Problem Sets

Each Ross Program problem set has the following rough structure in the types of problems:

• terminology,
• numericals,
• exploration, and
• PODASIPs (prove or disprove and salvage if possible).

This structure helps guide participants to observe patterns, make conjectures, explore further examples to test the conjectures, formulate theorems, write up proofs, polish the arguments, and investigate generalizations. Note that numerical problems are only one component of the problem sets. A large portion of the work that participants will be doing is exploring and formulating ideas and writing clear and precise arguments to demonstrate their ideas.

Participants submit their work on the problem sets to their counselor, who will provide constructive feedback and assign revisions if necessary. We value revisions to encourage participants to think more deeply about their work and mathematics, and ensure a solid understanding of the material. There is no numerical grading. Participants proceed at various paces through the problem sets. In fact, we encourage participants to "think deeply about simple things" and take the time to digest each problem set, instead of just rushing through for the sake of completion.

To provide an idea of the level of mathematics involved, here is an example problem set.