During the summer of 2003, I gave several lectures to advanced participants at the Ross program at Ohio State. The topic of the lectures was analogies between integers and polynomials (in one variable over a field). Topics included continued fractions, quadratic reciprocity (including characteristic 2), and the abc conjecture.
Here is a handout on polynomials which was distributed before the start of the course.
Below are problems sets distributed each day after my lectures.
Here are notes for my lectures on quadratic reciprocity in polynomials over a finite field of odd characteristic and characteristic 2. Only the part of the characteristic 2 notes preceding the introduction of residues was discussed.