> Specifically, when learning a new field of math, the proofs sometimes don't feel rigorous to me right away, but once I get used to the the basics and the ling

> Specifically, when learning a new field of math, the proofs sometimes don't feel rigorous to me right away, but once I get used to the the basics and the linguistic conventions, I'm more able to fill in the holes in my head the most complicated proofs i ever dabbled in were things like proofs of convergence for algorithms, but i encountered various types of proofs in several intro courses: computability and theory of computation, discrete math, introduction to higher math and then some upper div cs courses in ai/ml. what you say here rings absolutely true to me. as someone coming in with a long time background in coding and computers, i always found myself wanting to apply the same unambiguousness and precision that one uses to express computations in a programming language in mathematical proofs. this was a huge stumbling block for me! proofs are written in shorthand (!) by humans for other humans who have the same base knowledge, obvious things are omitted. once you have that knowledge it makes sense, but before that it seems like giant leaps are being taken without a rigorous line of reasoning between them. to answer op's question: "an introduction to mathematical reasoning" by peter eccles was helpful for me. it's basically an expanded version of what you'll find at the start of many intro cs/math courses. another option, if sets, number theory and such are confusing to you is the computability angle (cs theory, computation). personally i found this material a lot easier to reason about which then imputed confidence, which is really the magic ingredient for good proofs.