Discover Calculus
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discovercalculus.com
Discover Calculus
@discovercalculus.com
An open copyright, online textbook for single variable calculus with a discovery-based perspective from @mathprofpeter.bsky.social. We build the big ideas together through guided and interactive activities.

www.discovercalculus.com | (WIP)
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This book is free from any content generated from, built by, or influenced by Large Language Models and/or generative AI products.
Ok quick, is writing a "practice problem" that guides students through re-creating Euler's proof that the sum of reciprocal squares converges to π²/6 unhinged, yes or no?
#MathSky
#iTeachMath
November 24, 2025 at 4:02 AM
Even though the text itself is (mostly) finished, there are still lots of things to add! Textbooks *should* be good teaching and learning resources, so this one will have lots of extras to share with people to use (or change) as they want!

#MathSky 🧮
#iTeachMath
November 22, 2025 at 9:10 PM
Here's a cool proof-of-concept that happened recently. I missed some class time recently with conference travel, and instead of falling behind I sent some instructions to students on what to read about while we cancelled class. I figured I'd have to make it up in class still, like normal.
🧮 #MathSky
November 21, 2025 at 11:46 PM
It's done!
(For now)
October 31, 2025 at 3:53 PM
These triangles—used to demonstrate how to think about d/dθ sin(θ)=cos(θ) and d/dθ cos(θ)=-sin(θ)—are better than the other triangles—used to show the limit as θ→0 of sin(θ)/θ = 1, which you would then use to show d/dθ sin(θ)=cos(θ) and d/dθ cos(θ)=-sin(θ).

It's all about which triangles to show.
September 7, 2025 at 1:23 AM
I'm going to be giving a talk about accessibility, OER, and general updates on this project soon, and couldn't help but include this slide.

I'm going to also need to work in this statement in the quoted post about resisting LLMs and generative AI.

Should be fun!
July 24, 2025 at 5:49 PM
We should explicit about what mathematics *is*, even (especially?) in courses that are largely students not majoring in math. So we can (1) remind students why we impose conditions or restrictions for certain results and (2) explore removing those conditions or restrictions.
#MathSky 🧮
#iTeachMath
July 24, 2025 at 2:58 PM
Here are some of the kinds of visuals that I've been working on! You can see a mix of interactive plots (in the first 2 images) as well as images made to demonstrate some typical calculus tasks (the 3rd image) and some more generic figures describing processes (the last one).

#MathSky 🧮
#iTeachMath
July 3, 2025 at 9:54 PM
Students should know that definitions are choices, and these choices should come with both reasons for making them and an exploration of the consequences of those choices.
May 23, 2025 at 10:29 PM
I'm trying to build careful interactive elements for this book that will help students discover most of the ideas of calculus for themselves. Can you see how we'll bring this back around later on to discover the Fundamental Theorem of Calculus?
April 12, 2025 at 3:06 AM
This book is free from any content generated from, built by, or influenced by Large Language Models and/or generative AI products.
March 14, 2025 at 3:48 AM