The term paper is to be a ten-page essay on a topic related to the course. The goal is for you to learn something new, and to explain it clearly to others in the class, or better, to other upper-class math majors. The paper must be written in a professional style, and formatted in AMS-LaTeX, like the papers in MIT's Undergraduate Journal of Mathematics. Some helpful resources are found in the study materials section. If you do a good job on your paper, then, possibly after further editing, it can be published in the next volume. (MIT students only.)
Below is a list papers written for 18.704 in previous terms, to give you some idea of possible topics. These papers were published in MIT's Undergraduate Journal of Mathematics (not available to OCW users).
Volume 1, 1999
Volume 2, 2000
Volume 3, 2001
Volume 4, 2002
Volume 5, 2003
Volume 6, 2004
Volume 9, 2007
Volume 10, 2008
Our text, Ideals, Varieties, and Algorithms, describes a number of possible topics in Appendix D.
More topic possibilities are found in the following books:
Cox, D., and B. Sturmfels. "Applications of Computational Algebraic Geometry, Lectures Presented at the AMS Short Course held in San Diego, CA, January 6-7, 1997." Proceedings Symposia Applied Math, 53, AMS Short Course Lecture Notes, Amer. Math. Soc., 1998.
Dickenstein, Alicia, and Ioannis Z. Emiris. Solving Polynomial Equations: Foundations, Algorithms, and Applications. Algorithms and computation in mathematics, vol. 14. Berlin, Germany: Springer, 2005. ISBN: 9783540243267.
CBMS Conference on Solving Polynomial Equations, and Bernd Sturmfels. Solving Systems of Polynomial Equations. Providence, RI: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2002. A preliminary edition is available. (PDF)
Vasconcelos, Wolmer V., and David Eisenbud. Computational Methods in Commutative Algebra and Algebraic Geometry. Algorithms and Computation in Mathematics, vol. 2. Berlin, Germany: Springer, 1997. ISBN: 9783540605201.