Thanks to a recent PreTeXt development, all Preview Activities and Activities in both ACS2e and APC can be printed in PDF directly from the HTML version. For example, if you look at Activity 1.5.2 in ACS2e, you’ll see a printer … Continue reading →| Active Calculus
Over the past year, we have been busy working on what we plan to release as the 2nd edition of Active Calculus – Multivariable (ACM) in time for Fall 2026 classes. This post provides an update on our progress and … Continue reading →| Active Calculus
Several important changes are coming to Active Calculus (Single Variable) in time for the Fall 2025 semester, including a new Second Edition; at the same time, the current versions will remain fully available for the foreseeable future. If you are currently teaching with AC using the HTML at https://activecalculus.org/single/ and don’t want to make any changes, you won’t need to do anything other than update the link from which you access the HTML. The new, stable URL for the current vers...| Active Calculus
Let’s look at a nice little challenge: to find a cubic function with maximum and minimum at given locations – without using calculus. We’ll explore how to solve it with graphing software, and using algebra in a couple ways, and finally with calculus. And, surprise! They all give the same answer, though the results look …A Cubic Challenge Read More »| The Math Doctors
For over a century Chinese scientists have been puzzling over ancient human skulls that show pronounced brow ridges. Some assigned them to Homo, others to species that they believe were unique to C…| Earth-logs
I’m excited to announce a change in the layout of the workbooks for Active Calculus (Single) and Active Prelude. Thanks to some recent developments in the PreTeXt worksheet environment and especially thanks to Mitch Keller’s technical expertise and production genius, … Continue reading →| Active Calculus
As noted in an earlier post, at Mathfest in Tampa, Chrissy Safranski and I led a minicourse on teaching Active Calculus and using Runestone. We had a great time doing that and here I want to share a few updates … Continue reading →| Active Calculus
Normalising flows for PDE learning. Figure 1 Lipman et al. (2023) seems to be the origin point, extended by Kerrigan, Migliorini, and Smyth (2024) to function-valued PDEs. Figure 2: An illustration of our FFM method. The vector field (in black) transforms a noise sample drawn from a Gaussian process with a Matérn kernel (at ) to the function (at ) via solving a function space ODE. By sampling many such , we define a conditional path of measures approximately interpolating between and the f...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Diffusion models for PDE learning. Figure 1 Slightly confusing terminology, because we are using diffusion models to learn PDEs, but the PDEs themselves are often used to model diffusion processes. Also sometimes the diffusion models that do the modelling aren’t actually diffusive, but are based on Poisson flow generative models. Naming things is hell. 1 Classical diffusion models TBD 2 Poisson Flow generative models These are based on non-diffusive physics but also seem to be used to simu...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Figure 1 Placeholder. Levers for Biological Progress - by Niko McCarty In order for 50-100 years of biological progress to be condensed into 5-10 years of work, we’ll need to get much better at running experiments quickly and also collecting higher-quality datasets. This essay focuses on how we might do both, specifically for the cell. Though my focus in this essay is narrow — I don’t discuss bottlenecks in clinical trials, human disease, or animal testing — I hope others will take o...| The Dan MacKinlay stable of variably-well-consider’d enterprises
On BlueSky, Bryan Meyer asks: Henri, in your experience, what are the pros and cons of using function diagrams with kids (in addition to the more standard Cartesian representation)? My BlueSk…| Henri's Math Education Blog
Yesterday I was scheduled to teach my Calculus 2 class about the Second FTC at 10am, so of course I had a great idea for an activity at approximately 9:48am.| Spencer's blog
Materials and strategies I’ve used to create tactile images for people like me with limited sensitivity in their hands| Veroniiiica
My tips for using the free Brainfuse online tutoring service with low vision accessibility settings and assistive technology| Veroniiiica
Organizing math scratch paper and showing work can be challenging for students with low vision and dysgraphia- here are my favorite strategies| Veroniiiica
How I use Canvas as a student with low vision, including an overview of Canvas low vision accessibility features I used and what personally worked for me.| Veroniiiica
Change is logically possible because reality opposes itself.| 𝗗𝗔𝗥𝗞 𝗠𝗔𝗥𝗫𝗜𝗦𝗠
This week’s Fiddler is about a generalized notion of “radius”. For a circle with radius $r$, its area is $\pi r^2$ and its circumference is $2\pi r$. If you take the derivative of the area formula with respect to $r$, you get the circumference formula! Let’s define the term “differential radius.” The differential radius $r$ … Continue reading "When is a triangle like a circle?" The post When is a triangle like a circle? first appeared on Book Proofs.| Book Proofs
Given some f(x), what’s the taylor series of f(x)^p for some real p?| Toby Lam’s Blog
Last time we met, we found a Taylor series for the arctangent function, and we used the fact that π = 4 arctan(1) to find approximations to π. Unfortunately, this representation had really poor convergence behavior, because 1 is way the hell out at the edge of the interval of convergence for this series. I’m loath to abandon a fun trick, though; is there a way we can iterate on this idea?| Spencer’s blog
A fun thing to do at the end of a Calculus II class is to use Taylor series to compute values of various functions. For instance, I have a whole problem set about the “68-95-99.7” rule, where we find a Taylor series for the normal distribution and then integrate it. Here’s another fun application:| Spencer’s blog
If I ask you what shape an hourglass is, there is a very specific shape that leaps to mind. (Maybe there is also theme music.)| Spencer's blog
In this post, I’ll walk through the mathematical formalism of reverse-mode automatic differentiation (AD) and try to explain some simple implementation strategies for reverse-mode AD. Demo programs in Python and Rust are included.| rufflewind.com