Verified Certificate

Supported by the following organizations

This is to certify that João Afonso Azevedo Pereira da Silva successfully completed and received a passing grade in EC1011x: Principles of Economics with Calculus a course of study offered by CaltechX, an online learning initiative of Caltech.

Noted by

Antonio Rangel

Antonio Rangel

Bing Professor of Neuroscience, Behavioral Biology, and Economics California Institute of Technology

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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.