Reddit reviews Recursive Methods in Economic Dynamics

Romer's Advanced Macroeconomics is a pretty standard textbook that I bet you'll find in any future macro course you take. I think it's pretty clear and understandable.

For more mathematically heavy macro and Dynamic Stochastic General Equilibirum models, you should go for Ljunqvist & Sargent and/or Stokey, Lucas & Prescott. I know that at least in the former you have programming exercises and probably in the latter as well.

I think those are all very well known textbooks from very well known authors and they should fit what you're asking for.

Since you're a math major, go for Stokey Lucas. Strong overview, very finance focused.

Ljundqvist & Sargent alongside Stokey-Lucas-Prescott are pretty much the backbone of a PhD macro sequence, with SLP being a bit more technical out of those two. So something like Romer as a stepping stone is a good idea. This may be redundant, if your reference to Barro was Barro & Sala-i-Martin, but if not, then I highly recommend Economic Growth by - you guessed it - Barro and Sala-i-Martin, but of course that's growth models only. Having a good handle on RCK is, however, really useful moving on to L&S.

Many of the graduate level macro textbooks (e.g. SLP) are best read after getting some experience in mathematical analysis (at least one class at even a low level like that of Ross would probably make a huge difference in your comfort level with the material).

Romer's text is the first thing that comes to mind as something that is at a higher level than undergrad texts, but simple enough that someone well-versed in econ and differential equations can jump into without having a background in analysis.

If you're interested in autoreggresions, maybe a text on time series econometrics would be best.

A few others have mentioned Mas-Colell, Whinston, and Green's Microeconomic Theory. Personally, I would never recommend that someone read it as a first reference, but it is the most comprehensive book on microeconomics, and can serve as an excellent reference manual that can clarify concepts you come across in your other readings.

There are much better texts (though less comprehensive) than MWG that focus on specific subtopics of microeconomics, for example:

Contract Theory(covers Moral Hazards, Asymmetric Information, optimal wages etc)

General Equilibrium-Overlapping-Generations, optimal growth (covers micro-foundations of macroeconomic theory)

Primer on Game Theory

For macroeconomics, since you are from a Physics background, I would recommend Recursive Methods in Economic Dynamics.

Edit: One "popular" book I read that I found to be fairly decent on economic theory was "The Ascent of Money" by Niall Ferguson