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Yes and no, from what I understand he had a general solution for positive zeros or some other assumption like that and the way he wrote it down was more in words than symbols. The general case wasn't provided until the 16th century, but I think Descartes is responsible for the symbolic version of the formula we have today. I'm not 100% sure since a lot of the resources I read on this weren't very clear on who did what and I haven't had a lot of time to delve much deeper.

The professor of actuarial science that I work with uses game theory all the time as part of developing some of the premium pricing he models. He's why I included it as I am not an expert in actuarial science.

That's fair.

I think those would be subclasses of the topics that I listed rather than subjects themselves. You could argue that all those are included in the discrete math subject I listed first. But I agree that it's an ambiguous problem just how granular one goes to describe all types of math.

I'll be back in Fall 2025

This was all the parts I was planning to make. I will have a lot of new content in the new year though. I hope you'll tune in!

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Thanks!

That's certainly true of the term discrete. I guess it kind of depends on what you include under the umbrella of discrete mathematics. If set theory is part of discrete math, then some of that includes understanding uncountable sets. Also if you include logic in there, while the number of statements one uses is certainly countable, and even more commonly finite, the fact that the number of statements has a bijection to a countable set isn't really the point. And certainly one can make logical statements about continuous objects too. But I see your point, I mostly was trying to be as amenable to as many people's point of view as possible as to what is included.

Lol. I'm glad you liked it.

Yes that will be part 5.

Thanks!

It is definitely on my list of upcoming videos.

Thanks!

There's an ODEs one and a PDEs one. What part was the second PDEs one?

​@@scholarsauce I think 4:42 and 5:06

@@harrytaylor2479 I think it may feel that way because of the way I inflected that sentence. I was introducing the idea that many concepts in the sciences are described by partial differential equations. Listening to it, it does sound like the first introductory line of one of these, but it wasn't intended to be. Maybe I could have rephrased it as "Many functions in engineering and science happen are describe using partial differential equations..." or something like. Sorry for the confusion.

@scholarsauce makes sense. I'm keen to see what's coming next!

Oh man, that's a great one too. If anything having so many of these and missing some still just goes to show how much math there is. There are a few others I missed that I'll need to make a video of "Every type of math I missed..."

Thanks! That's much appreciated. I'm glad you enjoyed it.

Hey that's just how my kids respond!

That's an interesting idea and I like it. I've got a few other ideas in the works at the moment, but I'll think about this and see what could work. Thanks!

Thanks!

Not the heat equation, no. But Newton's law of cooling is an ordinary differential equation and is frequently taught as part of the single variable calculus sequence. Usually in the second semester.

@scholarsauce Right true, I misinterpreted it because the animation you added in that part of the video comes from the heat equation

That's fair. I thought about that when I used it too, couldn't find a good one for Newton's Law of Cooling and it was just a bit easier to use the same animation. Sorry for the confusion.

Lol! I looked it up and had to re-record it because I usually pronounced it See-lov.

@scholarsauce That's how I was taught too. I've been saying it wrong all these years then! (On a different note, I know operator algebra is technically a spin-off from functional analysis, but I've always related more with algebraists. Thoughts?)

Well, functional analysis in general is funky since it's doing linear algebra on something. Linear algebra is hard to place, is it algebra, is it geometry? Adding in functional analysis, is it analysis? Operator algebra seems to me to be channeling more of that vector space algebra vibe in the subject, so I can see how you would identify with algebraists. I do the same, but with the geometric side of linear algebra. I like the geometric aspects from functional analysis too. So it makes me get excited for things like dual spaces and the Riesz Representation when I teach linear algebra (even though not all textbooks in linear algebra call it the Riesz Representation outside of functional analysis) because of its connections to vector fields and one-forms in differential geometry. So I think you're just studying something that has deep connections to a lot of different things and you'll naturally be able to identify more with whatever flavor of it you happen to emphasize.

But Linear algebra is the queen with its myriad of concrete applications.

Thanks! I hope you enjoy part 2 as well!

Yeah someone else pointed that out. It's just a misread from my script. I tell this joke all the time and never mess it up, but put it on camera and you'll for sure not notice it until you post it on the Internet for everyone to see...🤣

But you are correct the joke is only half right now.

Thanks! I really appreciate that!

Yes, I would put it there. It's why you get a ton of different types of homological results in rings, modules, topologies, etc.