The best one right now is Proofs: A Long Form Textbooks by Jay Cummings. I wholeheartedly recommend it. And this is exactly the one you are looking for.
It is fully intended to teach learners how to write proofs, and not to impress one's peers or get citations.
I loved the book.
I picked it up because although I had a decent curriculum-based Maths education as a Physics undergrad and wrote many proofs, these proofs were always learned in a domain-dependent way. I was clueless about writing a new proof in a new domain.
This book filled a large hole in my life.
And I recommend it.
One other book that is good and should be read if you want to rigorously study Calculus from ground up, and it also teaches you a decent amount of Analysis, too. It's Spivak's Calculus. It's one of the best Math books ever written.
The best one right now is Proofs: A Long Form Textbooks by Jay Cummings. I wholeheartedly recommend it. And this is exactly the one you are looking for.
It is fully intended to teach learners how to write proofs, and not to impress one's peers or get citations.
I loved the book.
I picked it up because although I had a decent curriculum-based Maths education as a Physics undergrad and wrote many proofs, these proofs were always learned in a domain-dependent way. I was clueless about writing a new proof in a new domain.
This book filled a large hole in my life.
And I recommend it.
One other book that is good and should be read if you want to rigorously study Calculus from ground up, and it also teaches you a decent amount of Analysis, too. It's Spivak's Calculus. It's one of the best Math books ever written.