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Mathematics for Computer Science (2024)

ocw.mit.edu

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Re: Mathematics for Computer Science (2024)

#61

Post by cubefox »

monkeyelite wrote: post #55
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.

Which areas of math were the most applicable in practice?

Re: Mathematics for Computer Science (2024)

#63

Post by cubefox »

rramadass wrote: post #58
cubefox wrote: post #42

Earlier quoted context omitted.

> 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 {i…

Well, I'm familiar with model theory and Church's simple theory of types, but I don't think things like that are useful in practice. Perhaps the concept of currying would be an exception, if I were a Haskell programmer.

Re: Mathematics for Computer Science (2024)

#64

Post by amw-zero »

monkeyelite wrote: post #54
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

What will that accomplish?

You can write proofs along with the course, and since they are machine checked you can have confidence that they are correct.

If you don't know, writing a proof in isolation can be difficult, since you may be writing on that isn't actually sound.

Re: Mathematics for Computer Science (2024)

#65

Post by amw-zero »

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 first topic is "Predicates, Sets, and Proofs."

I use predicates and sets quite often in daily programming.

Re: Mathematics for Computer Science (2024)

#66

Post by OutOfHere »

hand2note wrote: post #57
OutOfHere wrote: post #2

The lecture videos are here: https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer... https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2H...

Where are the solutions to the problems?

I don't see them. Perhaps a reasoning LLM can generate them. Anyway, my interest is simply in learning techniques that are relevant to programming.

Re: Mathematics for Computer Science (2024)

#67

Post by jvanderbot »

isomorphic- wrote: post #62

I wish these courses would also provide the answer sheets or tell you where to find them. How am I supposed to check my work and verify my answers otherwise?

I hate to say it but a LLM provides at least some guidance, but you can always try to ask on MathExchange

Re: Mathematics for Computer Science (2024)

#68

Post by OutOfHere »

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.

Just because you don't doesn't mean others don't. Software engineering is nothing without computer science.

Re: Mathematics for Computer Science (2024)

#69

Post by roadside_picnic »

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…

> completed a PhD... But even so,

Not sure why you added "but even so", getting a PhD is fundamentally about believing in the necessity of the mentor/mentee relationship for learning. It's not at all surprising that you would find:

> You need someone to go through your work, correct you, and make sure you don't go off in a very wrong direction.

I've learned enough to publish (well received) technical books in areas I've never taken a single course in, and have personally found that in-classroom experiences were never as valuable as I had hoped they would be. Of course starting from absolute 0 is challenging, but one good teacher early on can be enough.

Though I also don't think video lectures alone are adequate. Rather than focusing on "exercises", I've found I get the biggest boost in learning when I need to build something or solve a real problems with the mathematical tools I'm studying. Learning a bit, using it to build a real project, and then coming back when you need to unblock the next hurdle is very effective.

On top of this, books are just better for learning than videos (or lectures in general). Lectures are only useful for getting the lay of the land, and getting a feel for how types of problems are worked out. Especially with mathematics, you need time to look at an equation, read ahead, flip back, write it in a notebook, etc until you really start to get it.You really can't possibly get any of these ideas in 45-60 minutes of someone talking about it.

That's why, for me, online lectures don't really change the autodidact game all that much. Reading books and solving problems seems to have been the standard way to learn things well for at least the last several hundred years, and lectures don't improve on that too much.

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