The end of 2025 was busy. I moved out of my home on my birthday, and from Vietnam back to Indonesia. In the last month I’ve moved through Bali, Surabaya, and back to Jogja. There’s a story behind that, but not one I’ll tell here. During that time I did my best to maintain my studies chipping away at my business sculpture. 2025 came to an end before I knew it, and went.
Somewhere in there I studied Polar Vectors, Polar Equations, and Calculus with Polar Equations. Many of the exercises I started in on quickly revealed themselves to be more dastardly taxing algebra problems. Given my time constraints, I ultimately let my foot off the gas and coasted across the finish line, “closing” the Calculus 2 book a few days before the end of 2025.
Rather than recount all I learned in Calculus 2, knowing full well I’d fall short, I’m opting for this, whatever it turns out to be.
Calculus 2 took me the better part of 5 months to complete. I could have done it in less, but I felt more comfortable putting in extra time to work through problems until I felt comfortable that I wasn’t doing myself a disservice by speeding through. There is soooo much material in Calculus 2, that at times it seemed like disparate courses squeezed into one. No singular concept stands out as really being more difficult to cogitate than the rest. It was just so much material that I felt like some concepts were slipping out of my ears while I tried to cram others in through my eyes.
I studied 3 hours a day, religiously (well, almost). In the end, I was always able to succeed in the exercises, moving forward enervated by my new discoveries. Without a doubt, there were many times I needed reminding how to perform some technique or concept – does anyone really remember all that stuff? But it’s in there. I’m sure I’ll need reminding again moving forward. Gauss I am not. I’m a simple hominid, and I will struggle from time to time (or often), but I’ll persist my way to success. I don’t remember the last time I focused for this long or channeled this much energy into one singular study. Calculus 2 was transformative. I went in a neophyte with surface level understanding of differentiation, and came out the other end a neophyte with a deeper understanding of how much I really don’t know, and how much more I want to learn.
I loved Calculus 2. Getting up and watching the lectures on a new concept, and digging in to problem sets, these were such a spectacular way to start my day. In fact, so much did I love this learning, that at times I felt I’d like to just dedicate the next few years to studying math….who knows, while I’m still breathing, much is possible. I want to extend a special thanks to Professor Leonard for being such a superb teacher and for making his classes available. You have played a special role in lighting a new fire of interest in my life. And I look forward to seeing you again when I come to Calculus 3.
A week ago I began studying Linear Algebra. There are many who say Calculus 3 should precede Linear Algebra, some who say Linear Algebra should come first, and others still who advise studying them both concurrently. I chose Linear Algebra because I was interested to see what it’s all about. I don’t think there can be a wrong way to learn. I’m confident that if I put in the time, consistently, that my brain will take care of the learning. There will always be gaps to fill, and interests to sate. So, for now I’m happy with my decision.
I’m following MIT’s OpenCourseWare 18.06 Linear Algebra with Professor Gilbert Strang. The course is broken into 3 main units, with units divided into sections. Each section has a lecture by Professor Strang, followed by reading in Strang’s Linear Algebra textbook, followed by a recorded recitation in which you follow along with a MIT instructor solving a problem, and then tackle problem sets to culminate the unit.
Strang’s textbook has many problem sets, but no key. Consequently, I’m complementing my studies with “Schaum’s Outlines” by Seymour Lipschutz and Marc Lipson. This is a great book because it has exercises with answers and rationale. So, between this and my trusty AI oracle, I’m set.
The first two sections of the OCW were Geometry of Linear Equations and Overview of Key Ideas. Here equations in their various forms (row, columnar, and matrices) are introduced, as are vectors and their geometric representations. This felt like a preface to the course, so I’ve decided not to report on it. I’m now dug in to Elimination with Matrices, and am taking my time to chew it and digest, savoring the flavor of new math. When I finish this section, I’ll return to write my first, real Linear Algebra blog.
Two days ago Bob Weir, of the Grateful Dead, died. With his passing, only the percussion remain of the original Dead lineup. I have long been a Grateful Dead fan. I experienced the pang of grief in the final closure of the band, and in the passing of time. Oddly, Bob Weir’s death, Linear Algebra, and the call to prayer over Sleman meld into one, right here …
Truckin’, like the do-dah man
Once told me “You’ve got to play your hand”
Sometimes the cards ain’t worth a dime
If you don’t lay ’em down
Sometimes the light’s all shinin’ on me
Other times I can barely see
Lately it occurs to me
What a long, strange trip it’s been
I’m layin’ ‘em down, I’m playing. It’s been a long, strange trip, indeed. And a long, strange trip is still to come, I’m sure. This E Matrix is for you, Bobby – Keep on truckin!