Here’s a GeoGebra applet that I made for my Real Analysis class. It can be used to explore the definition of limit: Definition. The limit of as approaches is , or equivalently if for any there exists such that whenever , it follows that .
Author: Dave Richeson
The danger of false positives
As I mentioned earlier, I’m teaching a first-year seminar this semester called “Science or Nonsense?” On Monday and Wednesday this week we discussed some math/stats/numeracy topics. We talked about the Sally Clark murder trial, the prosecutor’s fallacy, the use of DNA testing in law enforcement, Simpson’s paradox, the danger of false positives, and the 2009…
A neat probability rule-of-thumb
Disclaimer: I am NOT a probabilist. Not only have I never taught probability, the last time I took a course in probability was in my sophomore year of college. So if this is well known (or totally wrong), forgive me. A non-mathematician friend of mine shared this link with me. It compares the lifetime risk of dying by various…
Advice for new college students
I’m teaching a first year seminar this semester. This isn’t a math course. (The title of my course is “Science or Nonsense?” We will look at a wide range of topics including the paranormal, evolution, climate change, the vaccine/autism controversy, alternative medicines, etc.) We are required to focus on academic writing, library research, oral communication,…
A quick guide to LaTeX
This semester I’ll be teaching real analysis. I am going to have the students type their homework in LaTeX. To make this as easy for them as possible, I will give them a template that is all ready for them to enter their solutions. They shouldn’t have to worry about headers, packages, font sizes, margins,…
Highlights from MathFest 2011
Last weekend I was in Lexingon, Kentucky for MathFest 2011. I had a very nice time and saw some very good talks. I thought, just for fun, that I’d share a couple of juicy mathematical tidbits I learned. Fibonacci numbers and the golden ratio Ed Burger of Williams College gave a talk entitled “Planting your…
The Japanese theorem for nonconvex polygons
A couple of years ago I wrote blog posts about two beautiful theorems from geometry: the so-called Japanese theorem and Carnot’s theorem. Today I finished a draft of a web article that looks at both of these theorems in more detail. It contains all that you could want—connections between these theorems, generalizations of them, and consequence of…
Some LaTeX odds and ends
Here are a few LaTeX tricks I’d like to share. None of them are earth-shattering, but maybe they’d be useful to some of you. (If you want to try these out, you can download this sample tex file and bib file that contains these tricks.) 1. I have always wanted LaTeX to support inline comments. In many…
Extreme examples and counterexamples
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…
Hankel on Diophantus
Diophantus of Alexandria was one of the last (c. 250 AD) great mathematicians of the Hellenistic period. He is often called the “father of algebra.” An entire branch of mathematics is named for him. It was in the margin of his book Arithmetica that Fermat penned his famous note. Today, while looking up some information on…
David Richeson: Division by Zero 