Verified Certificate

Supported by the following organizations

This is to certify that Ralph Silva successfully completed and received a passing grade in 15.455x: Mathematical Methods for Quantitative Finance a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Paul F. Mende

Paul F. Mende

Senior Lecturer and Research Scientist Massachusetts Institute of Technology

Egor Matveyev

Egor Matveyev

Senior Lecturer Sloan School of Management Massachusetts Institute of Technology

Dimitris Bertsimas

Dimitris Bertsimas

Vice Provost for Open Learning Massachusetts Institute of Technology

Chris Capozzola

Chris Capozzola

Senior Associate Dean for Open Learning; Professor of History Massachusetts Institute of Technology

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About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.