Add to ORKGAbstract. These are essentially the lecture notes from a section on congruent numbers and elliptic curves taught in my introduc-tory number theory class at the Ohio State University spring term of 2007. The students in this class were assumed to only have a basic background in proof theory (such as sets and induction) and the material we had covered up to this point in the term (primes, congruences, and quadratic reciprocity). These notes are self-contained modulo basic facts from those subjects and do not assume a background of abstract algebra. Any abstract algebra that is needed is introduced. Calculations used in these noted were performed with SAGE ([6]) as the students in this class used this program throughout the term. Homework exer...