Fall 2007

**September 5**: Informational Meeting

**September 12**:- Important Concepts:

Singularities, Taylor's series expansion in several variables, node/cusp singularity type - Exercises

- Important Concepts:
**September 19**:- Important Concepts:

Tangent cone, intersection multiplicity, multiplicity of a point - Exercises

- Important Concepts:
**September 26**:- Important Concepts:

Rational functions, rational curves - Exercises

- Important Concepts:
**October 3**:- Important Concepts:

Ideals, generating set of ideals, monomial ordering - Exercises

- Important Concepts:
**October 10**:- Important Concepts:

Polynomial division, leading term ideal, Gröbner basis - Exercises

- Important Concepts:
**October 17**: No Meeting - Midterm Recess

**October 24**:- Important Concepts:

Buchberger's algorithm, Gröbner bases calculations, ideal membership problem, solving polynomial equations, implicitization problem - Exercises

- Important Concepts:
**October 31**:- Important Concepts:

Elimination, elimination ideal - Exercises

- Important Concepts:
**November 7**:- Important Concepts:

Irreducible factors, Sylvester matrix, resultant - Exercises

- Important Concepts:
**November 14**:- Important Concepts:

Resultant, discriminant - Exercises

- Important Concepts: