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.
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.
> 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.
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.
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.
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?
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.
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.
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.
>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.
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.
>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. ;)
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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).
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 [...]
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.
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.
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.
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.
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!
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!
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):
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.
> 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.
> 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.
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
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.
> 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.
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.
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.
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?
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
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.
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.
LLM could be the teacher, one of the best already..
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
> 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.
Says someone who's never used LLMs to learn
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.
I miss iTunes U from Apple (not iTunes, iTunes U, as in "University").
So many cool (free) courses and so easy to find, download.
>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.
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.
>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...
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.
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.
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.
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...
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.
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.
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.
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
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.
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.
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.
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.
“A world class education available for free, to the undistractable.”
Hmm. One could think of the cost as a hack to force you to not be distracted so much.
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:
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.
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.
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.
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.
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!
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...
The lecture videos are here:
https://ocw.mit.edu/courses/6-1200j-mathematics-for-computer...
https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2H...
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.
> 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.
> 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.