In my “intro-to-proofs” class, I like to have my students work on some induction problems that are not the usual proof of sums and products of integers. One lovely example is the following problem about tiling a grid with “trominoes” (three squares joined in an el-shape). Prove that for any n ≥ 1, a 2nx2n grid with…
Category: Academic Technology
Type Math on a Mac—Remapping My Keyboard
I use LaTeX to type mathematical documents. However, I often want to type mathematics when LaTeX is unavailable—for instance, in an email to a student, in a social media post, etc. To do so, I typically go to one of the many websites that offer “copy-and-paste” mathematical symbols, Greek letters, or subscript/superscripts. It is do-able…
Make a “Magic Eye” image using Excel
I’ve been on a weird kick lately making images using Excel. [Here’s one post. I hope to post more soon.] If you add a background color to each cell in a spreadsheet and resize the cell widths to make each one square, then you can zoom out so that each cell acts like a pixel…
Making the Mandelbrot Set with Excel
The Mandelbrot set is one of the most stunning geometric objects in all of mathematics. In this blog post, I will show how to generate the Mandelbrot set below using Excel. It is also an example of how you can use AI (I used ChatGPT) to help with a task like this. (Here is the…
Math class technology policy: Fall 2023 edition
I decided to address the use of technology—especially generative AI and large language models like ChatGPT and Bard—in the syllabi for my classes this fall. Here’s the current draft of my technology policy for my upcoming calculus classes. If you have thoughts or observations, leave them in the comments below. Also, feel free to copy,…
My Two-Day Crash Course in PGFPlots and TikZ
I will be teaching multivariable calculus in the fall. During the semester, I’ll have to make numerous figures in two-and three-dimensional space for exams and handouts. One of the things I wanted to do this summer was to learn how to use TikZ to create graphs and other graphics in my LaTeX documents. After a…
Undergraduate Math Bloggers
I was interested seeing how undergraduate math students used blogs (and related platforms, like Tumblr). So I posted a call on Google+ and Twitter: I'm looking for mathematics blogs written by undergraduate students. Any recommendations? I'll retweet/repost them as they come in. — Dave Richeson (@divbyzero) February 17, 2014 I received quite a few links. I’m looking…
Countability of the rationals drawn using TikZ
I’m continuing my exploration of TikZ (here is my first post about TikZ). I will be showing my Discrete Math class how to “count” the positive rational numbers. (See this old blog post for more information about countable sets.) I used TikZ to create the picture below. Here is the source code for this figure. If you click…
Bubble diagrams for functions in LaTeX using TikZ
I am teaching Discrete Math this semester (our intro-to-proof course). One of the topics is functions. Not surprisingly my students and I have to draw “bubble diagrams” for functions between finite sets—and we have to include them in LaTeX documents. Rather than simply sketching them in Adobe Illustrator and importing them as graphics, I decided…
Online LaTeX editors
For the last 10+ years I’ve taught topology using a modified Moore method, also known as inquiry-based learning (IBL). The students are given the skeleton of a textbook; then they must prove all the theorems and solve all of the problems. They are forbidden from looking at outside sources. The class types up their work as…
David Richeson: Division by Zero 