Verified Certificate

Supported by the following organizations

This is to certify that Naphat Piphattanakarn successfully completed and received a passing grade in 15.071x: The Analytics Edge a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Allison O’Hair

Allison O’Hair

Lecturer in Management Stanford Graduate School of Business

Dimitris Bertsimas

Dimitris Bertsimas

Boeing Leaders for Global Operations Professor of Management, Operations Research and Statistics Co-Director of the Operations Research Center MIT Sloan School of Management

Krishna Rajagopal

Krishna Rajagopal

Dean for Digital Learning Massachusetts 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.