Course Learning Outcomes:

1. Create and present rigorous solutions to problems and coherent proofs of theorems.
2. Define and illustrate the correspondence between ideals and varieties by translating between algebraic and geometric statements.
3. Describe and demonstrate a basic understanding of projective geometry.
4. Execute accurate and efficient calculations with ideals in a multivariate polynomial ring involving Gröbner bases, membership, intersections, and quotients.
5. Explain and use elimination theory to solve systems of polynomial equations.