Wednesday, September 11, 2019

Logic Design & Boolean Algebra

The original 1980's version of Applied Discrete Structures had a section on Logic Design, but when I reworked the book starting around 10 years ago, I didn't include that section.  The main reason was that I never could find a good application for drawing gate diagrams.  I still haven't found one that is exactly what I want, but Inkscape comes close. I was able to draw some basic diagrams. Although I'm still not perfectly satisfied with what I have, I think they are good for a draft.

So after a delay of several years, here is a draft version of Section 13.7 A Brief Introduction to Switching Theory and Logic Design.  I developed it as single-section PreTeXt book, so the numbering is 1.1.x instead of 13.7.x.   I intend to add this to the next version of Applied Discrete Structures, in spring 2020.

I'd be interested in whether many users would plan on covering this section in their courses.

Friday, August 30, 2019

Professor Al Doerr Memorial Scholarship Fund

One October 14, 2018, Prof. Al Doerr passed away. He was coauthor of Applied Discrete Structures He was on the faculty at UMass Lowell for 50 years. In his honor, the Mathematical Sciences Department has established an endowed scholarship fund in his name. If you or your students want to thank us for the book, you could donate even a few dollars to the Prof. Alan Doerr Scholarship Fund at All proceeds go to a scholarship endowment for our math majors.

Wednesday, January 2, 2019

Appendix on Determinants

Determinator Comic:
from Courtney Gibbon's
Brown Sharpie (CC: BY-NC-NA)
In our original 1980's text, we had an 11 page appendix on determinants.  That was probably overkill since our inclusion of matrix diagonalization isn't really mainstream discrete math, but back then the exact content of a discrete math course wasn't so well defined.   When I revived Applied Discrete Structures, I never got around to converting the determinant appendix.  We still have diagonalization in chapter 12 and for completeness I've put together a more compact appendix.  Right now, a draft is available as a pdf at  

I haven't decided whether to integrate it into the text or just leave it as a supplement. I'm concerned that the full print version is getting a bit unwieldy.  I'm hoping to find a way to automatically exclude it from the print version but include it in the web version, where length isn't an issue. 

Wednesday, December 26, 2018

Disjoint Sets

Randall Munroe (XKCD) recently posted a funny example of  two disjoint sets.   I've used one of his webcomics, with permission, in Chapter 1 of Applied Discrete Structures, so I probably won't use this but wanted to acknowledge it.

Link to this comic on XKCD

Wednesday, September 12, 2018

New in Version 3.5 of Applied Discrete Structures

The latest version of Applied Discrete Structures (3.5) has a few differences from the previous version.  Here is a list of the most significant changes:

In exercises:
  • replaced 2.4 exercises 5 and 6 with lattice paths exercises
  • added exercise 6 to section 4.1
  • added bakery exercise at end of section 5.1
  • added exercise #11 to 11.4
  • exercise change 11.7 new #5, old #5 moved to #10
  • changed exercise 4 of 13.4

Also, there is a new section (12.6)  on  linear equations mod 2.