Melanie Day successfully completed a free online course through Coursera provided by Stanford University titled "Algorithms: Design and Analysis, Part 1". The course covered topics in asymptotic analysis, divide and conquer algorithms, sorting and searching, basic randomized algorithms, graph search, shortest paths, heaps, search trees, and hash tables. It was an undergraduate course on designing and analyzing algorithms taught by Associate Professor Tim Roughgarden of the Computer Science department at Stanford University.