Projects for Abstract Algebra II
Mathematics 567: Spring 2004


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Purpose: The goal of the projects is to investigate mathematical ideas in greater depth,
to understand the connections between different topics, to develop skill in writing and speaking about math, and to have fun!

Things to consider:
mathematical content: theorems, proofs, examples.
written format: intro, conclusion, topic sentence, correct spelling and grammar, bibliography.
context and motivation: history, applications (real-world or mathematical), visual aids.
Don't drown yourself.

Possible topics and references:
A) Modules:
Projective or injective modules, DF 10.5.
Symmetric or exterior algebras, DF 11.5.
Bilinear forms, Artin 7.

B) Visual or computational topics:
Frieze and crystallographic groups, Gallian 28.
Constructible numbers, DF 13.3.
Solvable extensions (Cardano's formulas), DF 14.7

C) Extensions:
Integral extensions, DF 15.3.
Localization, DF 15.4
Base change

D) Geometric topics:
Reed-Solomon codes, Gallian 31.
Projective space, Silverman-Tate appendix A.

Characters
Endomorphisms of elliptic curves
Symmetries of lattices in C

I'm happy to spend time with anyone to figure out a good project.
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