Problems for your portfolio
- Prove this theorem: fix a field F and a
non-negative integer n. The dimension
of a vector space V over F is n if
and only if V is isomorphic to
Fn. Furthermore, show that if
V has dimension n and W has
dimension k with n not equal to k,
then V and W are not isomorphic.
Your solution should start
from the definitions and build up from there, proving everything
that you need along the way.
- The first draft (which will be peer-reviewed) is due on
Monday, April 18. Bring three copies to class that day.
- The second draft is due on Monday, May 2.
- Prove this theorem: any finite subgroup of the group of
units of a field is cyclic. Do this by following the outline
presented here (PDF file) or
here (LaTeX file).
- The first draft (which will be peer-reviewed) is due on
Wednesday, May 4. Bring three copies to
class that day.
- The second draft is due on Wednesday, May 18.
- Write an essay on your experiences in this course (and Math 403, and
also Math 402 if you took it with me) combining writing and
mathematics. Some questions you might consider: What writing-focused
aspects of the course worked well for you (for example, revising,
peer-critiquing, etc.)? Did paying attention to the writing help your
understanding of the mathematics? Did your mathematical writing
improve much? Please don't limit yourself to these questions; examine
the topic from whatever angles you want.
- I'd like an essay of 500-1000 words, typed. As long as
the essay is close to being long enough and is not completely
incoherent, you'll get full credit: I'm not going to grade the
quality of the writing (or the mathematical content
).
- The first draft (which will be peer-reviewed) is due on
Friday, May 20. Bring three copies to class
that day.
- The second (and final) draft is due on Friday,
June 3. Do this one individually, not in groups.
You may turn this in electronically if you want: email me a
PDF file, a LaTeX file, or (ugh) a Microsoft Word file. If
you want to use some other format, check with me before you
email it. When you turn in the final draft, include your
peer-reviewed first draft. No cover sheet is necessary.
Back to Math 404A home page.
John Palmieri Padelford C-538 (206) 543-1785
email
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