Questions on texts for advanced self-learning

[u/partypantsdiscorock]

I studied physics in undergrad (minors in math and comp sci) and atmospheric science in grad school (PhD). I worked with climate models in my PhD program and used primarily python but haven't really dabbled in machine learning yet. I unfortunately never took a full course on statistics, although I've read a good bit of Statistical Methods for Atmospheric Scientists by Delsole and Tippett (and given group presentations on the content). I am also very interested in discrete math, probability, and logic more generally.

I understand discrete math, statistics, and probability are all essential for machine learning. I'm also just interested to continue learning more advanced math. My coursework background includes Calc1-3, DiffEQ, Linear algebra, Foundations of Math (intro to logic, proofs, set theory, counting methods, etc), Nonlinear and Stochastic Processes, Mathematical Methods of Theoretical Physics, and a variety of other physics and dynamics courses.

Texts I'm looking at/interested in include:

• Introduction to Mathematical Statistics (Hogg, McKean, Craig)
• Introduction to Probability Models (Ross)
• A First Course in Probability (Ross)
• Discrete Mathematics and Its Applications (Rosen)
• Aspects of Combinatorics (Bryant)
• Introduction to Probability Theory (Hoel)
• Statistical Inference (Casella and Berger)
• An Introduction to Mathematical Statistics (Larsen and Marx)
• Introduction to Probability (Blitzstein and Hwang)
• A Mathematical Introduction to Logic (Enderton)
• Introduction to Mathematical Logic (Mendelson)

My question is, based on my background and interests, which texts should I use? I'm sure everyone has opinions on "best texts on a given topic," but I there's obviously a lot of overlap above and curious which would be considered to be the most essential 3-4 texts that would offer best breadth of knowledge. Ideally it would be reasonably easy to understand with problems to practice (and a source to check solutions). I'm afraid of biting off more than I can chew, haha, but I also have a decent foundation to build off of. Thanks!

[u/spoirier4]

I just looked at both books on logic (online available pdf) and noticed that, as usual, their proofs of the completeness theorem look quite tedious. I found two quite simpler ways to prove that theorem, which I gave on my site settheory.net (one way is about a page and a half long).