Massachusetts Institute of Technology This is to certify that Alexander Borochkin has successfully completed Vibrations and Waves Issued: Jan. 29, 2026
Yen-Jie Lee

Class of 1958 Career Development Associate Professor

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: 6693dd5d-6a3b-4793-ab6f-891b4a84fdcb

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