TERM PAPER

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 discontinued Undergraduate Journal of Mathematics; please click here for some helpful resources.

The Journal is stored in the following two MIT collections:

Hayden Library - Science Journals | QA.M679
Institute Archives - Noncirculating Collection 1 | QA1.M585

The following papers were written for 18.704, and may serve as models for yours:

Volume 1, 1999

Paul Grayson, Robotic Motion Planning, pp. 57-67.

Volume 2, 2000

Ted Allison, Complexity of Computations of Ideal Membership, pp. 1-9.

Volume 3, 2001

Ethan Cotterill, Syzygies over polynomial rings, pp. 29-41.
Geoffrey L. Goodell, Algebraic Coding Theory, pp. 71-80.
Matt Menke, Running time of Groebner Basis Algorithms, pp. 145-151.
Brian D. Smithling, A Proof of Hilbert's Syzygy Theorem, pp. 199-207.

Volume 4, 2002

Peter Ahumada, An Algorithm for Integer Programming Problems, pp. 1-11.
Nicholas Cohen, Automatic Geometric-Theorem Proving, pp. 29-38.
Leah Schmelzer, Implicitization via Resultants, pp. 179-188.

Volume 5, 2003

Eric Schwerdtfeger, An Introduction to Symmetric Polynomials, pp. 265-273.

Volume 6, 2004

Paul Gorbow, Ideals from Graphs, pp. 69-84.

Volume 9, 2007

Hyeyoun Chung, Computing Invariants of Finite Groups, pp. 11-29.

Anand Deopurkar, Normalization of Algebraic Varieties, pp. 43-63.

Pablo Solis, Splines on a Finer Subdivision, pp. 133-142.

Volume 10, 2008

Alessandro Chiesa, Companion Matrices for Systems of Polynomial Equations, pp. 31-41.

Philip Engel, Colorings and Cycles of Graphs, pp.43-52

Volume 11, 2009

Qingchun Ren, Finding Generators for Invariant Rings, pp. 79-89.

Pablo Spivakovsky-Gonzalez, Primality Testing for Polynomial Ideals, pp.107-116

Our text, "Ideals, Varieties, and Algorithms," describes a number of possible topics in Appendix D. More possibilities are found in the following books, which are on reserve in the Hayden Library Reserve Stacks.

QA251.3.A32 1994
Adams, W. and Loustaunau, P., "An introduction to Gr\"obner bases," American Mathematical Society, 1994.
QA564.C6883.
Cox, D., Little, J., and O'Shea, D., "Using Algebraic Geometry," Graduate Texts in Math., 185. Springer-Verlag, 1998; second edition, 2005. Google books has most of the book online; you can find it HERE.
QA1.S981 v.53.
Cox D., and Sturmfels, B., "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.
QA218.S65 2005
Dickenstein, A., and Emiris, I., "Solving polynomial equations: foundations, algorithms, and applications," Springer-Verlag, 2005.
QA251.3.E38 1995
Eisenbud, D., "Commutative algebra with a view toward algebraic geometry," Springer-Verlag, 1995.
QA251.3.G745 2002
Greuel, G.-M., and Pfister, G., "A Singular introduction to commutative algebra," Springer, 2002.
QA564.S29 (2003).
Schenck, H., "Computational Algebraic Geometry." London Math. Soc. Student Texts, 58. Cambridge Univ. Press, 2003.
QA1.R336 no.97.
Sturmfels, B., "Solving Systems of Polynomial Equations," CBMS Conference no. 97 (2002: Texas A & M University), Amer. Math. Soc., 2002. A preliminary edition is available at the URL http://www.math.tamu.edu/conferences/cbms/bernd020517.pdf
QA251.3.V365 (1998).
Vasconcelos, W., "Computational Methods in Commutative Algebra and Algebraic Geometry," with chapters by D. Eisenbud, D. Grayson, J. Herzog, and M. Stillman, Algorithms and Computation in Mathematics, 2. Springer-Verlag, 1998.