Massachusetts Institute of Technology This is to certify that Takayuki Mashima has successfully completed Chemical Thermodynamics I: Thermodynamics and Statistical Mechanics Issued: Dec. 16, 2025
Adam P. Willard

Francis Wright Davis Professor of Chemistry

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: 6a7396dc-b0c8-40d0-85ba-c9d690f78651

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