Probability Models and Axioms https://www.youtube.com/watch?v=j9WZyLZCBzs
The Exponential Function https://www.youtube.com/watch?v=oo1ZZlvT2LQ&t=100s
Vector Space https://www.youtube.com/watch?v=ozwodzD5bJM&t=36s
Tree cutting fails: https://www.youtube.com/watch?v=JHZkR6UVegY
Same here. I'm on a quest to run myself through the equivalent of a standard Calc I, Calc II, Calc III, Linear Algebra sequence, and I've managed to find great Youtube resources for all of those things (and more). It's times like these that you marvel at how awesome the Internet can be at its best. :-)
Essence of Linear Algebra (visualized) https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...
MIT Differential Equations: https://www.youtube.com/watch?v=ZvL88xqYSak&list=PLUl4u3cNGP...
Don't overlook mathematical analysis -- real analysis, complex analysis, etc -- that's another big leg of the mathematical stool, with geometrical foundations underpinning it all.
As you self-study and progress into upper level math, you'll come across abstract and unfamiliar topics you didn't learn about in calculus/algebra -- and sometimes it's hard to pin down what category the topic falls under -- when that happens, the topic will often be related to analysis, group theory, or topology (courses taken by math majors but not as widely known).
See http://nada.kth.se/~axelhu/mapthematics.pdf and http://space.mit.edu/home/tegmark/toe.gif
Crosslinks for all MIT courses: http://crosslinks.mit.edu/topics/?query=subject18.100
I'm about to start a self-directed learning exercise focused on CS related math. I've never used online resources to learn / brush up on complex topics before so I'm a bit unsure what to expect.
I only took through Algebra II in high-school, but honestly, I went to Algebra II class maybe 4 or 5 times all year, never did any of the homework, and took maybe 1 test. Needless to say I failed it. That was the year I was too busy being "mr rebel badass guy" to worry about studying, plus I didn't need the class to graduate, so I just didn't give a flip. OTOH, I did really well in H.S. Geometry the year before.
Anyway, when I started college I needed some maths refresher, so I took 2 semesters of College Algebra, and 2 semesters of Pre-Calculus. I also had a 1 semester Discrete Math class. I started Calc I but I dropped out about halfway through that semester.
Fast forward about 6 or 7 years, and I decided to go back to school. Having forgotten all the maths stuff I had learned before, I took College Algebra yet again, as well as Discrete Math (I don't remember now why I took Discrete again. It might be because my earlier credit was too old to transfer).
Fast forward another 7 years or so, and I've again forgotten what maths I'd learned before. But by now Khan Academy exists and that's where the online stuff kicks in.
So I've fiddled around on KA a bit over the past few years, just trying to keep up some of the really basic algebra stuff that you forget if you don't use (rationalizing denominators, factoring, etc., etc.) But that was always kind of hit or miss and piecemeal, not really a focused thing.
Fast forward just a hair more and Coursera and the like have come into being. I started taking the Johns Hopkins sequence on Data Science, and I also took the Andrew Ng class on Machine Learning. That whole experience reminded me "I've always meant to get serious about this maths thing".
Notably I'd never taken a proper course on statistics and probability, so I wanted to fill that gap. So on Coursera I took the first 2 or 3 classes in that Duke "Statistics With R" sequence (I plan to finish the whole thing eventually) to pick up some basic stats knowledge. It also dovetailed well with the first few classes in the JHU Data Science thing, as both use R. And looking back on that, from where I am now, I highly recommend both the Duke sequence (which is more about the stats and less about R) and the JHU sequence (which is arguably more about R than stats). I think they complement each other well, and if you do both you'll learn a decent amount about basic stats.
This is also where I discovered Professor Leonard on Youtube. I was searching for some stats videos to complement the other stuff I was doing, and found his videos. I never did go through the entire Stats class he put up, but I was impressed enough with his teaching style to bookmark his channel for future reference.
Anyway, at some point I hit a lull in things and decided "now is as good a time as any to go back through Calc I with an eye towards working through all of Calc I, Calc II, Calc III and Linear Algebra". I started the MOOCulus course on Coursera, and while I like certain things about it, I feel like the content is too "choppy" since it's broken up into such short segments. That was when I went back to the Professor Leonard channel and started going through his Calc I class. And I'm just now about up to where I was at when I dropped out of school the first time. Only 20 years later...
Anyway, there was other stuff mixed in there too, including offline stuff with actual paper books. But as far as the online stuff goes, I also found Youtube channel called MathBFF that has some really good videos (at least for Calculus topics), and I also watched a chunk of the "Big Picture of Calculus" videos linked to above.
So from here out, my plan is to continue through the Professor Leonard series of Calc I, II and III (and supplementing the videos with problems from dead-tree books) and then move on to Linear Algebra, probably using a combination of Gilbert Strang's videos and the "Essence of Linear Algebra" ones that were posted on HN a couple of days ago. I might also consult the Khan Academy videos on some of this stuff.
And to go back to dead-tree books for a minute... I have this weird obsession with mathematics books. I kindof collect them. I guess because in the back of my head, all these years, I've had that "I'll get serious about maths one day" thing going on. So I'm forever buying maths texts at used bookstores, or on Amazon, or random places. I have shelves and shelves of books on all sorts of mathematics stuff to consult. So my self-learning definitely involves a heavy dose of both online resources and meatspace stuff.
If I had to summarize, I guess I'd just re-iterate that the resources you need to learn a LOT of maths is available online, mostly for free. I mean, there's a TON of stuff out there, including a lot I didn't mention above. And even though I'm mainly interested just in the stuff I need to for AI/ML, I did some poking around on Youtube out of curiosity and found that you can find videos on just about every math topic there is: abstract algebra, complex analysis, topology, group theory, measure theory, etc., etc. It really is an amazing time we live in. :-)
There also used to be a course called Coding the Matrix, I'm not sure if it is still being offered online. The lecture notes form a book of the same title, which is available for less than 10$ (Kindle).
Books are a bit more painful, but forces my brain to actually make sense of abstractions actively instead of passively (which is not always the case on videos, but a lot more probable).
Also, libraries are a good place to reflect.