- Understand basic analytic arguments using such common notions as epsilon/delta, infinite sums, and limits.
- Understand basic algebraic and discrete notions, such as facts about vector spaces and counting arguments.
- Be able to follow and recreate algebraic proofs, with a good understanding of groups.
- Be able to both follow and recreate analytic proofs, including basic ideas involving abstract metric spaces and differential equations.
- Be able to independently investigate more advanced topics in mathematics and present their results to others in a clear way