This document discusses maximum torque per ampere (MTPA) control for permanent magnet synchronous motors (PMSM). It introduces Clarke and Park transforms which transform time-varying currents to direct currents. Field-oriented control with id set to 0 is presented, along with the method of calculating motor torque from d-q axis currents. MTPA control aims to find the ratio of id and iq currents to maximize torque while minimizing current. Analytical and numerical approaches are described and simulated results show MTPA control improves torque and reduces current compared to non-MTPA control. Future work involves implementing the golden search method on a microcontroller.