After being asked about it three different times in the last two weeks, Discover Calculus is listed on OER Commons (@oercommons.bsky.social): oercommons.org/courses/disc.... Hopefully this will make it easier for people to share, give feedback, etc.
Cover art for Discover Calculus. The background shows a plane flying over water in an arc. Reflected in the water is the plane and its arc but also diverging curves, rippling in the water. In the background is a bridge and some lights. The sky is dark with shining stars, a crescent moon, and beautiful clouds. The whole picture is a warm grey/brown with black hatch shading and white highlights. Discover Calculus Single-Variable Calculus Topics with Motivating Activities Peter Keep
It's here! @acidlich.bsky.social created this beautiful cover art, perfect as a representation of the book. While students will mostly be interacting with the book digitally, I'm very excited for the printed copies that we'll be making to give to students as well!
#MathSky 🧮
Here's a binomial-less version!
If you want to see more of what we're up to, here's how we'll move from thinking about the Power Rule for derivatives into thinking about derivatives of trig and exponential functions.
www.discovercalculus.com/web/sec-Deri...
Triangle with the binomial coefficients, ending with the row that begins 1, 8, 28, ... In each row, the first term (1) is red. The second number (1, 2, 3, 4, ..., 8) is red. The remaining numbers are blue.
Can you guess what we're talking about in class recently?
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Can I link your book in canvas or no? Yah, as like an extra resource for your class? Yeah. I showed a student the u-sub interactive and they asked if they could access it on their own. Thought I'd ask first
I got this very fun message the other day! I wrote this book for my own classes, but I'm happy to learn that it seems to be working for other people's students, too.
If you want to see the u-sub interactive, it's here:
www.discovercalculus.com/web/sec-uSub...
#MathSky 🧮
#ITeachMath
A page of one of the booklets with an activity titled "Activity 4.2.3 First Derivative Test Graphically." There is text and a picture of an interactive graph with a QR code beside it, linking to the interactive graph.
I've added links to every activity on Canvas, for those following along with a laptop or other device, and #PreTeXt automatically generates a QR code for any embedded interactive element.
A box full of spiral bound booklets. On top are two booklets, with covers that read "Discover Calculus I - Activity Book" and "Discover Calculus II - Activity Book."
It's "print shop pickup" day! Because this text is written in #PreTeXt, there are some pretty easy ways to automatically export and format activity booklets for Calculus I and Calculus II. These are what students will be working with in class all semester, and the full textbook will be online.
This was a great excuse to gather up some of the interesting problems for end-of-chapter "Explorations." Here's the Basel Problem Exploration, in case you'd like to check it out: www.discovercalculus.com/web/explore-...
I like this one because it's secretly about more than the reciprocal squares.
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Anyways, there are some more problems in here that are fun, and I'd like to keep adding more. This probably needs to take a backseat for now, though, since this project is coming up on some "end dates" (even though, of course, I'll keep adding to it).
It's a shame to leave the most fun mathematical thinking only to the few students that might pursue math further. Maybe including these Explorations at the end of most chapters in this book will remind me (and hopefully others) to give students the exciting problems so that they can love them too.
I think all of these Explorations should just be some way of thinking a bit more about something included in a standard calculus curriculum, but maybe from a slightly different perspective. And fun! The kinds of problems that got me hooked on mathematics because they're *fun* to think about.
This was a great excuse to gather up some of the interesting problems for end-of-chapter "Explorations." Here's the Basel Problem Exploration, in case you'd like to check it out: www.discovercalculus.com/web/explore-...
I like this one because it's secretly about more than the reciprocal squares.
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I probably *should* leave this until next semester, but I think I'll likely leave this as an end-of-chapter exploration, once we finish going over Taylor series. I'll try to remember to send it to you when it's ready!
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
Pixel book logo with links underneath: Home Read Online Other Downloads Instructor Resources On the right is the following text: Instructor Resources Python Demonstrations These python notebooks are hosted on Google Colab, with no python installations necessary. Each notebook demonstrates some concept from the text, and are suitable for in-class demonstrations or out-of-class explorations. These python notebooks have a mixture of pre-written code and text instructions and explanations, making them useful even without much (or any!) python background. Images and Animations There are many images and animations included in the text already, but several interesting relevant examples have not been included. These can still be used in classes for additional explanation or small deviations from the specific content in the text. Doenet Interactives Interactive Doenet elements are included throughout this text, whether in the activities or in the exposition between student explorations. Source code for all of these interactive elements can be found on the Doenet website. The source code for all of these can also be found in the Github repository for this text, but the Doenet website includes a free editor, making it easy to edit or copy any of these interactive elements.
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
Anyways, that was my small win for the semester, and I'm glad that this text was helpful to students.
If you want to see what they were up to, they were told to do these two activities:
1. www.discovercalculus.com/web/sec-FTOC...
2. www.discovercalculus.com/web/sec-FTOC...
Having these interactive activities has mainly been geared towards what to do in class, but I also hoped that they could be helpful for students who miss class or want to recreate the same kind of environment. It seems like it worked really well in this specific instance!
In class when we returned, about a third of the students told me about how they just kept reading and kept doing more of the "in-class" activities. They were excited about finishing the Fundamental Theorem of Calculus and learning what how to compute definite integrals.
Students were supposed to do two activities to build the first part of the Fundamental Theorem of Calculus. Then, I figured we'd construct the second part together, and not lose too much time.
Not only did most students actually do it, but many of them worked ahead!
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
Still lots to do compiling everything and updating the website, but we can celebrate for now!
It's done!
(For now)
A triangle on a unit circle, with standard lengths 1, sin(theta), and cos(theta). Another point is labeled on the unit circle. There is a triangle formed by the line connecting the two points, and then the vertical and horizontal components of the distance between the two points. The vertical distance is labeled sin(theta+Delta theta)-sin(theta) and the horizontal distance is labeled cos(theta)-cos(theta+Delta theta). The hypotenuse is labeled h, but it is very close to the same as the arclength between the two points, labeled Delta theta.
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.
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!
I think it's missing in a lot of early college courses, too! Students get the feeling (in calculus courses, at least) that math is more about computing things instead of exploring objects and their properties!
8.5 Alternating Series and Conditional Convergence Before we move too far forward, let’s circle back to a point made in Subsection 8.4.3 Why Do We Need These Conditions?. In the Integral Test, we required the terms of our series (and the continuous function we connected it with) to be positive. This was really just a mechanism that allowed us to say, in our proof, that the sequence of partial sums was monotonic. When we accumulate more of a positive thing, the total gets bigger. This is half of what we needed for us to employ the Monotone Convergence Theorem. Because this is such a useful tool, we’ll see more of this "positive term series" condition showing up in the tools we use to see if a series converges. But that makes this a perfect time to stop and ask a hallowed mathematical question: What happens if that property isn’t there? What happens when our series does not only have positive terms?
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
The third one is! The first two interactive ones are built using Doenet and the last one is just plain tikz.