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Section 2 Course Learning Outcomes

By the end of this course, students will be able to:

  1. Demonstrate familiarity with introductory concepts, definitions, and theorems in algebraic geometry, including:

    • Affine varieties and ideals
    • Regular and rational maps
    • Elimination and projection
    • Hilbert's Nullstellensatz

  2. Demonstrate familiarity with introductory concepts, definitions, and theorems in computational algebra, including:

    • Computations with multivariable polynomials, including division with remainder
    • Monomial orderings
    • Gröbner bases and Buchberger's algorithm
  3. Read and write rigorous proofs.
  4. Demonstrate good mathematical writing skills and style.
  5. Demonstrate familiarity with research and conjectures in algebraic geometry and computational algebra.