I've only read small amounts of this just to get a taster. My impression is that is readable, careful, and (so far) accurate.
It is readable enough that there is a danger that a reader might read it from cover to cover and believe that they now understand it all. But like programming, mathematics is not a spectator sport - you need to engage it in hand-to-hand contact to get the most out of it.
Reading a book about programming without trying to write programs leaves you with only a superficial understanding, and potentially no extra ability. However, reading a book about programming and writing programs is immensely valuable. And so it is with proofs, and mathematics in general.
So don't just idly read this book and believe you now understand proofs - engage with it. Try to find errors in it, do the exercises, go back and re-read - you will get more the second time through. And based on the quick dips I've had, it will be worth it.
I am planning on using "How to Prove it" by Daniel J. Velleman to prepare for Tom Apostol's Calculus Vol 1. How does "Book of Proof" compare to "How to Prove it" .
I read this book cover to cover and did all of the exercises earlier this year. I didn't take any upper math in college that involved proofs, and this book has really helped me get over my fear about it.
"Normal" math is usually not done using any formal logic at all. You can try, but you'll enter a world of pain regardless of the formal system you choose. Logic and foundational theories are designed to remain out of the way and relatively hidden. It's good to know that they're there, but you don't actually use them in the day-to-day (unless you decide that logic is your field of expertise, or you're interested in the sisyphean task of formalizing proofs).
"Book of Proof" is about basic objects in higher mathematics and writing proofs (as a human). There are only about 30 pages covering the basics of mathematical logic. So, I imagine Common Logic would not be very related to this book, since CL is much more advanced than the book's aims.
If you are referring to translating the book's theorems for an automated theorem prover, the book is not nearly pedantic enough to effectively do this from the ground up.
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It is readable enough that there is a danger that a reader might read it from cover to cover and believe that they now understand it all. But like programming, mathematics is not a spectator sport - you need to engage it in hand-to-hand contact to get the most out of it.
Reading a book about programming without trying to write programs leaves you with only a superficial understanding, and potentially no extra ability. However, reading a book about programming and writing programs is immensely valuable. And so it is with proofs, and mathematics in general.
So don't just idly read this book and believe you now understand proofs - engage with it. Try to find errors in it, do the exercises, go back and re-read - you will get more the second time through. And based on the quick dips I've had, it will be worth it.
Does anyone know how much of this "Book of Proof" would require re-write to handle Common Logic ?
If you are referring to translating the book's theorems for an automated theorem prover, the book is not nearly pedantic enough to effectively do this from the ground up.