## An application of graph theory to architecture

Several years ago I came across a fascinating application of graph theory to architecture. It is in the 1983 book Incidence and symmetry in design and architecture, by Jenny A. Baglivo and Jack E. Graver. I don’t know if it is well known among experts in the field, but I’ve never seen it elsewhere. So…

## Using wikis in mathematics classes

Wikipedia describes a wiki as a website that allows the easy creation and editing of any number of interlinked web pages… [Wikis] are often used to create collaborative websites, to power community websites, for personal note taking, in corporate intranets, and in knowledge management systems. I have used wikis in three of my classes: two…

## Thoughts on teaching induction

I don’t plan on doing this very often, but I thought I’d re-post one of my earlier blog posts—one that I wrote a year ago, when I had many fewer readers. Now is an appropriate time for me to re-post it because I am currently teaching induction in my Discrete Mathematics course. Enjoy. In their…

## Is or an inclusive or or an exclusive or?

(That was a fun title to write!) At the start of our discrete mathematics course we talk about symbolic logic. Students are often confused by the logical operator “OR.” If p and q are statements then p OR q is true if either p is true or q is true or if both p and…

## The nuts and bolts of writing mathematics

This was a handout that I made for my Discrete Mathematics class. At our college this course is the gateway to the mathematics major and is the students’ introduction to writing mathematical arguments. Here is a pdf version of the text shown below. The nuts and bolts of writing mathematics “Mathematics must be written so that…

## Fallacies, Flaws, and Flimflam it’s been good to know ya

At the end of 2008 the College Mathematics Journal will stop running its 20-year column “Fallacies, Flaws, and Flimflam.” The column was devoted to “mistakes, fallacies, howlers, anomalies, and the like”—usually found on student work. In honor of the departure of this entertaining column I submit the following FFF which was submitted as a solution…

## Euathlus and Protagoras

In my Discrete Mathematics class we discussed a few famous paradoxes, such as Russell’s paradox/barber paradox/librarian paradox, the liar’s paradox, and the naming numbers paradox. Afterward, a student of mine shared with me this old legal paradox featuring Euathlus and Protagoras. Euathlus wanted to become a lawyer but could not pay Protagoras. Protagoras agreed to…

## Thoughts on how to teach induction

In their article “Some observations on teaching induction,” (MAA Focus, May/June 2008, pp. 9–10) Mary Flahive and John Lee give tips on how to teach induction. For a variety of reasons, they encourage professors to downplay proofs of theorems such as the “baby Gauss” formula for all . Indeed, I have noticed that students can…

## What is the difference between a theorem, a lemma, and a corollary?

I prepared the following handout for my Discrete Mathematics class (here’s a pdf version). Definition — a precise and unambiguous description of the meaning of a mathematical term.  It characterizes the meaning of a word by giving all the properties and only those properties that must be true. Theorem — a mathematical statement that is proved using rigorous mathematical reasoning.  In…

## The nuts and bolts of writing mathematics

This was a handout that I made for my Discrete Mathematics class.  At our college this course is the gateway to the mathematics major and is the students’ introduction to writing mathematical arguments. Here is a pdf of the handout. The nuts and bolts of writing mathematics You know that I write slowly. This is chiefly…