Massachusetts Institute of Technology This is to certify that Homero Abrego Valle has successfully completed Thermodynamics of Materials Issued: Jan. 30, 2026
Rafael Jaramillo

Assistant Professor, Department of Materials Science and Engineering

Massachusetts Institute of Technology

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: 7ab59530-0228-407a-a190-1ea20531f08a

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