Designing On-Screen Versions of Mathematics Texts?

Help 1?
I have redesigned the on-screen versions of our real analysis textbooks. They are here
if you want to download them. BBT is the graduate level real analysis, TBB is the undergraduate level real analysis and TBB-Dripped is ...well something else.

Open one of these in Adobe Reader, resize the reader, resize the fonts, and open the bookmarks. Is this design workable on your screen? Pick your favorite real analysis topic, look it up in the index, click to see the text and scan a couple of pages. Any suggestions?

Help 2?
Specifically, does anyone know how to work around the fact the the LaTeX packages endnote and hyperref ignore each other? That is one of the bugs in my on-screen version. SEE NOTE in yellow doesn't link forward to the hint in the NOTES. I do have a link back though.

Help 3?
We are working on a PRINT-ON-DEMAND service for all three of these titles. Does anyone have stories, good or bad, to relate about CreateSpace, the new Amazon.com service?

[Some students in a class in the midwest used the on-screen versions for their assigned text, but most ended up finding used copies anyway. So, if this is a common reaction, we are trying to supply inexpensive trade paperback copies. Or, perhaps, we just needed a better on-screen version.]


The texts here are Elementary Real Analysis and Real Analysis by Bruckner, Bruckner and Thomson, previously published by Prentice Hall (Pearson) in 2001 and 1997. Full versions of these texts (recently corrected) are available as free downloads.

COVER DESIGN (cont. again)?

This one is a little more conservative. Very elegant, but I think I prefer the other two.

COVER DESIGN (cont.)?

I think this one is my favorite though. Anyone have an opinion that you would like to share?

COVER DESIGN?

We are currently selecting our cover designs for the trade paperback copy of Elementary Real Analysis.

Anybody like this one?

[I am negotiating with my colleagues to correct the spelling of my name.]

OLD EXAMINATIONS AND ASSIGNMENTS

I have posted some old examinations and homework assignments for courses in Elementary Real Analysis that I taught in the past. You can download them directly from here

[Download now]

or you can find them on the DOWNLOAD page of our website

http://classicalrealanalysis.com/download.aspx

There is a lot of material, with a high level of redundancy. If you are a student of real analysis at the undergraduate level it might be useful to try some of the examinations as part of your review. Any instructor who wishes to steal any of this material for their own use should likely ask for the LaTeX source file from me, since that will be a lot easier to pilfer from.

Top Ten Reasons for Dumping the Riemann Integral #9.

#9. Does the phrase "mildly interesting exercise" suggest anything?


The quoted remark is from Jean Dieudonne, the French mathematician and well known Bourbakiste, in his dismissal of the Riemann integral as a suitable object of study for undergraduate mathematicians.

Actually I find the history itself more than mildly interesting and, with your indulgence, will give a fractured account of it here. What happened to Riemann follows a pattern that I can describe this way:

Suppose that you (Jones) discover an old theorem of Smith that you think you can improve on.

Theorem [Smith] Every object Y has the property Z.

You (Jones) decide that it might be worthwhile to characterize this property Z, especially since Smith seems to have gotten some fame from it. You succeed and write it up like this:

Definition [Jones] We say that any object possessing the property Z is a zamboni.

Theorem [Jones] A necessary and sufficient condition for an object to be
a zamboni is [insert your characterization].

Corollary [Smith] Every object Y is a zamboni.

Thus you (Jones) have, with a stroke of the pen, transformed Smith's theorem into a trivial corollary of Jone's theorem.

The success of Jone's manoever here is whether zambonis are going to have any lasting interest. If they do and prove to be a significant concept, then your fame exceeds Smith's, even though Smith had the original insight. If zambonis fall flat on the mathematical world then move on to something else.

Well, Riemann's zamboni is his integral. He took a theorem of Cauchy asserting that every continuous function on a compact interval [a,b] had a certain property with regard to its integral. He then characterized that property and gave it a name. Hence the definition of the Riemann integral, Riemann's characterization of integrability, and Cauchy's theorem dropping down to the status of a corollary. In fact the sums that Cauchy had used are now called "Riemann sums," so history has taken all the credit from Cauchy and shifted it to Riemann.

Well Riemann doesn't need that credit since he did far better things. Even the Riemann integral was just a throwaway in a 1854 paper about trigonometric series and not anything that he likely spent too much time thinking about. If he had seriously directed his enormous intellect at the problem of integration itself he would certainly have discovered the correct integral.

Unfortunately for Riemann, however, is the fact that this particular zamboni was misguided. Certainly it is a worthwhile professional project to characterize the property that Cauchy had discovered, but it was a sad mistake that future generations employed Riemann's integral as the central tool of integration theory.

For the next fifty years or so (1854--1901) mathematicians took Riemann's integral as if it were the correct one for bounded functions, and spent their time on the problem of integrating unbounded functions. Perhaps they thought of their program as "extending the integral to unbounded functions." Too bad. If you look at the problem this way you fail. If, instead, you tackle the problem of how best to integrate bounded functions, then the unbounded case takes care of itself. Enter the 20th century and Lebesgue. Lebesgue's thesis swept away all the previous theories.

At that point the history gets a bit strange. Lebesgue's theory is considered too difficult for some to learn and for many to teach. So many did not teach it, and many did not learn it. In the last 100 years there have developed many different ways to teach integration theory, some not any more difficult than teaching the Riemann integral itself. But, even so, we still don't teach it until graduate school at many places.

Google Base?

I put one of the textbooks up on GOOGLE BASE.

http://base.google.com/base/a/briansthomson/3109186/D4317767210028435757

Does anyone actually use GoogleBase?