Calculus Within
Def: A spiritual and mathematical exploration of change, drawing on what we all know within ourselves, and supported by poetry, literature, philosophy, and (of course) calculus.
I am typing this first draft of my intro from my rented apartment’s riverside patio in Brisbane..
…having hand written the draft from Little Cove in Noosa.
What. a. prick.
And also, how fucking1 lucky am I? I am wrapping up a two week trip to Australia, paid for by a conference for which I was a keynote speaker. This comes a semester after the factually worst semester of my career, capping off a hard few years. In Spring 2025, in the span of a few weeks my department chair told me that he no longer supported me to go up for promotion to full professor (even though I had in writing that my CV was strong and was on track for promotion a year earlier, and I was working my ass off with 5 papers published in 2024 and mentoring 5 grad students) and the US government illegally terminated my team’s grant because the abstract included the words “diversity, equity, and inclusion.” These two events cost me about $20,000, caused me to stop wearing mascara because I was sick of looking like a train wreck after crying at work, and shattered my ego. I questioned my worth, and had long moments of believing that this confirmed my imposter syndrome’s biggest fear: that I really had snuck in the backdoor of the math department and they had finally figured out I wasn’t actually good enough to be there.
These two events also really pissed me off. And, thank fuck, they changed me. They grew me up.
Some of the things that have changed through this: I stopped drinking alcohol, learned I have anxiety and ADHD, developed a much healthier relationship with work (I think), and somewhere in there2 decided to write this book: Calculus Within.
Calculus within has two meanings:
Calculus is well understood as a (mathematical) tool to understand change in our physical world (and this is how it was developed by Newton); in Calculus Within I articulate how it is also a tool for understanding change within our internal worlds.
I start each chapter by sharing how people have discussed our main ideas of calculus without (explicitly) using mathematics. I do this before bringing in the mathematics to emphasize that the concepts we develop in calculus are human ideas, and that we have an understanding of them independent of a mathematical understanding. In other words, we all have Calculus within us.
By bringing these perspectives together (our human understanding with our mathematical understanding) we can have a fuller, more internalized understanding overall. Can this help you study for a calc final? Maybe!? But, more so, I hope it will help you engage in the world as a full (and mathematical) human.
On this Substack, I am working out drafts and having a space to be accountable.
I would LOVE feedback, positive and negative, ideas, questions, clarifications, etc. I absolutely do NOT want anyone to feel like “it’s too mathy” and so they “just can’t get it.” If that feels true for you, then it’s because I didn’t (yet) explain it well. If there is a term I use or idea that keeps coming up that you feel like I need to explain before you can understand something I am talking about, please send me a comment. I’m not going to write them in the order I think they should go because I am starting where my head is at, and then will go back and forward from there. So, I will be grateful to know if there are more things I should bring in to make other things make more sense.
So far, I am planning to discuss:
variable
function
limit
continuity
differentiation
integration
and the Fundamental Theorem of Calculus, bringing it all together.
Yes, it will be mathy and I will relearn how to type in LaTex. It will also bring in spiritual prose and principles, literature, poetry, and some personal reflections.
We will think about calculus as the study of change, as both a process of change and as a product of change. Writing this is part of my process. Hopefully reading it3 is part of yours.
Sorry mama, but I learned my language from you. The ‘colorful’ language will be for Substack only, but it is helping me write and feel like a real person doing this instead of a person who is pretending to be a book author.
ok, I know exactly when it was; I was an a short run along the cliffs in Shell Beach, about to give a talk at Cal Poly SLO, listening to Golden from K-Pop Demon Hunters, because I have young kids and young friends and I love this song: No more hiding, I’ll be shinin’ like I’m born to be.
Substack is encouraging me to give details about how often I will post and what a subscription will mean. I have two young kids and I am working towards promotion still, because as much as I want to tell some folks to fuck off and that I don’t need their promotion, I also want to take my earned raise and my earned title and tell them to fuck off. So - this book is my five year goal, a project I am doing for myself in between my work as a (for now, associate) math professor, math ed researcher, mama to two amazing young ones. Between now and the end of 2030 (George Jetson and my youngest kiddo will both be 8) I hope to be done, and from then to now I will write and rewrite chapters, hopefully based on feedback from you, my currently very hypothetical and slightly intimidating subscribers. You feel like pretend but very important beings.