Massachusetts Institute of Technology This is to certify that Alp Jakop has successfully completed Microeconomics Issued: Dec. 19, 2025
Dimitris Bertsimas

Vice Provost for Open Learning

Associate Dean, Online Education and Artificial Intelligence

Boeing Professor of Operations Research

Massachusetts Institute of Technology

Valid Certificate ID: 0f3616a0-b952-4130-a998-893d2cc41a22

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