Practical Foundations of Mathematics

  "Even now, mathematics students are expected to learn complicated (e- d)-proofs in analysis with no help in understanding the logical structure of the arguments. Examiners fully deserve the garbage that they get in return."

Oh yes, speaking from personal experience, calculus professors are so guilty of that one - "oh, don't worry that you don't know formal logic, use your intuition", "let's fix our delta to be epsilon / ( 2 * (b-a) ). Don't worry, it will work out".

And more generally, many of the academics I know seem to be underestimating the inferential distance to their students not by one, but by a dozen or so degrees. And then they're surprised that 75% of the would-be computer scientists with questionable interest in formal mathematics fail. Surprised!

It's certainly not the only fallacy going around, but it can be surprisingly pervasive.

As for the book. I've only read a very small part of it, but if it does turn out to be a comprehensible description of the basics of mathematics - well, it's something that would benefit a lot of people if it gained mainstream attention.

tl;dr: Haven't read it but it's on top of my to-read stack. A slightly better version from the author's home page:

http://www.paultaylor.eu/~pt/prafm/

Firefox didn't pick up the proper encoding for the pages; it looks to be closer to MacRoman than anything else (View -> Character Encoding -> More Encodings -> West European -> Western (MacRoman)), but that's still leaving bizarre symbols in some places.