Michael McBride continues Yale's Freshman Organic Chemistry II with a lecture on reactions that build three-membered rings from alkenes. After finishing a drill on the pinacol rearrangement mechanism, he uses molecular-orbital analysis to explain simultaneous electrophilic and nucleophilic attack by a single atom on a double bond. He presents two competing mechanisms for cyclopropane formation via the Simmons-Smith alkylzinc carbenoid reagent, showing why theory favors a concerted one-step pathway over a stepwise one. The lecture then turns to epoxidation of alkenes by peroxycarboxylic acids, arguing this too proceeds through a single concerted transition state rather than discrete steps. McBride closes by comparing the stereochemistry and industrial scale of different routes to epoxides, connecting the mechanistic analysis to their commercial importance. Throughout, curved-arrow notation is used consistently to track electron-pair shifts across each proposed mechanism.