Carefully chosen rigorous course training provided me with a solid and broad foundation. In particular I endeavored to take all the compulsory courses required for math graduate students at Stanford and strived to meet the performance expectation on a math graduate student. This systematic education on mathematics cultivated my mathematical maturity and enabled me to serve as a "bridge" between physicists and mathematicians.
To prepare for the transition from atomic physics to condensed matter physics I leveraged the resources from both Berkeley (thanks to Aaron Szasz and Byungmin Kang) and Stanford. In particular I audited quite a few condensed matter physics and related courses offered at Berkeley and Stanford.