Mathematics for Computer Science (2024)

There are a few unusual parts, like the last lecture ("Large Deviations"). I'm not familiar with the entire course, but IMO the lecture on state machines is very good; it discusses invariants and uses an approchable example (the 15-puzzle).

Text (last revised 2018): https://courses.csail.mit.edu/6.042/spring18/mcs.pdf

If you have never looked at it, the problems there are very nice. For example, instead of some dry boolean logic problem about A and Not(B), you have Problem 3.17 on page 81, which begins:

    This problem examines whether the following specifications are satisfiable:
    1. If the file system is not locked, then. . .
    (a) new messages will be queued.
    (b) new messages will be sent to the messages buffer.
    (c) the system is functioning normally, and conversely, if the system is
    functioning normally, then the file system is not locked.

    [...]

    (a) Begin by translating the five specifications into propositional 
    formulas using the four propositional variables [...]

Re: Mathematics for Computer Science (2024)

#4

Post by [deleted] » Wed, Jul 23, 2025, 6:22 AM UTC

fn-mote wrote: post #3

The page listing topics (just like the playlist): https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer... Lecture notes: https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer... There are a few unusual parts, like the last lecture ("Large Deviations"). I'm not familiar with the entire course, but IMO the lecture on state machines is very good; it discusses invariants and uses an approchable example (th…

[deleted]

Re: Mathematics for Computer Science (2024)

#5

Post by mturmon » Wed, Jul 23, 2025, 6:23 AM UTC

fn-mote wrote: post #3

The page listing topics (just like the playlist): https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer... Lecture notes: https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer... There are a few unusual parts, like the last lecture ("Large Deviations"). I'm not familiar with the entire course, but IMO the lecture on state machines is very good; it discusses invariants and uses an approchable example (th…

I was also pleased to see large deviations, although the lecture notes don’t actually define what a large deviation is.

They do give an example of a Chernoff (exponential) bound for a sum of iid random variables. The bound of course has an exponential form - they just don’t call it a large deviation. So it’s a bit of a missed opportunity, oven that the name is in the chapter title.

These bounds come up all over the place in CS, but especially lately in learning theory.

Re: Mathematics for Computer Science (2024)

#6

Post by overfl0w » Wed, Jul 23, 2025, 6:40 AM UTC

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 halfway as well. Perhaps the real motivation to keep up with the material comes from actually enrolling the university? Has anyone completed such type of lectures by themselves? How do you stay consistent and disciplined?

I find courses in some platforms (coursera/khanacademy) a bit more motivating because they kind of push me with deadlines. I guess I am used to deadline-oriented studying.

If anyone else is struggling with attention span and is looking for shorter lectures (although they may not have the same depth): https://www.youtube.com/@ProfessorDaveExplains/playlists

Re: Mathematics for Computer Science (2024)

#7

Post by rhubarbtree » Wed, Jul 23, 2025, 6:44 AM UTC

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…

“A world class education available for free, to the undistractable.”

Re: Mathematics for Computer Science (2024)

#8

Post by globalnode » Wed, Jul 23, 2025, 6:52 AM UTC

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…

Its so hard to be self disciplined like that, I find I have to enroll to force myself to engage. I know its a weakness.

Re: Mathematics for Computer Science (2024)

#9

Post by William_BB » Wed, Jul 23, 2025, 7:14 AM UTC

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…

In my experience, coursera/khan academy courses have never been able to compete with a rigorous university course. They're great resources when you need alternative explanations, but never stood up on their own.

I think long lecture playlist is a feature, not a bug. It's much harder to commit to such material when you're not full timing education.

Re: Mathematics for Computer Science (2024)

#10

Post by onetimeuser24 » Wed, Jul 23, 2025, 7:21 AM UTC

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 got through a few lectures by recognizing that I didn’t have the mathematical training/practice to finish up one video in one sitting. Often times I would need to scurry on over to have some basics explained to me on another site. I did one lecture over several days (weeks if I had to). I think most of the discipline comes from expectation management. Expect to get stuck and need a few moments or days or weeks to mull something over until it becomes more intuitive. Keep a list of things you do and don’t understand (a simple text file / paper is enough) and keep doing it for a few months if you have to and you’ll get there.