Groebner Bases and Algebraic Geometry.
       MATH 439, MATH 739, MATH 819, Spring 2008.
       
 Instructor : Dr. Michael Monagan.
 Office: Room: 10501
 E-mail: mmonagan@cecm.sfu.ca 
 URL:    www.cecm.sfu.ca/~mmonagan
 Tel: (778) 778-4279
 Lab: (778) 782-5617

 Classes:    Tuesdays and Thursdays at 9:30am-11:20am in K9509
 Final exam: April 16th, 12:00-3:00pm, format TBA
 Course webpage: www.cecm.sfu.ca/~mmonagan/teaching/MATH439


                       Course text and outline.

 Ideals, Varieties, and Algorithms: An Introduction to
 Computational Algebraic Geometry and Commutative Algebra.
 Cox, Little, O'Shea, 3rd edition, Springer-Verlag.

 Chapter 1 (1.5 weeks) Geometry, Algebra, Algorithms.
 Chapter 2 (3 weeks) Groebner Bases.
         The division algorithm in k[x1,x2,...,xn]
         Diskson's lemma and the Hilbert basis theorem
         Grobner bases and Buchberger's algorithm
         Application to solving systems of polynomial equations
 Chapter 3 (1.5 weeks) Elimination Theory.
 Chapter 4 (3.5 weeks) The Algebra-Geometry Dictionary
         Hilbert's Nullstellensatz
         The radical of an ideal
         Irreducible varieties and prime ideals
         Decomposition of a variety into irreducibles
         The prime/ary decomposition of an ideal
 Chapter 5 (1 week)  Polynomial and rational functions on a variety
 Chapter 6 (1.5 weeks) Applications
         Theorem proving in geometry
         Circle packing problems
         Wu's characteristic sets method


 Grading:          MATH 439 and MATH 739       MATH 819
           6 Assignments    60%                   60%
           Final exam       40%                   30%
           Course project   ---                   10%

                               Cheating Policy

 If you cheat on an assignment, you will get zero for the whole assignment.
 If you cheat on the final you will get zero for the final.
 All instances of cheating will be notified to the chair of the
 department and will go on your record.
 If you collaborate on assignment questions, which is fine, just be
 prepared to explain your solutions to me.


                                Maple

 We will be using Maple for calculations throughout the course.
 SFU has a site license for Maple.  Maple 11 is available in all
 the instructional labs in the AQ under "Statistics Applications".
 Maple 11 can be purchased from the SFU micro computer store.
 Older versions of Maple will be fine for this course.