Saturday, November 20, 2010


We are preparing a new book on Mathematical Discovery. It is intended for students with just the usual high school background in mathematics (algebra and geometry) who wish to learn how mathematicians discover new methods to attack problems. It is based on a course Andy Bruckner gave to students at UC Santa Barbara for non math majors, covering interesting topics that require less background preparation than the usual university-level courses would need.

There will be (as usual) FREE PDF FILES as well as a trade paperback version. The first chapter on Tilings discusses the famous problem of "squaring the rectangle," i.e., tiling a rectangle with a number of unequal sized squares. You can download this one now.

Friday, February 26, 2010

Riemann integral indeed?

For fans of this BLOG and the DRIP crusade (yea, both of you) it may appear that I have gone to the dark side since my two most recent papers are studies of properties of the Riemann integral:

  • B S Thomson, "Monotone convergence theorem for the Riemann integral", American Math Monthly, Vol. 117, no. 6, June-July 2010.
  • B S Thomson, "Characterizing the indefinite Riemann integral", Real Analysis Exchange, 2010 [to appear].

You can download preprints from here and here respectively. I hope you will (both) grant me absolution if I promise to return to a polemic on this unfortunate integral. Please write.