Verified Certificate

Supported by the following organizations

This is to certify that Pranav Rajesh Krishnan successfully completed and received a passing grade in PUP01x: Pre-University Physics a course of study offered by DelftX, an online learning initiative of Delft University of Technology.

Noted by

Sander Otte

Sander Otte

Full Professor Quantum Nanoscience Delft University of Technology

Timon Idema

Timon Idema

Associate Professor Bionanoscience Delft University of Technology

Liedewij Laan

Liedewij Laan

Associate Professor Bionanoscience Delft University of Technology

Jeroen Kalkman

Jeroen Kalkman

Assistant Professor Imaging Physics Delft University of Technology

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

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.