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Mathematics for Computer Science (2024)

ocw.mit.edu

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Re: Mathematics for Computer Science (2024)

#31

Post by libraryofbabel »

abhink wrote: post #19
vouaobrasil wrote: post #14

Earlier quoted context omitted.

I love math, completed a PhD, and am very self-disciplined. 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. For some reason, it seems like you need to reach a "critical mass" of knowledge first before you can do that, and I've observed that a crucial component is being in a program with others, and definitely having a very experienced mentor. W…

> 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…

LLMs are indeed excellent as conversation partners for helping with difficult concepts or for working through problem sheets. They’re really opened up self-learning for me again in math. You can use them to go much deeper with concepts much deeper than the course you’re taking - e.g. I was relearning some basic undergrad probability and stats but ended up exploring a bit of measure theory using Gemini as well. I would go so far as to say that an LLM can be more effective for explaining things than a randomly selected graduate student (though some grad students with a particular talent for teaching will be better).

What the LLM still does not provide is accountability (a LLM isn’t going to stop you from skipping a problem set) and the human social component. But you could potentially get that from a community of other self-learners covering the same material if you’re able to pull one together.

Re: Mathematics for Computer Science (2024)

#32

Post by samrus »

kindkang2024 wrote: post #28
AnimalMuppet wrote: post #25

Earlier quoted context omitted.

I don't think "one of the best" would be wrong that often.

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

Re: Mathematics for Computer Science (2024)

#33

Post by zehaeva »

abhink wrote: post #19
vouaobrasil wrote: post #14

Earlier quoted context omitted.

I love math, completed a PhD, and am very self-disciplined. 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. For some reason, it seems like you need to reach a "critical mass" of knowledge first before you can do that, and I've observed that a crucial component is being in a program with others, and definitely having a very experienced mentor. W…

> 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 don't think I would be able to tell where the LLM was wrong/mistaken.

I think LLMs are great for learning new things, but I also think you have to be skeptical of everything it says and need to double check the logic of what it's telling you.

Re: Mathematics for Computer Science (2024)

#34

Post by rramadass »

cubefox wrote: 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 individual here. What Mathematics gives you is a structure and concepts to systematize our thinking and rigorously apply it so that problem solving becomes more mechanical. Thus you learn to specify the problem rigorously using mathematical concepts and then use mathematical logic to derive a "Program" satisfying those requirements.

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.

The following books are helpful here;

1) Introductory Logic and Sets for Computer Scientists by Nimal Nissanke. A very nice overview and wide coverage of needed basic mathematics.

2) Understanding Formal Methods by Jean-Francois Monin. A fire-hose overview of mathematical models and tools implementing those models.

Re: Mathematics for Computer Science (2024)

#35

Post by vkuncak77 »

dernett wrote: post #17

I'm going to try formalizing this course in Lean--not sure how hard it is going to be. If anyone is interested in doing the same, please feel free to contribute! https://github.com/dernett/Lean61200J

This sounds very interesting and relevant to the goals of the CSLib initiative that apparently just got started. I don't have a better public link to it now except this LinkedIn post (perhaps there's a Zulip tag):

https://www.linkedin.com/posts/lean-fro_leanlang-cslib-forma...

Re: Mathematics for Computer Science (2024)

#37

Post by jrvarela56 »

hiAndrewQuinn wrote: post #30
overfl0w wrote: 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…

>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 mind would go through a syllabus-like sequence - it is just boring, dull as hell.

Re: Mathematics for Computer Science (2024)

#38

Post by PeeMcGee »

Epitaque wrote: post #29
overfl0w wrote: 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…

Georgia Tech has a great online MSc CS program (OMSCS) that's very affordable for what it is, though the amount of direct interaction with the professor varies from class to class.

Re: Mathematics for Computer Science (2024)

#39

Post by eumenides1 »

Epitaque wrote: post #29
overfl0w wrote: 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…

Try not to beat yourself up too much about it, I certainly have and it hasn't been very useful to do so.

You have a finite amount of energy in a day and learning takes a lot of energy. It's why a kid's job is the learn.

You could try front running the learning, but it will impact your energy levels at work. It still takes a monumental amounts of discipline, but you may have the energy to make it work.

Re: Mathematics for Computer Science (2024)

#40

Post by [deleted] »

vouaobrasil wrote: post #14
overfl0w wrote: 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 love math, completed a PhD, and am very self-disciplined. 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. For some reason, it seems like you need to reach a "critical mass" of knowledge first before you can do that, and I've observed that a crucial component is being in a program with others, and definitely having a very experienced mentor. W…

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