Alexander attended Central High School and graduated in 1917, delivering a speech "The Future of the American Negro", at the commencement ceremony. He enrolled at the University of Pennsylvania on a merit scholarship and became the first black graduate of the Wharton School of Business in 1920. He then enrolled at Harvard Law School. While there, Alexander earned a living by working as a teaching assistant during the school year. In the summers, he took classes for a master's degree in political science at Columbia University, though he did not finish the degree. At Columbia, Alexander supported himself by working as a porter for the Delaware, Lackawanna and Western Railroad. While still in law school, Alexander brought his first discrimination lawsuit, suing Madison Square Garden for refusing him entry on account of his race, a violation of New York's equal rights law. As he was not yet admitted to the bar, Alexander hired an attorney to represent him.