The book that has served as the gatekeeper and the guide for decades is by Carl P. Simon and Lawrence Blume.
First published in 1994, it is often affectionately called "the bible" by Ph.D. students. But is it still relevant in 2024? Absolutely. Here is why. This is not a remedial high school algebra book. Simon & Blume target a specific audience: students entering intermediate micro/macro theory or graduate school who already know calculus but don’t know how to prove a theorem or solve a dynamic optimization problem.
Twenty years after its publication, no better textbook has replaced it for bridging the gap between "I know calculus" and "I can read Econometrica."
If you have ever taken a graduate-level economics course, or even a rigorous upper-division undergraduate course, you have likely heard the whispered warning: “You need to know your math.”