| There is a common category of misguided book review that the parent comment falls under: the reviewer has some particular things they are looking for from a book and fails to see that there are more uses for it than their own; so they generalize, reading the book's failures to meet their personal criteria as a failure intrinsic in the book's content, and mistakenly lambaste the work. > 19 pages of droning before you start with something concrete. One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. I can offer another perspective that what the author wrote on polynomials within the first 19 pages there is in fact pretty unique and interesting. > Imprecise definitions. This defeats the purpose of learning mathematics. The commenter is again taking a minority viewpoint and baselessly extending it. There is a special kind of paranoia that often manifests in discussions of mathematical pedagogy that any departure from perfect rigor will weaken the minds of students. This is a blatantly shallow and one-sided view of things: the fact that rigor has value does not imply that the most effective method of teaching—which is a matter of both mathematics and human psychology—is to offer nothing but the most rigorous presentation possible. This particular book is explicitly targeted at helping to transition programmers into mathematics. Given that goal, do you really think the pedagogically superior approach would be to offer a more rigorous definition of polynomial than: "A single variable polynomial with real coefficients is a function f that takes a real number as input, produces a real number as output, and has the form: f(x) = a0 + a1x + a2x^2 + ... + anx^n" —in the introductory chapter of the book? I would urge potential readers to take the parent comment with a grain of salt. And also, if you're among this book's target audience and trying to teach yourself mathematics, be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell, and are all too ready to belittle any alternatives perceived as softer/weaker. These aren't necessarily the most impressive programmers—they just project the most intimidating auras. Don't let their counterparts in mathematics scare you off. |
You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me.
You are very wrong on the other point: none of what I said is borne out of a view that mathematics should be difficult and "hard" an impenetrable (rather than soft and approachable). Indeed I view this sort of overlong prose as impenetrable and confusing, and the succinct style of e.g. Landau textbooks much clearer (see my other comment).
>The commenter is again taking a minority viewpoint and baselessly extending it.
This is not a minority viewpoint. I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head.
It is also plainly true: mathematics is about rigour. It is not an obstacle, nor is it an end in itself, but it is a fundamental part of mathematical study and reasoning. If you aren't being rigorous, you're not doing mathematics, it's just a waste of time. I'll let Michael Spivak speak for me:
"In addition to developing the students’ intuition [...], it is important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions."
>be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell
Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart), and again, not in the least bit what I mean with my criticism.