MATH 499: VIGRE Computational Algebraic Geometry Junior Seminar
Fall 2007

Schedule:

• September 5: Informational Meeting
  
  

• September 12:

  • Important Concepts:
    Singularities, Taylor's series expansion in several variables, node/cusp singularity type
  • Exercises
  
  

• September 19:

  • Important Concepts:
    Tangent cone, intersection multiplicity, multiplicity of a point
  • Exercises
  
  

• September 26:

  • Important Concepts:
    Rational functions, rational curves
  • Exercises
  
  

• October 3:

  • Important Concepts:
    Ideals, generating set of ideals, monomial ordering
  • Exercises
  
  

• October 10:

  • Important Concepts:
    Polynomial division, leading term ideal, Gröbner basis
  • Exercises
  
  

• October 17: No Meeting - Midterm Recess

  • Handout
  
  

• October 24:

  • Important Concepts:
    Buchberger's algorithm, Gröbner bases calculations, ideal membership problem, solving polynomial equations, implicitization problem
  • Exercises
  
  

• October 31:

  • Important Concepts:
    Elimination, elimination ideal
  • Exercises
  
  

• November 7:

  • Important Concepts:
    Irreducible factors, Sylvester matrix, resultant
  • Exercises
  
  

• November 14:

  • Important Concepts:
    Resultant, discriminant
  • Exercises