The purpose of this paper is to give you the opportunity to read and research mathematics on your own, as well as explore topics that interest you that are outside the pre-calculus curriculum.  You may work individually, though I would prefer for you to work with a group of  two to four students.  Those who work in a group will submit one paper for the group.

Things to Do

Your paper should be mathematically correct.  It should contain mathematical background along with proofs and/or problems related to your topic.  Seek your references from the main public library, bookstores, WSHS library, college/university libraries, or the Internet.  You may approach me for help if you are unable to find sources.  The University of Memphis has a mathematics library in addition to the main library.  Bookstores often have paperback books that are not too expensive that you might choose to purchase.  I do not expect for you to have a lot of sources.  In fact, one or two books could be ample.  Sometimes, because of different notation from one book to another, too many sources could cause confusion.  This is the most important part of your paper.  Show some mathematics.  Find some that you understand.

Your paper should be neatly done in the form of a research paper with endnotes and a bibliography.  If you choose to write a computer program, build geometric figures, make a poster, do a demonstration, etc., the quality of these additions to your paper will be evaluated in this category.

Below is a list of suggested topics.  You may choose one of these, but you are not restricted to this list.  However, your topic must have my approval.

Suggested Topics
Chaos
Conic Sections (more than what is taught in class)
e
Formulas for Solving the 3rd and 4th Degree Polynomial Equations
Fractals
Functions in 3-dimensions – their equations and graphs (computer software and/or the
      TI-92 could be helpful here)
Geometry of the 4th Dimension
Graph Theory (Davis-Kidd has a great book by Chartrand on this.)
Group Theory
Linear Programming and the Simplex Method
Matrix Applications:  (Examples – Coding Theory, Markov Chains,
         Leontief Input-Output Analysis, Game Theory)
n-dimensional Vectors
Non-Euclidean Geometry
Patterns in Pascal’s Triangle
Pi
Projective Geometry
Spherical Trigonometry
Steiner Points – Mathematics with Bubbles
Tessellations (for the artsy type)
The Buffon Needle Problems
The Fibonacci Sequence – its patterns and applications, proof of explicit formula
The Mathematics of Technical Drawing
The Platonic Solids
The Pythagorean Theorem – various proofs
Topics in Number Theory:  (Examples: Perfect Numbers, Prime Numbers, Fermat’s Last
                 Theorem, etc.)
Topics in Topology
Trisecting an Angle

This list is certainly not exhaustive.  If you have ideas of your own, please let me know.  You might want to look at the list on the Web under Second Six Weeks Project again.