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I’m doing something similar, except for Stats. I’ve cobbled together a plan based on degree programs from Stanford, CMU, and Berkeley. It would seem easier to stay on track with directed course learning, but how do you stay on track with the self-directed learning?
Is this doable for someone with less basis in math? I almost stopped studying math after two years of undergrad, when I went to a more practically-focused school. It'd be nice to get back into shape, because I've started reading research articles and always feel like I'm behind on the theory side of ML.
It depends very much on your own skills and drive. At some point, you need people to check your work, though, but you can search for online communities to do that. E.g. a post to mathoverflow asking about whether the following proof is correct, for example. Try to find a community of others online and work with them. Also remember that math is about ideas . It is not just an exercise in formal deduction. The field is…
Agree with that, 100%. Most of my students will, at some point in a course, respond to questions with things that are completely wrong. It's just how people learn. If there was not someone to correct their mistake then they would struggle a lot to find the error and fix it.
One of the most rewarding things about working with students is helping them through tough spots. But it is real work, and takes the time and attention of someone who has training.
> but you can search for online communities to do that. E.g. a post to mathoverflow asking about whether the following proof is correct, for example.
I'll just observe that MO, while a great community, can not scale to helping lots of people check their homework. For instance, in a Linear class session I might have 20 people, each with 12 homework questions. MO is just not set up for that.
Now, sometimes students are sure they got questions right, and usually their certainty is right, so there is no need to ask that one online. And sometimes people can find a relevant previous answer (although learners often struggle to find those, in my experience). Nonetheless, even after taking those out, there are still a lot of people with a lot of questions.
> Try to find a community of others online and work with them.
Yes, very good advice. I just wanted to observe that while it might work for OP (and I hope it does), it cannot work for lots of people. I don't know what the answer is, and maybe MO could help a lot, but it can't be the answer alone.
Personally I would add integration and measure theory (the sigma algebra and lebesgue stuff), but there seems no such module?
This guy was my TA in a GT for a course on Educational Technology. He totally blew off giving me any feedback until the last possible moment, super frustrating experience. I guess now I know where his time went?
this had me curious into looking this person up - honestly looks like they are trying super hard to get followers by making up substance about their own work and experiences.
(Currrently at GT for part-time program and for some of my classes, the TAs are receptive and very helpful! I would hate to have someone who waited until the end, especially when everyone is figuring out how to schedule their coursework on top of their job)
I’m doing something similar, except for Stats. I’ve cobbled together a plan based on degree programs from Stanford, CMU, and Berkeley. It would seem easier to stay on track with directed course learning, but how do you stay on track with the self-directed learning?
Personally I would add integration and measure theory (the sigma algebra and lebesgue stuff), but there seems no such module?
Is this doable for someone with less basis in math? I almost stopped studying math after two years of undergrad, when I went to a more practically-focused school. It'd be nice to get back into shape, because I've started reading research articles and always feel like I'm behind on the theory side of ML.
It depends very much on your own skills and drive. At some point, you need people to check your work, though, but you can search for online communities to do that. E.g. a post to mathoverflow asking about whether the following proof is correct, for example. Try to find a community of others online and work with them. Also remember that math is about ideas . It is not just an exercise in formal deduction. The field is…
Homework type questions (anything before PhD student level) are typically asked on https://math.stackexchange.com/
Personally I would add integration and measure theory (the sigma algebra and lebesgue stuff), but there seems no such module?
I think that would be more likely to be covered in a pure math program than applied math.
Integration is pretty basic and used extensively, and I'd say it makes no sense to cover contour integrals within the scope of complex numbers and differential equations but leave out integrals.
To me, applied mathematics is the art of transforming something into a linear system, which is something that we can tangibly solve on a computer. There are lot's of ways to do this such as Taylor series and Galerkin methods, so a lot of the field is understanding how, when, and why each method can be used. This is coupled with mastery over linear solvers, which includes direct methods, iterative methods, preconditioners, etc.
I wanted to write this comment, though, to focus on certain areas that may end up blocking what I view as appropriate progression in the field. These are things that I believe are necessary to understand advanced topics, but don't necessarily fall under applied mathematics. First, you really do need mastery of real analysis. It's necessary because it covers formally topics such as differentiation, integration, and series, which are required to understand theorems and algorithms. In my opinion, calculus books are not sufficient. Rudin's Principle's of Mathematical Analysis is the most concise, well written book that contains enough. Second, enough functional analysis to understand Hilbert Spaces is required. This prerequisite to this is the real analysis above. The issue here is that algorithms for things like differential equations require function spaces to do properly. Certainly, you can go really deep in this regard, but Hilbert Spaces are generally enough for practical algorithms. This also affects optimization theory, which impacts machine learning. Technically, you can do optimization theory with only real analysis, but the theory is cleaner in Hilbert Space. Questions that need to be answered are things like does the infimum exist and can it be obtained? Working with a general inner product is also a valuable tool for parallelization as well as a modeling tool. Third, some integration or measure theory is required. It depends on what you're doing, so I don't think mastery is strictly necessary, but spaces like L2 don't make a lot of sense unless you know what a Lebesgue integral is. Even if you want to just work with spaces that are Riemann integrable, measure theory helps understand when this is possible and the ramifications of it. And, to be clear, this is important outside of differential equations. If you want to understand optimization theory in a Hilbert Space, the inner products used will require some understand of measure theory.
Anyway, these are some random thoughts and ideas about the field. I do believe strongly that any amount of study is beneficial as most engineering fields benefit from applied mathematics.