Projects for Abstract Algebra II Mathematics 567: Spring 2004
This page is not yet complete. 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