Term Paper Proposal
The purpose of the term paper is to allow you to pursue some topic in
Modern Algebra in more depth than there is time for in the syllabus,
or to learn about an application of Group Theory in your own major
field of study. The scope of the term paper should be comparable to
that of a Section in the textbook: three to six typeset pages
introducing your subject and presenting proofs of some of its basic
theorems.
In the Term Paper Proposal, due Friday, March 12, 1999, include the following.
- A statement of the proposed topic for your term paper. Choose a
topic from the list below, or, after consultation with your
professor, an original topic of interest to you. [No proposal
for a topic not listed below will be accepted without a prior
consultation with your professor.]
- A statement of the theorems in the subject that you intend to
prove in your term paper.
- A list of at least two relevant scientific references besides the
course textbook.
Some Topics in Modern Algebra
- The Euclidean Algorithm and Continued Fractions
- Generating Pseudo-Random Numbers by the Linear Congruential Method
- Symmetry Groups of the Five Regular Solids
- Crystallographic Groups
- The Burnside-Polya Counting Theorem and its Applications in Chemistry
- The Rotation Group and Eulerian Angles in Mechanics
- Applications of Group Theory in Quantum Mechanics
- The Lorenz Group and Special Relativity
- Combinatorial Group Theory (Tesselations)
- Public-Key Cryptography
- The Chinese Remainder Theorem and Fast Modular Arithmetic
- Groups and Statistical Designs
- Groups and the Theory of Equations
The Paper
Imagine that you are writing a section of the textbook that introduces
and explains your topic to readers who know the basics of Modern
Algebra.
- Be sure to include definitions of all terms, entities and concepts not
encountered before in this course.
- Enhance your presentation, when appropriate, with well-chosen examples.
- State hypotheses and conclusions of all theorems clearly, and make sure
proofs are airtight.
- Cite clearly (if possible by name, e.g. Lagrange's Theorem) any theorems
of group theory used in your exposition.
- Use Lemmas to isolate results needed in proofs of theorems.
