Supported by the following organizations
This is to certify that Sophia Espinosa successfully completed and received a passing grade in QMB1: Quantitative Methods for Biology a course of study offered by HarvardX, an online learning initiative of Harvard University.
Noted by
Michael Springer
Associate Professor of Systems Biology Harvard
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- Verified Certificate Issued November 3, 2025
- Valid Certificate ID c6642addc16642c2bdc9057abf81e69d