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Mathematics for Computer Science (2024)

ocw.mit.edu

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Re: Mathematics for Computer Science (2024)

#51

Post by linhns »

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.

This is not really true, especially if you're involved with physics and robotics even just a bit like a do. Without mathematics, you won't understand a thing.

Re: Mathematics for Computer Science (2024)

#52

Post by ducttapecrown »

owlbite wrote: 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.

You could make an analogous course titled "Mathematics for [subfield of mathematics]" for any subfield of math. It would be a good(ish) title (I have never titled a course), and the content would be nicely focused.

Such courses are generally titled "Intro to".

Re: Mathematics for Computer Science (2024)

#53

Post by monkeyelite »

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…

When it comes to math and CS, doing exercises is a much stronger indicator of self-learning then reading/watching.

Re: Mathematics for Computer Science (2024)

#55

Post by monkeyelite »

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.

I have been a software engineer with and without math knowledge and it’s a different level of contribution and effectiveness.

Re: Mathematics for Computer Science (2024)

#58

Post by rramadass »

cubefox wrote: post #42
rramadass wrote: post #34

Earlier quoted context omitted.

> 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 r…

I am afraid you have not really understood the mathematical theory and its mapping to programming. Relational Algebra doesn't just mean RDBMS/SQL but is a general algebra where algebraic Operations are defined over mathematical Relations i.e. over a Cartesian Product of one or more Sets.

As a first approximation; a) Type = Set b) Function = subset of Relation (i.e. set of Tuples) obtained from Cartesian Product of {input type set X output type set} c) Logical conditions define new relational sets where its members have a ordering relation d) A Program is a series of functions which prune and transform the tuples from the above cartesian product.

Re: Mathematics for Computer Science (2024)

#59

Post by cubefox »

linhns wrote: post #51
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. This is not really true, especially if you're involved with physics and robotics even just a bit like a do. Without mathematics, you won't understand a thing.

But the average software engineer probably doesn't do physics simulations or things like that.

Re: Mathematics for Computer Science (2024)

#60

Post by roadside_picnic »

kindkang2024 wrote: post #18
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…

LLM could be the teacher, one of the best already..

I've found you have to be very careful with LLM as teacher since, especially when it's the one explaining, it is wrong more often then you might think, and there's no way to know.

The best use of an LLM I've found in learning is for when I explain to it my understanding of what I learned and have it critique what I've said. This has greatly reduced the amount of backtracking I need to do as I start to realize I've misunderstand a foundational concept later on when things stop making sense. Often simply having the model response with "Not quite, ..." is enough to make me realize I need to go back and re-read a section.

The other absolute godsend is just being able to take a picture of an equation in a book and ask for some help understanding it notationally. This is especially helpful when going between fields that use different notation (e.g. statistics -> physics)

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