As you may recall, I am writing a math book, and I finally have more drafts ready for test-reading (just click here)! There are revised versions of the Preface and Chapter 0, as well as first drafts of Chapter 1 (Problem-Solving and Proof) and Chapter 2 (Numbers). As usual, any and all feedback is welcome!
By the way, the drafts are hosted on a new blog which I’m using for more academic/professional/mostly-computer-related things, in case anyone reading this is interested in that sort of thing too.
The Math Less Traveled 
Pingback: The Math Less Travelled « Vlorbik on Math Ed
so i printed out chapter 2 & read it last night
(i’ve looked at some of the rest on the screen).
some remarks.
i’m sure very pleased that you’re doing this;
at least *some* of my “102” students would
undoubtedly benefit *much more* from
a quick-and-dirty presentation like yours
than the ponderous bury-the-point style
of our textbook. also, i quite imagine
that your wiseguy writing style will generally
be found much more appealing than the textbook
i-am-a-committee-pretending-to-be-a-machine stuff.
p. 12 has “we’ll define exponentiation as repeated
mult. and see where …”: ugh. good style demands
that one use entire words; this isn’t a doggone memo.
the last line of p. 15 sez “Computer software
(e.g. or J)”. what’s this mean? typo, right?
i feel somewhat cheated by your treatment
of the real numbers. you’ve implicitly assumed
that *all numbers* live on the number line
(and so, again implicitly, that trichotomy applies)
in the crucial “problem 2.21”. the fact that the reals
are ordered by “
arg. ordered by “less than”.
the program ate everything
after the angle bracket.
damned if i’m gonna rewrite
the entire rest of my comment now.
complex #’s were mentioned.
also modular arithmetic.
also the induction proof of “2.4”
(shouldn’t this get more exposition?).
thanks for lots of good work so far.
ill be back.
Hi vlorbik,
Thanks much for the comments! I’m so sorry that half of them got eaten by WordPress (both for your sake and mine!) — it’s a known quirk that has caused me no end of grief. It hasn’t yet driven me to another blog platform but it just might.
The “mult.” actually IS part of a memo — a memo to myself that I forgot to replace with something more suitable! Thanks for pointing it out.
As for ordering of the reals and so on, of course there is always a difficult balance to be struck somewhere between a complete and logical treatment (which would be too long and miss the point) and too much intuitive hand-waving (which is, as you say, cheating). I will go back and consider harder what to include and what not to in the section on the reals.
Complex numbers and modular arithmetic I plan to talk about in other chapters, although perhaps it would be good to mention them in chapter 2.
Thanks again for the comments, and I look forward to hearing any more you might have!
I’ve only read part of Chapter 1, but since I’ll be on vacation before I can read more, I’ll give you the notes I have:
– On page 6, I imagine that parts like “to and .” are where you intend to insert words later, but I’m pointing it out in case some code got eaten without your notice.
– I feel that I must fault you for abuse of semicolons, such as at the top of page 6. Periods often work better to help readers in pacing, if you will. Try “It’s quite expensive, but there is a very generous discount for students.”
– Sometimes you use parentheses where none are needed. In high frequency, they upset the flow. I put up with frequent footnotes as a kind of signature style, but those are easy to skip. Try “It essentially acts like a very advanced calculator….”
– Footnote 9 is a little confusing: “a pedal-powered Wienermobile”? As opposed to what? Were you thinking of bicycle pedals rather than a gas pedal?
– What do the large stars mean? They do not appear after every problem.
@Steve: Thanks for the comments, I’ll look forward to receiving more.
re: page 6, I hadn’t noticed that, actually, thanks for pointing it out!
re: pedal-powered, of course I meant like bicycle pedals. Even cars are not powered by the gas pedal, they are powered by gas. Hmm… you really think that’s unclear?
The large stars indicate that a hint is available. It’s explained in the (revised) preface, which you understandably did not read a second time.