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https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-...
How to Prove It: A Structured Approach by Velleman. New edition came out in 2019. It appears to be aimed at your level, and pricewise isn't too bad.
So really any math text appropriate to your level will work.
Take a real, formal class. You really can't self-study in my experience. I highly recommend the Harvard Extension School math 23 sequence.
And it actually tries to teach you rather than documenting math knowledge or impressing peers.
I highly recommend it.
Take a real, formal class. You really can't self-study in my experience. I highly recommend the Harvard Extension School math 23 sequence.
It's unfortunate that each course is over a thousand USD.
Earlier quoted context omitted.
It's unfortunate that each course is over a thousand USD.
It's a serious undergrad class with very accessible TAs, lots of resources. My experience there was orders of magnitude better than taking courses at my local public university. For proof-writing you really need an experienced human to be reviewing your work because the mistakes can be very subtle -- you'd never catch them by yourself.
I can second "Proofs from the Book", but would advise against it unless you're already comfortable with the basics of linear algebra and perhaps some analysis. For a total beginner there is no better choice than Steward and Tall's "The Foundations of Mathematics", an incredibly readable guide which takes you from high-school calculus through a good portion of intro analysis and algebra. Reading this and doing the exe…
Does The Foundations of Mathematics focus on performing calculations, or does it have proofs as well? I feel like I'm in a hard place because I'm not a total beginner; I've taken calculus I and II, some discrete math, and I'm fine with the basics of algebraic manipulations. But I need something to bridge the gap between calculation and proving theorems. As I mentioned in the original post, Linear Algebra Done Right i…