Massachusetts Institute of Technology This is to certify that Olga Bartczak has successfully completed Calculus 1A: Differentiation Issued: Dec. 17, 2025
David Jerison

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: ea1987f0-55e0-42a9-b351-b1732eca7879

© 2026 Massachusetts Institute of Technology