Now listed with the American Institute of Mathematics

Applied Discrete Structures is now listed among the Approved Textbooks by the American Institute of Mathematics as part of their Open Textbook Initiative.

The American Institute of Mathematics (AIM) seeks to encourage the adoption of open source mathematics textbooks. The AIM Editorial Board has developed evaluation criteria to identify open source books that are suitable for use in traditional university courses. The Editorial Board maintains a list of Approved Textbooks which have been judged to meet these criteria.

If you're looking for a text for a college/university mathematics course, consider books on this list!

Sage Trees

New Sage Worksheet: Trees

I was updating a few things in Chapter 10, Trees, and took the opportunity to do a few things with Sage. ADS2_Trees.sws

• Cataloging trees by degree sequence.
• Finding a minimal spanning tree using Kruskal's algorithm.
• The binary tree sorting algorithm

Actually, the last item only uses Python.

Video illustrating the construction of minimal spanning trees.

I've been tweeking Chapter 10 (Trees) and put together a short example of how to construct a minimal spanning tree for a weighted undirected graph.

---

Revised version of Chapter 6: Relations

A revised version of Chapter 6 is now available. It will become part of Version 2 of the larger pdf versions of Applied Discrete Structures in 2013. The most significant changes are:

• Hasse diagrams are not introduced until partial orderings are defined, avoiding some confusion that was reported with the original version of the chapter.
• Congrence modulo m has been added as an example of an equivalence relation on the integers.

Click here to get either a pdf or Mathematica Notebook of Chapter 6

Sage notebook on relations

I filled in for Al Doerr in his class this morning and he asked me to cover some material on relations. So I took that opportunity to figure out how to implement some relations in Sage. It went pretty well. One exception is that in squaring an adjacency matrix of a relation, I'd like to get a simple adjacency matrix with just 0's and 1's. The way I did the calculations, I got the numbers of different paths of length 2 connecting the vertices. That's fine except that the graphs of the squared relations become messy. If anyone knows how to fix this, I'd appreciate the help.

http://www.sagenb.org/home/pub/4715