I am Alistair Forsyth, a high school senior at Urbana High School and an intern in the Calculus and Algebra group at Wolfram.
I have spent the last few months developing a new mini-course on Discrete Calculus for Wolfram-U with the guidance of Devendra Kapadia. As of right now, the first 5 videos are live on YouTube and there will be a new lesson coming every week until the end of the course. I would appreciate it if you could take a look at the Wolfram Calculus and Algebra YouTube channel and check out what we have so far!
An update to this: the next two videos have now been posted, focusing on the harmonic numbers and partitions, respectively.
I appreciate the constructive criticism a ton, it's helpful to have feedback on these kind of things. I agree that using some more graphical/visual examples would be helpful, as I'll be sure to keep that in mind in the future.
An update to this: videos 8, 9, and 10 have now been posted, focusing on the Bernoulli numbers, the Stirling numbers and techniques for sequence recognition, respectively.
The material was professionally presented. Great video and audio quality. You clearly had much preparation on the material and practice presenting it.
I found the speed of your speaking a bit fast; I would have liked to hear the material at about 80% of the speed you used. Also, I would have liked a couple of seconds of pause when you were going to change topics. Short breaks in the speaking could function as a cue to pause the video and think about a particular concept -- perhaps enter/explore the concepts in a Mathematica Notebook. The speed of speaking might be an issue for viewers who are not fluent in English.
I personally like to manually visualize/verify calculations; I'd like you to do that a big more frequently (but, of course, I can always do that on my own). The summation of 1/(2^k) is straightforward, but I'm not quite as fast doing the summation of 1/k!. After pause, I see how we immediately get to 5/2. Fascinating that the summation converges to e; it's the constant that won't quit! It was also great showing an example that graphically shows rectangles of integration that could be manipulated to slice with a finer/coarser granularity. In their 2022 Calculus with 3DP book, Joan Horvath and Rich Cameron note that traditional visualizations are the bane of some math students. That example could be used as a starting point for physically curve-fitting segments (with under a rubber band?) with a 3DP model. IDK if Wolfram U has considered physical models to supplement teaching of abstract concepts. Given the large support for them in the Language, it should be straightforward to do. Maybe optional exercises...
I love your reactions on certain examples. Sometimes, this stuff is fun, interesting, or just a bit strange. That's why videos and courses like this are a great path for learning. Thank you.