Verified Certificate

Supported by the following organizations

This is to certify that Arianna Quesada Ramírez successfully completed and received a passing grade in 3.012S.2x: Structure of Materials, Part 2: The Crystalline State a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Silvija Gradecak

Silvija Gradecak

Professor, Department of Materials Science and Engineering Massachusetts Institute of Technology

Krishna Rajagopal

Krishna Rajagopal

Dean for Digital Learning Massachusetts Institute of Technology

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.