1 First mid-term exam for Math 204
The exam consists of three questions. You are expected to work on the exam in collaboration
with the other members of your group. The task of writing up the problems, however, should
be divided among the group, with each member writing up one solution.
The exam is open book, which means not only your book but any other book you care
to look at. (However, none of the problems require any mathematics not contained in your
textbook.) Calculators, computers, websites, etc. are also ﬁne. The only resource I ask you
not to employ is advice from people outside your group.
A successful write-up consists of the following two parts:
1. Your solution to the problem. Since the time pressure is mild, I ask that your solution
be written in complete sentences and that you make it clear what theorems you are using
(i.e., if you use a theorem from the book, please tell me so and give a reference.)
2. A description of how you came to the solution you wrote down in part 1. Typically,
this part will be between 1/2 and 1 page.
It is absolutely acceptable
for the description
to be, ”Ms. X in my group told me how to do it.” If this is the case, you must get Ms.
X to explain to you how
came by the solution, and you should describe that process
in your own words. It is also ﬁne for the description to be, ”I found a solution in the
Introduction to the theory of Y
.” If so, your job in part 2 is to describe your personal
understanding of the solution so that it is clear to me you did more than copy out an answer.
Please be aware that these problems have many parts, some of which are relatively deep.
It’s OK not to be able to solve every section of every problem. But
give me some
indication of what things you tried and what ideas you had.
Grading: Each group will be graded as a whole. We expect to give generous partial
credit; we am also open to giving extra credit, if the problems suggest to you further ideas
for exploration. We will be less forgiving about sloppiness than we are on ordinary exams–
you have plenty of time to check your work.
”How long should I spend on this exam?” We don’t have a ﬁxed amount of time in mind.
You should think of it as you would writing a paper. You can put as much or little time as
you like into it; the more work you put in, the better exam your group will write, and the
more your understanding of the material will increase.
The exam is due at the beginning of class on Wednesday, March 8.
This format will be new to most of you. Please don’t hesitate to ask us if anything is
unclear about what we expect. And now, the questions–good luck!