VICKY: My name is Vicky. I'm from Canada. I think I got a little overeager. I asked two questions, and now I'm not sure which one you're referring to. 

SPEAKER 1: I think you had a math question. 

VICKY: OK, yes. So my question was a little desperately worded. But it was, can you please promise me that all of these linear algebra, and discrete math, and calculus classes will come in handy in my future career? 

SPEAKER 1: Yeah, a common sentiment for the group. This was asked essentially in all capital letters, too. So let me turn to Brian, who's studied these topics most recently and also, I think, can speak to just how applicable they can be in some domains. 

BRIAN: Sure, well, thank you for that question. I definitely felt the same way when I was taking some of my linear algebra and calculus classes. I think ultimately whether or not it will come in handy will depend in part on what your career path is. But there are definitely areas within computer science where calculus, linear algebra, discrete math, where all of that becomes relevant, especially in the world of artificial intelligence and machine learning nowadays. 

So as you think about using calculus, you're doing it very abstractly to do things like how do you find the maximum point of a function. You could translate that into machine learning setting to how do you maximize the accuracy of your machine learning system. So a lot of the ideas that are taken from calculus and linear algebra have a lot of application nowadays in terms of modern machine learning research. 

Linear algebra, in particular, also a lot of applications to graphics. So, some of the stuff that Colton's just been talking about, about games and game development. A lot of graphics right now was ultimately based on linear algebra. And a lot of what graphical processing units are doing are just like pieces of hardware that are designed to do these linear algebra operation very, very quickly. So definitely a lot of applications, depending on where within computer science or other domains you're interested in, but they do become important that some point. 

SPEAKER 1: And I can say, too, I felt some of the same frustrations taking math classes in college and also in high school. And I think it's in part because of how the classes I took were taught. Many of the math classes I took were just so mechanical. Like it was just problem after problem after problem. And I worry that a lot of classes sort of lose sight of the forest for the trees, so to speak, which is they focus on a lot of the lower level details without appreciating that what's really important is the higher level concepts like what a derivative is or what an integral is in the world of calculus. 

And frankly, in retrospect-- and I can say this with some confidence 20 plus years later-- I really didn't need to know 12 different ways to take a derivative or do an integral, especially now when we have computers that can help with some of those processes. Hands down important to understand the applicability of finding the min or the max and what problems you can solve with those kinds of techniques, let alone matrices and the like in the world of linear algebra. 

But take some comfort in knowing that even though courses you're taking now in math might be kind of belaboring the point again and again, the ideas are useful even if you start to forget some of the mechanics and don't get all of the answers right when trying to do things by hand.