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Description

In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required.

Prerequisites

Linear Algebra (18.06 or 18.700) or Algebra I (18.701)

Textbook

Cox, David, John Little, and Donal O'Shea. Ideals, Varieties, and Algorithms. 3rd ed. Undergraduate Texts in Mathematics. New York, NY: Springer, 2007. ISBN: 9780387356518.

Portions of the book are  online.

Grading

Grades are based equally on classwork, homework, and the term paper; no exams or final. Written work will be graded in part on the quality of the writing. The term paper is to be ten-pages long in TeX: a full outline is due by Ses #16; a complete first draft, by Ses #22; and a revised final draft, by Ses #26.

Homework

Problems with numbers between braces are to be written up formally in TeX and passed in the week after they are assigned.

Calendar

The lecture sessions follow the contents of the course textbook. Two to four sessions are required to cover each chapter in the book. See the readings section for specific topics per session.

Topics

• Geometry, algebra, and algorithms
• Groebner bases
• Elimination theory
• The algebra-geometry dictionary
• Polynomial and rational functions on a variety
• Robotics and automatic geometric theorem proving
• Invariant theory of finite groups
• Projective algebraic geometry
• The dimension of a variety

Key Dates

• Ses #16: Term paper outline due
• Ses #21: Term paper first draft due
• Ses #26: Term paper final draft due