I've only read small amounts of this just to get a taster. My impression is that is readable, careful, and (so far) accurate.<p>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.<p>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 <i>writing programs</i> is immensely valuable. And so it is with proofs, and mathematics in general.<p>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.
I'm interested in Common Logic (a form of First Order Logic that allows for some almost Second Order Logic activities)
(info at <a href="http://cl.tamu.edu/" rel="nofollow">http://cl.tamu.edu/</a> )<p>Does anyone know how much of this "Book of Proof" would require re-write to handle Common Logic ?
Great to see Virginia Commonwealth University(VCU) highlighted for something other than NCAA basketball. There are some real gems at this university that often times get overshadowed by the numerous other universities also residing in Virginia.
A good resource for books that are Free, including this one, is the American Institute of Mathematics <a href="http://aimath.org/textbooks/approved-textbooks/" rel="nofollow">http://aimath.org/textbooks/approved-textbooks/</a>.
This is a great resource! I would have loved to have had it in undergrad. I ended up reading a semi-expensive used copy of 100% Mathematical Proof by Rowan Garnier and John Taylor for my Abstract Algebra class.
Excellent book. The chapter on cardinality gives a well-written, clear treatment of this important concept (e.g. # of elements in countably vs. uncountably infinite sets).
Good explanations! As I recall this stuff is usually introduced as part of classes along the boundary between basic and higher math, so having a mini-book about it seems a bit unconventional -- but it's a really good idea. Nice straightforward presentation. Very readable.