I’m doing TA-work for a maths course; it’s about (redacted).

It has a course book, too: “(redacted)” by (what do you mean he’s still alive and has a home page?); an old bound typewriter-written compilation of lecture notes from the University of Helsinki.

Reading that book is like being hit with two-by-fours.

In the head.

*From the inside.*

With no reason given, or any emotion expressed; none at all. Just, suddenly, two-by-fours, wham! In the head.

What I mean by that is, the book is only a hundred smallish pages long. The course follows it pretty closely, and lasts this semester.

It seems likely there will be things left out of the course.

The book is so damned dense and no-nonsense it’s almost zen. And the part we’re in right now is fast approaching a perfect union of horrendously convoluted nitpickery and soul-crushingly protracted tedium. It’s the academic equivalent of the Bataan Death March. (And oh yeah personal opinion not representing the university and so on.) I’m not blaming the writer, because the tedious things are exactly the ones you should get to understand on such a level you can quickly bypass them later; but it’s not pretty.

Other than that, it’s a nice course with a good lecturer and bright young uns; and of course a maniac TA; but dear empty heavens the book’s written for bald professor types that spend their days on a mountaintop with gradients on their mind, ingesting pure caffeine, extruding perfectly formed lemmata in small brown nodules, and getting balder and chalkier day by day. Not that I’m saying things should be written in a different way, because if you soft-pedal mathematics you lose rigor; and once you do it’s in one emeritus’s words “swordfights and other anecdotes” instead of the really interesting axiomatical thingamajics; but one has to gripe now and then, right?

(A quick turn around, and a final gripe: The popularization of mathematics, and equations. If you ask me, popularizing mathematics while avoiding equations and lines of formulas is a bit like learning to read without using letters. I suspect one reason the old Egyptians never really got on with their mathematics was they had to write everything down in long, mundane sentences; that’s no way to do mathematics. Mathematical matters need more detail, rigor and brevity than these monkey languages of ours have. Then again, the Hawking anecdote was “the sales will drop to a half for each equation, so I included just one” — hard to see what a mathematician can do when faced with that, except experience a gibbering loss of composure.)

October 5, 2010 at 0:11

I strongly disagree that this is the way maths should be. A bevy of examples; explaining the key ideas and motivation of an argument or even proving special cases before diving into the body of it; clear and explicit notation; structuring proofs so that each step follows from the last intuitively as well as logically; explanations of how the more technical results are most often used; historical context to pad out the denser sections; and if all else fails diagrams. All these things can make almost any maths book (or paper) far easier and more pleasant to read without sacrificing rigor in the slightest.

Yes, the tedious parts need to be covered and covered thoroughly – that doesn’t mean they have to be covered as painfully as possible.