6 ms·

At this point we might benefit a lot from a forum where mathematical concepts are discussed for a particular application in the most explicit ways and not just

At this point we might benefit a lot from a forum where mathematical concepts are discussed for a particular application in the most explicit ways and not just question and answers. We can then build up on that to further the mathematical concepts and also to rope in more people into proper Machine Learning domain. Is this objective a little too unrealistic to obtain?

jacobolus 9y ago
That forum has existed for centuries, and is called a university.
- foo101 9y ago
  How is that relevant? Many of us are not going to spend our entire lives in a university.
  - jacobolus 9y ago
    The general way to master a large pile of difficult abstractions is to study for years, ideally in a context focused on that study. This can be done independently of any expert feedback (e.g. by reading books, watching lecture videos, and doing a big pile of ungraded self-assigned homework problems), but it’s not easy or typically very efficient. For the majority of people who want to deeply learn mathematical topics but who are starting from a low level, the most efficient and effective advice for them is to go attend a university. An online discussion forum isn’t typically going to cut it, IMO. People won’t be at the same level, won’t be working on the same topics, won’t have the same goals and interests, the same level of commitment, coordinated schedules, etc. This has been tried many times, but I have not heard many successful reports. Online discussion forums are great for handling independent limited-scope questions–answers (including for current university students), and okay for coordinating research efforts among people who are already experts, but in general are not very effective for getting a group of people to diligently work through years of prerequisite material in an organized fashion. You shouldn’t spend your life in a university, but if you have a goal of learning advanced mathematics, you might benefit from spending a few years there. YMMV. As an alternative, if you can find an expert tutor/coach to meet with one-on-one on a regular basis, that is even better than a formal course. But that is expensive and hard to scale.
    - jimhefferon 9y ago
      Very well put. > it’s not easy or typically very efficient It is also very possible for folks to think they have it right, and go off in entirely wrong directions. In my experience it is likely, even in quite good and hard-working students. I teach an inquiry-based proofs class and so I sit through the students's discussion. Even on material that would be considered trivial in many of the books mentioned here, there are people saying aloud things in that discussion that are just simply wrong. It is not that these folks are dummies, it is that this stuff is hard. I'm not a people person but one thing I've seen from this class is that a lot of learning is about community. It makes a big difference.
    - mindcrime 9y ago
      You shouldn’t spend your life in a university, but if you have a goal of learning advanced mathematics, you might benefit from spending a few years there. YMMV. The problem is, that simply isn't possible / practical for many people. Assuming we're talking about people who are career professionals who are already past their first (and maybe only) stint at a university, most people just don't have the free time (and other resources) to sit in classes at a university. Especially since most universities still cater almost exclusively to "traditional" students who take classes in person, during the day. If universities made more night classes available, or more online/hybrid classes, I could buy this. But for a lot of us, the best we can do is some combination of "watch Youtube videos, do MOOC's, self-study, do ungraded problems, and ask for help on Internet forums". That said, not all problems you do on your own have to be exactly "ungraded". For many mathematical subjects you can find books of exercises that include the answers so you can "grade" yourself (assuming you can resist the temptation to cheat and look at the answers first), or you can find previous years problem sets and exams on many course websites. Yeah, learning the stuff outside of a university setting is probably harder in some sense, but it's not impossible. And if that avenue is the only one available to somebody, then it is - by definition - the best avenue available to them.
      - deleted 9y ago
        [deleted]
      - 9y ago
  - dsacco 9y ago
    This might sound callous, but most of us are not going to master advanced mathematics or theoretical computer science. If you want to self-study, all the material you could ever hope to need is available in a mulitude of books targeted to various levels of prior experience and with many different styles of exposition. If you want to study with others, this is precisely what college is for. People who don’t want to study in a college setting basically don’t want to study in a group setting in general, because the college setting actually is the most efficient group setting. I think most people underestimate the sheer vastness of the material you have to learn and the requisite time you need to learn it. Reading isn’t enough, you have to do it - over and over. It’s frankly a slog, and there’s no more efficient way than being immersed in coursework. The entire benefit of a course structure is the instructor. The community forum helps, but really it’s an extension of the instructor. A qualified instuctor can quickly resolve a complex question that might take you hours or days to (maybe incorrectly) answer yourself. If you’re capable of learning genuinely unfamiliar math without an instructor, that means you have sufficient mathematical maturity that you don’t need a group forum. At that point it’s actually more efficient to self-study. I get the sense people believe mathematicians are pretentious when they say things like this, but I think that’s uncharitable. They typically give advice like this because they have a significant amount of personal experience and know very well what tends to work (and how efficiently it works).
dsacco 9y ago
What does “most explicit ways” mean? Do you mean in the most straightforward language possible, with as much jargon as possible removed? Do you mean extremely patient exposition? Do you mean a first principles approach that builds advanced probability theory, linear algebra and statistics from set theory, then dives into machine learning? Murphy’s Machine Learning: A Probabilistic Perspective is just over 1000 pages long. It’s an exceptionally good book for the mathematical theory behind machine learning. What would this book look like under your proposal? If we add in Axler’s Linear Algebra Done Right and Chung’s A First Course in Probability Theory, we’re adding another 350 pages or so each. Both of those books have prerequisites, and Murphy’s book isn’t the top either. In my opinion your proposal is unrealistic, yes. I don’t mean for that to sound harsh, I just don’t see a way to achieve what you’re asking for without making a monolithic tome larger than Knuth’s The Art of Computer Programming, and potentially even more diverse in scope.

jacobolus 9y ago

That forum has existed for centuries, and is called a university.

foo101 9y ago
How is that relevant? Many of us are not going to spend our entire lives in a university.
- jacobolus 9y ago
  The general way to master a large pile of difficult abstractions is to study for years, ideally in a context focused on that study. This can be done independently of any expert feedback (e.g. by reading books, watching lecture videos, and doing a big pile of ungraded self-assigned homework problems), but it’s not easy or typically very efficient. For the majority of people who want to deeply learn mathematical topics but who are starting from a low level, the most efficient and effective advice for them is to go attend a university. An online discussion forum isn’t typically going to cut it, IMO. People won’t be at the same level, won’t be working on the same topics, won’t have the same goals and interests, the same level of commitment, coordinated schedules, etc. This has been tried many times, but I have not heard many successful reports. Online discussion forums are great for handling independent limited-scope questions–answers (including for current university students), and okay for coordinating research efforts among people who are already experts, but in general are not very effective for getting a group of people to diligently work through years of prerequisite material in an organized fashion. You shouldn’t spend your life in a university, but if you have a goal of learning advanced mathematics, you might benefit from spending a few years there. YMMV. As an alternative, if you can find an expert tutor/coach to meet with one-on-one on a regular basis, that is even better than a formal course. But that is expensive and hard to scale.
  - jimhefferon 9y ago
    Very well put. > it’s not easy or typically very efficient It is also very possible for folks to think they have it right, and go off in entirely wrong directions. In my experience it is likely, even in quite good and hard-working students. I teach an inquiry-based proofs class and so I sit through the students's discussion. Even on material that would be considered trivial in many of the books mentioned here, there are people saying aloud things in that discussion that are just simply wrong. It is not that these folks are dummies, it is that this stuff is hard. I'm not a people person but one thing I've seen from this class is that a lot of learning is about community. It makes a big difference.
  - mindcrime 9y ago
    You shouldn’t spend your life in a university, but if you have a goal of learning advanced mathematics, you might benefit from spending a few years there. YMMV. The problem is, that simply isn't possible / practical for many people. Assuming we're talking about people who are career professionals who are already past their first (and maybe only) stint at a university, most people just don't have the free time (and other resources) to sit in classes at a university. Especially since most universities still cater almost exclusively to "traditional" students who take classes in person, during the day. If universities made more night classes available, or more online/hybrid classes, I could buy this. But for a lot of us, the best we can do is some combination of "watch Youtube videos, do MOOC's, self-study, do ungraded problems, and ask for help on Internet forums". That said, not all problems you do on your own have to be exactly "ungraded". For many mathematical subjects you can find books of exercises that include the answers so you can "grade" yourself (assuming you can resist the temptation to cheat and look at the answers first), or you can find previous years problem sets and exams on many course websites. Yeah, learning the stuff outside of a university setting is probably harder in some sense, but it's not impossible. And if that avenue is the only one available to somebody, then it is - by definition - the best avenue available to them.
    - deleted 9y ago
      [deleted]
    - 9y ago
- dsacco 9y ago
  This might sound callous, but most of us are not going to master advanced mathematics or theoretical computer science. If you want to self-study, all the material you could ever hope to need is available in a mulitude of books targeted to various levels of prior experience and with many different styles of exposition. If you want to study with others, this is precisely what college is for. People who don’t want to study in a college setting basically don’t want to study in a group setting in general, because the college setting actually is the most efficient group setting. I think most people underestimate the sheer vastness of the material you have to learn and the requisite time you need to learn it. Reading isn’t enough, you have to do it - over and over. It’s frankly a slog, and there’s no more efficient way than being immersed in coursework. The entire benefit of a course structure is the instructor. The community forum helps, but really it’s an extension of the instructor. A qualified instuctor can quickly resolve a complex question that might take you hours or days to (maybe incorrectly) answer yourself. If you’re capable of learning genuinely unfamiliar math without an instructor, that means you have sufficient mathematical maturity that you don’t need a group forum. At that point it’s actually more efficient to self-study. I get the sense people believe mathematicians are pretentious when they say things like this, but I think that’s uncharitable. They typically give advice like this because they have a significant amount of personal experience and know very well what tends to work (and how efficiently it works).

dsacco 9y ago

What does “most explicit ways” mean? Do you mean in the most straightforward language possible, with as much jargon as possible removed? Do you mean extremely patient exposition? Do you mean a first principles approach that builds advanced probability theory, linear algebra and statistics from set theory, then dives into machine learning? Murphy’s Machine Learning: A Probabilistic Perspective is just over 1000 pages long. It’s an exceptionally good book for the mathematical theory behind machine learning. What would this book look like under your proposal? If we add in Axler’s Linear Algebra Done Right and Chung’s A First Course in Probability Theory, we’re adding another 350 pages or so each. Both of those books have prerequisites, and Murphy’s book isn’t the top either. In my opinion your proposal is unrealistic, yes. I don’t mean for that to sound harsh, I just don’t see a way to achieve what you’re asking for without making a monolithic tome larger than Knuth’s The Art of Computer Programming, and potentially even more diverse in scope.