Learning Outcomes

Students in this program will be expected to:

• Deeply understand analytic arguments, using such common notions as epsilon/delta, infinite sums, and limits, as well as considerations for more general spaces than the real numbers, such as spaces of functions;
• Develop a basic understanding of measure theory and use it to study the Lebesgue integral;
• Deeply understand basic algebraic and discrete notions, such as facts about vector spaces and counting arguments, and expand this to include ideas about rings and fields;
• Develop a basic understanding of Galois theory;
• Follow and create analytic proofs involving abstract metric spaces;
• Follow and create algebraic proofs, with an understanding of groups, rings, and fields; and
• Independently investigate advanced topics in mathematics and present results to others in a clear way.