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\large{\textbf{Math 404 portfolio}} \\
Spring 2005
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% \paragraph{Assignment.}
During the quarter, I will assign several \emph{portfolio problems}; I
anticipate four such assignments.  Your goal is to have, by the end of
the quarter, nicely written solutions to these problems.  To
accomplish this,

\begin{itemize}
\item You will peer-review the first draft of each problem.
\item You will turn in a second draft of each problem, and the TA
will read and comment on it.
\item At the end of the quarter, you will turn in a third draft,
and I will grade it.
\begin{itemize}
\item Your third draft will be done as a group project: after working
on the first two drafts individually, you will collaborate with other
students to produce the third draft.  You should work in groups of
three or four; I reserve the right to give less than full credit for
papers done in smaller or larger groups.
\item You must turn in your earlier drafts with the third draft.
\item You should write a cover sheet for each problem, describing your
progress from the earlier drafts to the third one, and how the
collaboration went.  If you're in a group that doesn't have three or
four people in it, then your cover sheet should also explain this.
\item Different problems can be done in different groups: just make
sure that the appropriate names are on the appropriate solutions when
you turn then in.
\end{itemize}
\end{itemize}

Turning in the first and second drafts on time, and participating in
the peer-review processes, will determine 10\% of your grade for the
class; the quality (both in mathematics and writing) of your portfolio
will determine another 10\%.

In the best of all possible worlds, your solutions would be typed up 
on a computer rather than by hand, but I'm not requiring this.  If you
want to do it on a computer, a program called \LaTeX{} is the best
thing around for doing mathematics.

The final drafts of your portfolio problems are due on \textbf{Friday,
May 27}.

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\noindent 
[The following is unchanged from Winter quarter.]

\paragraph{Grading criteria.}
I will award points from 1 to 5 for two criteria: mathematical
correctness, and quality of writing.  Your grade on the portfolio will
correspond to your total score.

\subparagraph{1. Mathematical correctness.}  Is your solution essentially
correct?  Does it have any mistakes; if so, how many, and how crucial
are they?  Have you proved everything that was asked?  Did you in fact
prove a generalization of what was asked?  Are there any serious
logical flaws?  Have you ``proved'' something false?  Did you use
relevant techniques?  Did you use all of the hypotheses?

Here is what the numbers represent, roughly, for this category:

\begin{enumerate}
\item Most of your proofs contain serious logical flaws, and so are
wrong, or purport to prove something false.
\item Many of your proofs contain serious logical flaws, or do not 
prove everything that was asked.
\item There are a number of small-to-medium mistakes, or a just a few
major ones, or some mix of these.  Your logic is occasionally shaky,
but more or less correct.  You have used material or techniques from
the appropriate section of the book.  You have used all of the
hypotheses, or explained why you didn't.
\item There are no major flaws, but there are some (easily
correctable) mistakes.
\item There are only a few easily correctable mistakes.  You may even
have proved a more general result.
\end{enumerate}

\subparagraph{2. Quality of writing.}  There are ``local'' and
``global'' writing issues.  Local ones: Have you chosen good notation?
Are you using (mathematical) language well and appropriately?  Is
everything you're written relevant?  Have you included a good level of
detail?  Do you have good transitions?  Are there grammatical errors
or misspellings?  Does your solution sound good when read aloud?

Global writing issues: Have you broken the proof into ideas and
paragraphs well?  Have you recognized and separated out lemmas and
intermediate results?  Did you make an appropriate choice of method of
proof?

Here is what the numbers represent for this category:

\begin{enumerate}
\item You have only provided pseudo-random strings of symbols on the
page.  It's not clear what's being proved in which part of your
solutions.
\item You have some garbled mathematical language (for example, you
refer to the group of integers as a homomorphism).  There is some
extraneous material.  You prove the same thing several times.
\item Most of the time, you have chosen an appropriate method of
proof, and have good notation.  You have enough detail.  You have
mathematically sensible sentences.  You have targeted the right
audience: your classmates.  For the most part, you use good grammar
and don't misspell things.
\item Your solutions are well-organized.  There is no extraneous
stuff.  You don't have too much detail.  You have good transitions.
Your solutions sound good when read aloud.  There are very few
grammatical errors or misspellings.
\item There are almost no errors.  You have recognized lemmas where
appropriate.  Your best solutions are elegant and to the point:
terse, but not overly so; they are good enough to be publishable in a
solutions manual for this course.
\end{enumerate}

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