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: Teaching
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…
Essential Trigonometry for Calculus
My son is taking a calculus course in high school this year. While talking to him about his homework, I have come to realize that his knowledge of trigonometry is pretty weak. He said that they were supposed learn trigonometry last spring after the COVID-19 pandemic hit and school switched to fully online. Needless to…
How to Present a Mathematical Proof or Problem
There are many useful websites containing advice on how to give a good mathematics presentation (such as those listed here). But these are written for scholars who are giving lectures on their research. They focus on organizing the talk, putting the research in context, deciding what to include or not include, designing slides, pacing and…
Math Crafts: Salt Designs, Newton Snowflakes, Fractal Christmas Trees, Paper Pentagons, and Flip Books
I have had a crafty late fall and early winter. I’ve been good about posting my crafts on Twitter, but not so good at blogging about them. So, I’ve collected them all and will share them all here in one blog post. The Geometry of Salt I came across this neat pdf by Troy Jones…
Zip-Apart Möbius Bands
I’ve taught topology many times. One of the highlights for the students (and for me) is the investigation of the Möbius band—the one sided, one edged, non-orientable surface with boundary. On the day we introduce the Möbius band I bring many strips of paper, clear tape, and scissors and have the students make conjectures about what…
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…
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…
Editing mathematical writing
As I mentioned in a previous post, I’ve been assigning large-scale collaborative writing projects in my mathematics classes. I’ve had my topology students write a textbook for their class, and this semester I’ve been doing the same in my discrete mathematics class. As I mentioned in that post, the approach has been very successful, but…
David Richeson: Division by Zero 