Project
Math 505 Term Project
The term project consists of an inclass presentation and a written
report. The report will be a written account of your inclass
presentation but may include additional material that you did not get
to in class. (Don't just copy verbatim from whatever sources you
used. That would be plagiarism.) The report
should be type set using LaTeX or your favorite
technology. It is due on the last day of class. If
you turn it in significantly before the end of the semester, I will
mark it as soon as I can and return it to you. You will then have the
option of turning in an improved version.
Your term project will explore a topic relevant to the numerical
solution of differential equations of evolution. See the list below
for some suggestions. A good project will
have a numerical component and an analysis component. Your project
may also include an inclass presentation. This is optional.
Your report should be type set using LaTeX or your favorite
technology. (Please don't just copy verbatim from whatever sources you
used. That would be plagiarism.) It is due on the last day of class.
If you turn it in significantly before the end of the semester, I will
mark it as soon as I can and return it to you. You will then have the
option of turning in an improved version.
Project Topic Suggestions (may be updated periodically)
 (Steve)
Chinese remainder theorem: concrete version, abstract version, an
application or two (2.3.6, 2.3.7)

Classification of finite (or finitelygenerated) abelian groups
(you could start
here, for example)

Relationships between PID and UFD (2.6)
 (Anya)
Noetherian rings
 (Clinton)
A PID that is not an ED (with detailed proofs)

Existence and uniqueness of algebraic closures (appendix to Ch. 3)
 (Ian)
Modules; definition and basic properties, compare and contrast with
vector spaces, examples (early sections of Ch. 4)

Smith normal
form (4.5)

An application of group theory to combinatorics (5.3)

Generators and relations (5.8)
 (Ben?)
Finite fields (6.4)

Any topic from Ch. 7, 8, 9 or 10

Something related to your research

Some other topic of your choosing
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