[HN Gopher] Mathematics for Computer Science (2024)
___________________________________________________________________
Mathematics for Computer Science (2024)
Lecture videos: https://ocw.mit.edu/courses/6-1200j-mathematics-
for-computer...
https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2H...
Author : vismit2000
Score : 275 points
Date : 2025-07-23 03:47 UTC (19 hours ago)
(HTM) web link (ocw.mit.edu)
(TXT) w3m dump (ocw.mit.edu)
| OutOfHere wrote:
| The lecture videos are here:
|
| https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer...
|
| https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2H...
| hand2note wrote:
| Where are the solutions to the problems?
| OutOfHere wrote:
| 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.
| fn-mote wrote:
| 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 (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 [...]
| mturmon wrote:
| 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.
| vardhanw wrote:
| The Units seem to be independent i.e. could be followed in any
| order. Can someone knowledgeable confirm this? I know Set
| theory etc is the basis of many things usually in a formal
| mathematical setting, hence asking.
| overfl0w wrote:
| 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
| rhubarbtree wrote:
| "A world class education available for free, to the
| undistractable."
| AnimalMuppet wrote:
| Hmm. One could think of the cost as a hack to force you to
| not be distracted so much.
| globalnode wrote:
| 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.
| William_BB wrote:
| 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.
| barrenko wrote:
| My 5 cents, the value of KA is that it gives you some sort of
| basic curriculum you can follow. To finish calculus (the
| "basic", single variable) I've had to pull in lots of other
| books, youtube channels, courses from other universities, but
| it still has it's worth. It's like a rope bridge over a high
| river.
|
| Major weaknesses are some cool sections like Linear Algebra
| that have no exercises in their respective "tree", but that's
| very rare.
| onetimeuser24 wrote:
| 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.
| t8q8 wrote:
| I completed an earlier version of this class and found
| structure to be helpful. Found consistent time and place each
| day to spend some time learning and that helped a ton, but
| still had weeks of not touching it so the struggle is real :)
|
| A bit of a side note but I find that the lectures are not the
| most interesting/useful part of those courses. The problem sets
| and the time spent trying to solve them ended up solidifying so
| many ideas that I had fooled myself into believing I
| understood. So I highly recommend heads-down solving some
| problems. It sinks much more time than the lectures but you
| come out of it better off
| vouaobrasil wrote:
| 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.
|
| Without a very experienced mentor, I think it's very difficult
| to get to the independent-learning stage with math. That's the
| key. You need someone to go through your work, correct you, and
| make sure you don't go off in a very wrong direction.
|
| So my advice is find at least a graduate student in math to
| help you. It's like a piano teacher, if you've ever taken
| piano, you know it's absolutely mandatory to have a teacher.
| People who self-learn from the start end up being able to play
| but not very well.
|
| Edit: one other crucial component is time. If you're really
| interested in knowing something like linear algebra, analysis,
| or calculus with fluency, expect to spend at least 10 hours per
| week on it for a year. Two hours per week will give you a
| cursory and very weak understanding only.
| ktallett wrote:
| I would say that you need to start at a lower level when self
| learning with a simpler resource. Something like Openstax.
| People get far too obsessed with the name attached to a
| resource than whether it is the right method of learning.
| j7ake wrote:
| Like piano it's important to tackle courses that are
| appropriate for your level
|
| Self taught people often skip too much of the basics so they
| struggle to properly tackle the fancy stuff
| vouaobrasil wrote:
| Even if they don't skip, they adopt weird hand positions
| that are hard to correct. There is just too much motor
| movement that needs to be done right that cannot really be
| explained or learned by watching a video or reading a book.
| It's actually similar to math in a certain way, where motor
| memory is replaced by subtle steps in logical reasoning.
| kindkang2024 wrote:
| LLM could be the teacher, one of the best already..
| AnimalMuppet wrote:
| I don't think "one of the best" would be wrong that often.
| kindkang2024 wrote:
| Sure, it's not perfect -- but most of the time, it gets
| things right. Also it can answer instantly, and always
| patiently...
| samrus wrote:
| 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
| baby wrote:
| Says someone who's never used LLMs to learn
| kindkang2024 wrote:
| > 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.
| roadside_picnic wrote:
| 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)
| abhink wrote:
| > 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 just
| by repeating the sections in the video.
|
| Now, years ago, to clear up the concepts, I would go to math
| stack exchange, write down exactly what I wanted to
| understand using mathjax and hope that someone will provide a
| detailed enough explanation. Most of the time I did learn
| from the answers, but sometimes the answer would be too
| succinct. In such cases there would be a need for a back and
| forth and stackexchange is not really designed around that
| usage pattern. This hassle would eventually make me give up
| the whole endeavor.
|
| Now however there are LLMs. They don't need mathjax to
| understand what I am talking about and they are pretty good
| at back and forth. In the past 6 months I have gone through 2
| full MIT courses with practice sheets and exams.
|
| So I would encourage anyone who went through the route of
| self learning via videos and found it to be too cumbersome
| and lacking to give it another go with your favorite LLM.
| libraryofbabel wrote:
| 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.
| zehaeva wrote:
| 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.
| hennell wrote:
| 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?
| monkeyelite wrote:
| When it comes to math and CS, doing exercises is a much
| stronger indicator of self-learning then reading/watching.
| maweki wrote:
| I am about finished with my CS PhD and I taught databases at
| the university during covid. I, personally, would have failed
| in the remote learning environment we were providing.
|
| I am amazed at those wo fought or even flourished through
| that.
| odyssey7 wrote:
| I'm currently enrolled in an online MS program, and I had
| never struggled so much in courses. The lack of social
| component might be what's causing that. The material is
| mostly a recap of undergrad and things I already knew, so
| the coursework should not be so difficult for me, but it's
| been incredibly difficult.
|
| Then again, William & Mary had some incredible teachers,
| and maybe the online program through a different school
| just isn't very good at designing assignments and teaching
| by comparison. But I feel that there was a difference in
| how I could succeed at challenging assignments when I was
| among other students in a social setting. The work in
| undergrad was highly rigorous, though exploring it
| alongside other real-life students made it a very different
| undertaking.
| roadside_picnic wrote:
| > 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.
| vouaobrasil wrote:
| > Not sure why you added "but even so"
|
| Because the "even so" was for the "self-motivated" part,
| not the "getting the PhD" part.
|
| > I've learned enough to publish (well received) technical
| books in areas I've never taken a single course in,
|
| I'm talking about pure math here, not other technical
| fields which are more hands on and don't require as much
| mentorship. Programming is easier to self-learn than math
| for sure, because it is not very abstract compared to math.
| It's also guided by whether the code works or not.
| roadside_picnic wrote:
| > I'm talking about pure math here
|
| Well the post is "Mathematics for Computer Science" which
| I don't think anyone considers "pure math". Most of my
| writing has been in the area of applied mathematics, the
| closest I've gotten to pure math would be some stuff on
| measure theory.
|
| So yea, it might be a challenge to self teach something
| like cluster algebras, but at that level much of the work
| in the field is academic communication anyway.
| WillAdams wrote:
| This course has been a _huge_ help to me in my current project
| (a G-code previewer and programmatic 3D modeling system written
| for (Open)PythonSCAD).
|
| I would recommend pairing it with:
|
| https://ocw.mit.edu/courses/6-001-structure-and-interpretati...
|
| and some additional online resources which I've found very
| helpful:
|
| -
| https://mathcs.clarku.edu/~djoyce/java/elements/elements.htm...
|
| - https://www.motionmountain.net/
|
| and of course https://librivox.org/ and
| https://www.gutenberg.org/ --- for a benchmark on why, well,
| when my father retired to a rural Virginia county, the library
| was a metal carrel of books in the basement of the old
| courthouse, and my favourite books during the summer (when I
| didn't have access to the school libraries) were Hal Clement's
| _Space Lash_ (which my father found in a tower at the prison
| where he worked where reading material was forbidden) and an
| English textbook containing a number of short stories which my
| mother purchased from a table of remaindered books in a
| department store in a town 26 miles away to which we might
| drive once a month or so.
| FilosofumRex wrote:
| Explore use of LLM instead of passive viewing of videos. Pass
| the link to LLM and ask to summarize it and generate a synopsis
| and quiz you. We don't learn from lectures, we learn from
| problem solving
|
| Also, be modest and assume you're dumber than you think you are
| - start with courses where you already know at least 50% of
| materials covered.
| Epitaque wrote:
| 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 fun.
| Though the problem I have is that I think the Venn diagram of
| colleges that are online, aren't expensive, have advanced CS/ML
| courses, have an experienced professor that you get to interact
| with is pretty much zero. If anyone has suggestions, do let me
| know.
| PeeMcGee wrote:
| 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.
| eumenides1 wrote:
| 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.
| snozolli wrote:
| 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...
| hiAndrewQuinn wrote:
| >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 this course any closer to having an MIT degree.
|
| >I guess I am used to deadline-oriented studying.
|
| You can always reverse the curse, and promise to pay someone if
| you don't finish X material by Y date. You probably also want
| some kind of proof mechanism to show that you actually did it,
| like eg a graded test.
|
| >Has anyone completed such type of lectures by themselves? How
| do you stay consistent and disciplined?
|
| I've read through several textbooks cover to cover including
| problem sets since graduating. My motivation is mostly just
| burning curiosity. I can't stand the feeling of not only not
| knowing a thing, but knowing that I don't know it or feeling
| like I'm faking it every time I do act on what I know.
| jrvarela56 wrote:
| 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.
| hiAndrewQuinn wrote:
| >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...
| cgriswald wrote:
| 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.
| JKCalhoun wrote:
| I miss iTunes U from Apple (not iTunes, _iTunes U_ , as in
| "University").
|
| So many cool (free) courses and so easy to find, download.
| somethingsome wrote:
| Part of the value of a university is exactly that. It builds
| momentum and incentives. Self paces lectures can be available,
| but it's extremely hard to follow them if you don't have a good
| evaluation at the end, or if you don't have deadlines to give
| assignments.
|
| But also remember, many of those lectures are at a slower
| peace, so one or two lectures per week. It takes time to
| internalize the material. People that don't follow university
| usually try to binge watch them, but this leads to low
| outcomes.
|
| I think the best strategy is to put deadlines and risks for
| yourself, and follow them at a natural peace. And, do the
| exercices.
| cubefox wrote:
| 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.
| rramadass wrote:
| > 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.
| cubefox wrote:
| > 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.
| rramadass wrote:
| 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.
| cubefox wrote:
| 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.
| linhns wrote:
| > 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.
| cubefox wrote:
| But the average software engineer probably doesn't do physics
| simulations or things like that.
| monkeyelite wrote:
| I have been a software engineer with and without math knowledge
| and it's a different level of contribution and effectiveness.
| cubefox wrote:
| Which areas of math were the most applicable in practice?
| monkeyelite wrote:
| Linear algebra, numerical analysis, and combinatorics are
| my most commonly used techniques.
|
| But It's less about the particular field and more about the
| mindset for thinking about problems. That's kind of like
| asking what your most used library functions are.
| amw-zero wrote:
| The first topic is "Predicates, Sets, and Proofs."
|
| I use predicates and sets quite often in daily programming.
| OutOfHere wrote:
| Just because you don't doesn't mean others don't. Software
| engineering is nothing without computer science.
| dernett wrote:
| 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
| vkuncak77 wrote:
| 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...
| monkeyelite wrote:
| What will that accomplish?
| amw-zero wrote:
| 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.
| monkeyelite wrote:
| Learning math is more about the big ideas. Behind each
| proof is an insight. Formalizing in a computer is like
| spell checking a document. It helps you catch small
| mistakes but doesn't change the content,
|
| I just think this is a distraction unless your goal is to
| learn lean and not math.
| jvanderbot wrote:
| Has anyone navigated a career change using OpenCourseware? I have
| a suspicion that the MOOC era mostly catered towards already-
| educated, self-starters and hobby learners, moreso than
| empowering a generation of workers, as was advertised.
|
| Not to knock it. I've been working through quantum computing
| between work-related fire drills and household commitments, so I
| should be up to speed in a few decades.
| owlbite wrote:
| 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.
| recipe19 wrote:
| 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!
| FuriouslyAdrift wrote:
| My CS program (at Purdue) was from the math department. We
| didn't even start designing real programs until the 4th
| semester (and that was in Forth or C).
|
| At that time, if you wanted to do application programming,
| you took software engineering (OO Pascal and C++) or computer
| technology (Java) from either tech or engineering schools.
| ducttapecrown wrote:
| 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".
| hand2note wrote:
| Where can I find solutions to the problems in the course?
| isomorphic- wrote:
| 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?
| jvanderbot wrote:
| I hate to say it but a LLM provides at least some guidance, but
| you can always try to ask on MathExchange
| FuriouslyAdrift wrote:
| Wait... what? CS is a math degree. Title is like saying
| mathematics for math.
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