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Ask HN: What are the best math sources to learn Machine Learning?
4 points by hackernewsacct on Jan 9, 2017 | hide | past | web | favorite | 6 comments
Hacker News can we generate a list of mathematical requirements for a beginner to understand machine learning? I am specifically interested in beginner friendly sources to: Calculus, Linear Algebra and Statistics/Probability.

I want to take this a step beyond the "Learn Machine Learning through Python/MatLab" approach and make this a "Learn Machine Learning through math" approach but targeted for beginners. If the focus is more on coding and less on math then it doesn't fit what I am looking for.

Whenever I say beginners I am defining it is a smart layperson that is a non-math major. Think of it like a "very smart high school senior that hasn't seen calculus yet" kind of beginner.

So here are my questions:

What are very good beginner friendly introductions to Calculus, Linear Algebra, Statistics & Probability?

Can we generate a beginner friendly list of textbooks, MOOCs, youtube videos, lecture notes, etc. for the above fields?

If you only know of say beginner friendly sources for Linear Algebra, but not the rest of the above fields then that is ok, just list the ones you know for Linear Algebra.

If I am leaving any field of mathematics out (that a beginner should know) please include them and what beginner friendly sources they should start with.




Coincidentally, today is the first day for the coursera course 'Data Science Math Skills'[1]. I've signed up. Hopefully this is what we are looking for.

[1] https://www.coursera.org/learn/datasciencemathskills/home


Thanks for the link. The last two weeks of the course pique my interest esp. the "Introduction to Probability Theory" section. Is this apart of a sequence of courses in data science? It wasn't clear to me if this is a standalone course or apart of a larger sequence.


I'm in that boat... I only took up through Calc I originally and even that was so long ago that I've forgotten most of it. So I'm working on a self-learning plan to go through Calculus (equivalent to traditional Calc I, II, III courses), Linear Algebra, Differential Equations, and Probability / Statistics. I can share some of what I've been using.

1. The "Mooculus" Calc class via OSU / Coursera. https://mooculus.osu.edu/

I've found this to be useful, but the videos are all really short and the content is kind of "choppy". That is, it jumps around quickly, giving small nuggets of content, and doesn't flow super well. Still, there's some good stuff in here.

2. "Professor Leonard" on Youtube. https://www.youtube.com/user/professorleonard57/playlists I'm going through his Calc I sequence now. This is basically a traditional college class, just recorded and put on Youtube. Flows better than the Mooculus class as a result. Leonard is a good lecturer and keeps things interesting. He has videos series on Calc I, II and III, Statistics, as well as pre-calc / intermediate algebra, etc.

3. Gilbert Strang's Calculus lectures on Youtube. https://www.youtube.com/watch?v=X9t-u87df3o&list=PLBE9407EA6... Pretty good explanations of Calculus concepts, at least up to where I'm at (somewhere near the end of the section on differential Calc, just before the stuff on integration starts). Strang also has a very famous series of videos on Linear Algebra, but I haven't gotten to those yet.

4. MathBFF's Youtube videos. https://www.youtube.com/user/mathbff Short videos covering specific topics: how to evaluate limits, how to use the chain rule, etc. Helpful for an alternative explanation of a concept you might need more help with.

5. Khan Academy. https://www.khanacademy.org/ Everything from basic arithmetic up through Linear Algebra.

6. On Coursera there is a series of classes in a "specialization" titled "Statistics with R" from Duke University. I've done the first 3 of those and they've been very useful for both learning Statistics / Probability, as well as help ramp up my R knowledge.

I also have a whole pile of "dead tree" books I consult, ranging from traditional college texts (mostly acquired for dirt cheap at used book stores), to those high-school AP test study guides, to a bunch of books in the "For Dummies" series (eg, "Calculus I for Dummies", "Linear Algebra for Dummies", "Differential Equations for Dummies", etc.), and the like.

Edit:

I almost forgot. If you get stuck, there are various forums where you can ask questions / get help, like:

http://math.stackexchange.com (note, this is different from MathOverflow, which is more for research level questions and answers)

https://www.reddit.com/r/learnmath/

http://reddit.com/r/cheatatmathhomework

https://www.reddit.com/r/homeworkhelp

https://www.reddit.com/r/askmath

https://www.physicsforums.com/


The OSU Coursera course you recommended isn't bad, but the UPenn course I feel is higher quality.

[1]https://www.youtube.com/playlist?list=PLKc2XOQp0dMwj9zAXD5Ll... [2]https://www.coursera.org/learn/single-variable-calculus [3]https://www.math.upenn.edu/~ghrist/


Thanks for the recommendations. Esp. Professor Leonard. Never knew such videos existed.


My understanding is that he covers pretty much everything you'd expect. I think it's just a question of ordering. Different Calculus classes sometimes cover certain things at different times in the sequence. See, for example, the distinction between the "early transcendentals" and "late transcendentals" Calculus courses out there.

If you want yet another take on Calculus, the MIT Calc series stuff is on Youtube as well.

https://www.youtube.com/watch?v=7K1sB05pE0A&list=PL590CCC2BC...

https://www.youtube.com/watch?v=PxCxlsl_YwY&list=PL4C4C8A7D0...

https://www.youtube.com/watch?v=XDhJ8lVGbl8&list=PLEC88901EB...




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