Self studying the MIT applied math curriculum (2019)

Post by porknubbins » Mon, Oct 25, 2021, 4:29 AM UTC

tzs wrote: post #49

ai_ia wrote: post #3

I have a pretty similar background. I have an undergrad in ChemE who fell in love with machine learning research. As I didn’t had the appropriate background so I taught myself Computer science using mostly resources such as OCW and teachyourselfcs, videolectures etc. However, what stood out to me was how difficult it is to self study? Universities provide a setting which helps you learn difficult subjects over a long…

> However, what stood out to me was how difficult it is to self study? Universities provide a setting which helps you learn difficult subjects over a longer period of time. Outside of that, no such avenues exist. It’s not just reading up a book or making Anki flash cards(which is quite tedious to be honest) but the process of selecting, vetting what to read next and actually completing it. One major thing I found whe…

This is definitely one of the hardest parts of self study and what gives me enormous appreciation for good teachers. Progress can slow or even halt because you are forced to be so rigid about understanding everything before moving on- otherwise you risk serious gaps in knowledge. I have found CS classes with autograded programming assignments far better than other types of online courses because I known if I at least learned one thing.

Post by laichzeit0 » Mon, Oct 25, 2021, 9:15 AM UTC

tgflynn wrote: post #39

nuerow wrote: post #29

Earlier quoted context omitted.

> 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.

Integration is covered in any calculus course, the comment I was replying to do was about Lebesgue integration which is a much more advanced topic that as far as I know is only needed for integrating functions which are so pathological that they probably don't occur in the physical world.

I am no expert here, but as I understand it, measure theory is used as the basis for all modern probability theory for the reason that it simplifies a lot of things as you get to more advanced topics, like Markov chains on general state spaces [1]. So if you want to study Stochastic Processes you probably want to use measure theory. So thus the Lebesgue integral is not just for "pathological" sets (I remember reading somewhere that even the Lebesgue integral still breaks down on some really pathological examples). If you've studied mathematical statistics, you'll typically see proofs for expectations of discrete distributions and continuous distributions. They're typically similar, but different since you're using summation for the one, and integration for the other. When you get to random vectors, you can have weird distributions where some components are discrete and others continuous. Apparently using a measure-theoretic approach to probability, it unifies these into one general theory (again, I'm no expert, this is how I understand it).

[1] https://www.stat.umn.edu/geyer/8501/measure.pdf

Re: Self studying the MIT applied math curriculum (2019)

Re: Self studying the MIT applied math curriculum (2019)