TeX
throughly. All professional mathematicians know some version
of TeX - we formatted the Test in Plain TeX - but now, when you are
trying to think about our Test, is not the time to learn TeX!)
Note that it is the correct reasoning that earns the score, not the
beauty of the page layout. The only requirement about how your answers
look is that the presentation be readable.
3. What is your scoring
scheme for the answers?
A. This is the wrong
question! You should be worrying about doing the best you can and not
about how we score. Our Test is not a competition, where everyone
must be assigned an exact score because someone will be declared a
winner. In fact, there is no exact grading rubric, no exact cutoff
for admission, and you will never be told your score. (If you are
admitted to MathPath and come, you will learn whether you were
basically right or not because all test questions will be discussed
when we go over student work on it in our plenary writing
sessions.)
Of course, we have rough grading guidelines.
Generally problems are worth 10 points, divided among the parts of a
problem depending on difficulty level. Sometimes a problem is worth more
if there are many parts. Answers alone are worth
little. What can gain points is reasoning, good intuition,
elegance, and clear communication. It's actually infrequent for
someone to get full credit on a problem, but there is lots of partial
credit. Overall, we are looking to see if a student has the sort of
interest and aptitude that can grow at MathPath. We also are
checking whether students have the basic geometry and algebra skills
needed as a starter.
So the bottom line is: Try all the questions
and do the best you can. If you are not sure (part of) one of your
solutions is correct, say so, indicating what you are not sure of.
Knowing when you don't know is an important mathematical skill, and
sometimes gains points.
4. I have answered four
questions on the Qualfying Test and I am on the brink of solving the
fifth. I am absolutely sure that the answers to the problems I did
are correct, but I am just a tiny bit worried about the fifth. Do you
suggest I try another question just to be safe?
A.
See the answer to the previous question. Do as many
questions as well as you can, first because we want to see as much of
your thinking as we can, and second because you never know how your
work will be evaluated or what quality of work you need to be
admitted.
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