At the REU I’m at, we listen to daily lectures. The current topic is “geometry of polynomials,” by Sergei Tabachnikov; it will continue for two weeks. I’ve been live-TeXing notes in class.

It’s not something I anticipated doing—after all, typing is slower, right? I find that’s not really the case. First, out of concerns of laziness efficiency, I always predefine macros (e.g. \e = \mathbb) in my source files that reduce the amount of typing.  Second, since this is a talk, there are pauses in the mathematical exposition that allow one to catch up. (I actually fall behind very rarely–even though I run pdflatex and scan the output every now and then.*)  The most serious problem is that this is a geometry course. I may try whipping out an image editor and trying to copy down the various diagrams (and insert them as figures into the document later).  But it’d be hard to keep up when there are so many figures, as seems to be the case in this course—and it’ll likely be even harder in the next course (“fractal geometry and dynamics”).

But, on balance, I think I’m pretty sold on live-TeXing.  Mostly because my handwriting is awful, and I’m really bad at keeping organized sheaves of papers.  By contrast, LaTeX output is pretty and computer files don’t (usually) vanish.  I recommend it to others, as well as this post of Chris Schommer-Pries.

So, without further pontification, here are my notes from the past two days.

*On the subject, I definitely recommend using evince as a PDF viewer–it has the nice property of being able to update the document automatically without your having to close and reopen it.

The book Real and Complex Analysis, by Christopher Apelian and Steve Surace, was recently released.

It’s mainly for an introductory upper-level undergraduate course in real and complex analysis, especially at small liberal-arts colleges.  In this post, I’ll describe this book and how I was involved in its production.

At the start of my freshman year, my analysis teacher, Professor Surace, asked me to check over the drafts of a book he and his colleague (and my former teacher) Prof. Apelian were working on. It was the textbook for the course. At the time, if I remember correctly, there were six chapters: on the real and complex spaces, basic topology, limits, continuity, convergence of functions, and derivatives. The complex analysis part of the book was in its infancy (e.g., there was only a rudimentary outline of one chapter, which had been written some time back and was typeset in Word—they wrote it well before before they had switched to LaTeX).

Anyway, since one of my hobbies that year was playing around with LaTeX and trying to figure out all the cool formatting tricks used in books, and since they hadn’t yet done much to change the (somewhat bland) default book style, I pointed out a few tweaks that, in my opinion, would make it look better. They agreed, and I ended up being put in charge of the layout. It turned out that I would need to learn a lot more about LaTeX though (or at least, learn to look up things a lot more). As you can see from the sample pages, the authors—or to be precise, one of them :-)—had fairly detailed ideas of how the book should appear. I don’t know if I learned LaTeX properly, but I sure learned a lot of hacks.

I also ended up sketching the figures, which enabled me to pick up the useful (and definitely nontrivial) skill of using Adobe Illustrator. In fact, I’ve used it in making some of these blog posts.  (Though I would recommend interested passers-by also to consider, say, Tikz depending on your aims; I’m not familiar with it, but it has the benefit of being free.) (more…)