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Mathematics for Computer Science (2024)

ocw.mit.edu

41–50 of 115 posts

Re: Mathematics for Computer Science (2024)

#41
post #36

Having "Mathematics for Computer Science" as a course title rubs me the wrong way, I always believed Computer Science was a specialized subfield of Mathematics.

In principle. But in practice, the industry doesn't need nearly as many mathematicians as it does software engineers, and almost no one is getting into CS out of the love of math. CS coursework reflects that. Here are some important algorithms and data structures, here's how you write Python, good luck at big tech!

Re: Mathematics for Computer Science (2024)

#42
post #13

A lot of these topics sound interesting, though I think the average software engineer needs approximately none of that. When I first started programming, I was surprised how little mathematics was involved in practice. Of course, these MIT lectures are aimed at computer scientists, not software engineers, which US universities consider to be quite different.

> the average software engineer needs approximately none of that. Not true. He/She doesn't need to know all of it nor in depth but a conceptual understanding is very much needed to write "correct" (w.r.t. a specification) code. We Humans are natural algorithmic problem solvers and hence can always muddle our way through to a ad-hoc solution for a given problem. Obviously, a lot depends on the intelligence of the indi…

> At the very least a knowledge of Set Theory, Logic and Relational Algebra goes a long way towards understanding the mapping from Mathematics to Computer Programming.

I know all these from university, but I did programming and SQL before that without any issues. Learning these mathematical details seemed really not useful in practice, at least for me.

Of course, coming up with something like SQL in the first place requires a lot of theoretical mathematics (set theory, relational algebra), but as someone who only uses those systems, like 99% of software engineers, understanding the mathematical theory here doesn't seem very helpful.

Re: Mathematics for Computer Science (2024)

#43
post #6

It's unbelievable that the average human being has access to the lectures of some of the best universities in the world for free. 31 hours of in-depth mathematics by some of the best people in their field. Although I have always been struggling with keeping up with long lecture playlists. I always try to find shorter videos which explain the concept faster (although probably lacking depth). And end up ditching it hal…

I echo this sentiment. One of my favorite periods of my life was college, actually getting to learn about some advanced topics in CS. Then I graduated and got a job and now I struggle so hard to learn new things (despite lecture videos and textbooks and LLMs existing) without a professor grading assignments/giving exams/that you can talk to, or classmates. I’m thinking about enrolling in an online college just for fu…

Maybe the public commitment method would help. I kind of think that's fundamentally what makes college inherently motivating.

This is about weight loss, but I think it can be applied to anything:

https://www.medicspot.co.uk/weight-loss/behaviour-change/pub...

Re: Mathematics for Computer Science (2024)

#44

Earlier quoted context omitted.

>Perhaps the real motivation to keep up with the material comes from actually enrolling the university? For most people in most situations, the real motivation to keep up with the material comes from the wage premium one gets after getting the sheepskin. It is unsurprising you, a humble autodidact, are having a lot more trouble than an actual MIT student, because unlike an actual MIT student, you will not walk out of…

At first your comment rubbed me the wrong way, too cynical. But it is completely true. No one would ‘learn’ the way college courses are structured. The only reason these courses get completed is the pace/cadence, GPA requirements to get jobs and the degree. In the ‘real world’ you just learn enough to solve the problem in front of you and as you face more and more your knowledge tree expands. No one in their right mi…

>At first your comment rubbed me the wrong way, too cynical.

It's only cynical if you think making money is bad! I think it's terrific that your average B student and up is mature enough to reliably take on tens of thousands of dollars in debt, and work hard for several years without any immediate reward, in exchange for a pretty reliable pathway towards high paying specialized labor for the rest of their lives. It spits in the face of the narrative that young people are too stupid, or too naive or whatever to have agency in their own lives.

>The only reason these courses get completed is the pace/cadence, GPA requirements to get jobs and the degree.

I cite The Case Against Education, as usual. [1]

>In the ‘real world’ you just learn enough to solve the problem in front of you and as you face more and more your knowledge tree expands. No one in their right mind would go through a syllabus-like sequence - it is just boring, dull as hell.

I cite too John D. Cook's "Just-in-case versus just-in-time" blog post. [2] I don't work through actual syllabi, but I love working through textbooks from start to finish. But you are also correct that I am emphatically not in my right mind, and my career has suffered for it. ;)

[1]: https://www.youtube.com/watch?v=_t957pTcJ0E&t=2s

[2]: https://www.johndcook.com/blog/2010/03/03/just-in-case-versu...

Re: Mathematics for Computer Science (2024)

#45
post #6

It's unbelievable that the average human being has access to the lectures of some of the best universities in the world for free. 31 hours of in-depth mathematics by some of the best people in their field. Although I have always been struggling with keeping up with long lecture playlists. I always try to find shorter videos which explain the concept faster (although probably lacking depth). And end up ditching it hal…

Discipline is just making the same choice every time no matter how you feel or what thoughts enter your mind. Your mind will lie to you with thoughts and feelings about why you can’t attend to a lecture. Treat your mind like a child pretending to be sick to get out of school.

Even if it is true that in the moment you aren’t focused or whatever other excuses your mind comes up with, so what? “Go to class” anyway. At worst you learn nothing but improve your discipline skills.

Set a regular time to watch the lectures so you can’t lie to yourself about doing it later.

I want to be clear, it isn’t about willing yourself through it despite everything even if it can read that way. It’s about honoring the choice you made to attend to the lectures and not accepting excuses from your mind.

Recognizing that you can choose, recognizing that past you had good intentions for you and deserves you to honor those intentions, and recognizing that your thoughts and feelings in the moment may not be true and “aren’t the boss of you” even if they are true helps tremendously.

Re: Mathematics for Computer Science (2024)

#46
post #33
post #19

Earlier quoted context omitted.

> But even so, I don't think I would have been able to learn much on my own with video lectures, at least not at the start. This was exactly my situation. Videos can give you a lot of structured, well presented information. And for MIT courses you'd get this knowledge from the very best. The problem is that no matter how well the subject matter is presented, I would hit some conceptual snag that I couldn't resolve ju…

My only concern with using LLMs to learn new material is being certain that it's not leading me astray. Too many times I've used LLMs for tasks at work and some of the answers I've gotten back are subtlety wrong. I can skip past those suggestions because the subject is one I'm strong/experienced in and I can easily tell that the LLM is just wrong or speaking nonsense. But if I didn't have that level of experience, I…

I have the same doubts, it's like the old rule of reading a newspaper story. When it's outside your area of expertise you think they're a genius. When it's something you know a lot about you think it's an idiot.

But it might still help, especially if you think about the LLM as a fellow student rather than as a teacher. You try to catch it out, spot where it's misunderstood. Explain to it what you understand and see if it corrects you?

Re: Mathematics for Computer Science (2024)

#47
post #32

Earlier quoted context omitted.

Sure, it’s not perfect — but most of the time, it gets things right. Also it can answer instantly, and always patiently...

LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck. You need to guide your own study and you might not know what you need to learn to get unstuck

Says someone who's never used LLMs to learn

Re: Mathematics for Computer Science (2024)

#48
post #32

Earlier quoted context omitted.

Sure, it’s not perfect — but most of the time, it gets things right. Also it can answer instantly, and always patiently...

LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck. You need to guide your own study and you might not know what you need to learn to get unstuck

[deleted]

Re: Mathematics for Computer Science (2024)

#49
post #32

Earlier quoted context omitted.

Sure, it’s not perfect — but most of the time, it gets things right. Also it can answer instantly, and always patiently...

LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck. You need to guide your own study and you might not know what you need to learn to get unstuck

> LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck.

Many teachers cannot do that either.

I find ChatGPT and the Gemini model quite good at problems whose solutions are already known. We just need the Wille—the will—to ask it.

Re: Mathematics for Computer Science (2024)

#50
post #6

It's unbelievable that the average human being has access to the lectures of some of the best universities in the world for free. 31 hours of in-depth mathematics by some of the best people in their field. Although I have always been struggling with keeping up with long lecture playlists. I always try to find shorter videos which explain the concept faster (although probably lacking depth). And end up ditching it hal…

I miss iTunes U from Apple (not iTunes, iTunes U, as in "University").

So many cool (free) courses and so easy to find, download.

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