Thursday, October 26, 2023

Word Clouds of ADS Chapters

 I'm teaching the second semester of our Discrete Structures sequence and gave a quiz simply asking students to define group.  The results were not so good.  The emphasize how important it is to know this and other definitions, I decided to construct a word cloud of Chapter 11, which is an introduction to Algebraic Structures, mostly groups.   

My first attempt - just asking Mathematica to construct a word cloud of the text -  was not satisfactory since all the non-math words got in the way, although group was still prominent.  My solution was to take the index of the book and generate a list of the words in it.   Then I selected from the text only those words that appear in the index, keeping duplicates.  The result is pretty good.  I did the same for the chapter on graphs, Chapter 9.

Word Cloud for Chapter 11

Word Cloud for Chapter 9

One benefit of doing this is that I could catch words that should be in the index that are missing. One word I expected in the graph cloud was edge.  It was totally missing because I had neglected to include it in the index - something that I'm going to fix!

Thursday, October 5, 2023

Applied Discrete Structures now available on LibreTexts!

Without having to ask me, the LibreTexts project has adopted Applied Discrete Structures (ADS) to their library!  Don't get me wrong - the point to making ADS an OER project is to make it available to as many instructors and students as possible at no cost. So I'm delighted that they've added the project.  

I was unfamiliar with LibreTexts until now. Understandable because its a relatively new project.  It started with Chemistry content but has since branched in to other sciences, mathematics, engineering and more.

For a good introduction to LibreTexts check out this video from LibreFest 2023

Applied Discrete Structures is still available in other form factors at

Saturday, August 12, 2023

New: Applied Discrete Structures is on Runestone Acadamy

Applied Discrete Structures is now available on
Runestone Academy. To access it, go to the Runestone Library Mathematics list

 At this point the book doesn’t have reading questions so the fully capabilities of Runestone are  not being fully utilized.  By 2024, I’m hoping to have added a pool of reading questions for most sections. This will allow students to test their reading comprehension in a low-stakes environment. Instructors can incentivize students’ reading by grading completion of reading assignments. Currently, a record is only kept of which sections of the book have been opened by each student. 

Applied Discrete Structures is still available in other form factors at

Friday, May 26, 2023

Version 3.10 of Applied Discrete Structures - May 2023

 The new version of Applied Discrete Structures has been released in all but the print version. The two most significant changes in this version are 

  • Equivalence classes are now defined within the text (Section 6.3) as opposed to being introduced in an exercise.
  • A glossary. Many of the words in this glossary are not formally defined in the book either because they are viewed as prerequisites to a course in discrete mathematics or are terms in computer science that some students may be unfamiliar with.
The usual minor typos have been corrected and a few exercises have been added or revised. 

The html and pdf versions are available now at  

The print version will be available later this summer. It’s available roughly at cost, but prices have been inching up in recent years.  Last year the full version was $43+shipping.  Seems high to me, but still not as bad as many of the prices for books offered by publishers. As expected, sales have also dropped. No big deal - the print form factor exists mostly to qualify the book for a few OER listings that require it.

Friday, October 14, 2022

A new matrix multiplication record

In Chapter 5, we mentioned Strassen’s algorithm for matrix multiplication. Not many improvements have been made since 1969 when Strassen discovered how to multiply a \pair of 4 by 4 matrices with 49 multiplications - a reduction of 15 multiplications from the  basic definition. A further reduction by one multiplication was announced by two Austrian researchers at Johannes Kepler University Linz in October 2022.