Verified Certificate

Supported by the following organizations

This is to certify that Ryan Butler successfully completed and received a passing grade in ROBO1x: Robotics: Kinematics and Mathematical Foundations a course of study offered by PennX, an online learning initiative of the University of Pennsylvania.

Noted by

Camillo J. Taylor

Camillo J. Taylor

Professor, Computer and Information Science University of Pennsylvania

Mark Yim

Mark Yim

Professor, Mechanical Engineering and Applied Mechanics University of Pennsylvania

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.