I recently read this puzzle at the Futility Closet and it reminded me of a technique that I like to use to test conjectures (when possible). I don’t know if it has a name, so I’ll call it “looking for extreme examples and counterexamples.” I like this technique because when it works it is fast and…

# Tag: proofs

## 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…

## 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…

## Jenga mathematics

I like this: on his blog The Endeavor, John D. Cook draws an analogy between strengthening a theorem and the game Jenga. Jenga is a game where you start with a tower of wooden pegs and take turns removing pegs until someone makes the tower collapse… I use the phrase “Jenga mathematics” to refer to generalizing…

## 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…