Resources for young mathematicians

I have collected below some resources for aspiring and young mathematicians:

Advice to a Young Mathematician

Career advice from Terrence Tao

NSF CAREER Proposal Writing Tips

A particularly insightful comment from Prof. Michael Atiyah is "one could say that all the really creative aspects of mathematical research precede the proof stage."

Prospective and current UCSD Math graduate students should consult the UCSD Mathematics Graduate Handbook, which is full of useful practical advice.

Computational Geometric Mechanics at San Diego

The computational geometric mechanics group has relocated to the University of California, San Diego, where it is housed in the Department of Mathematics within the Division of Physical Sciences, and it is affiliated with the Center for Computational Mathematics, the Program in Computational Science, Mathematics, and Engineering, and the Cymer Center for Control Systems and Dynamics.

It focuses on developing a self-consistent discretization of geometry and mechanics to enable the systematic construction of geometric structure-preserving numerical schemes based on the approach of geometric mechanics, with a view towards obtaining more robust and accurate numerical implementations of feedback and optimal control laws arising from geometric control theory.