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Mathematics
Algebraic Geometry
1. Foundations of Algebraic Geometry
2. Polynomial Rings and Commutative Algebra
3. Gröbner Bases
4. Affine Algebraic Geometry
5. Projective Algebraic Geometry
6. Rational Maps and Birational Geometry
7. Local Properties and Singularities
8. Introduction to Schemes
9. Coherent Sheaves and Cohomology
10. Divisors and Line Bundles
11. Algebraic Curves
12. Algebraic Surfaces
13. Advanced Topics
Gröbner Bases
Motivation and Applications
Solving Polynomial Systems
Ideal Membership Problem
Elimination Theory
Buchberger's Algorithm
S-polynomials
Reduction Process
Algorithm Description
Termination and Correctness
Applications of Gröbner Bases
Elimination of Variables
Implicitization
Solving Polynomial Systems
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2. Polynomial Rings and Commutative Algebra
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4. Affine Algebraic Geometry