How to direct a friend's genuine curiosity in mathematics? I recently met up with an old friend, and asked how high up he's gone with mathematics. I said "So, what, like algebra?" He said, "Yeah." I can see that he is genuinely interested in mathematics, but he's in a situation where he can't feasibly get a college education like myself, and I want to point him to a resource on building up his mathematical wit without just saying "Just wikipedia it." There is a build up of concepts that tie together with structure, and I just wonder what this community would recommend as an online resource for building a strong foundation in being able to touch higher level mathematics, say, at a senior undergraduate level. A framework of topic precedence that can be used as a guide. I wanted to lend him my "Art of Problem Solving" book series, which I think does a good job, but I think he's into something more open source and digital. Also, these books were kinda expensive.
 A: This is not a complete answer by any means.  Just one of many ideas.

There are a number of quality YouTube channels out there.  3Blue1Brown is one that immediately springs to mind.  His linear algebra playlist in particular is rock solid and a phenomenal supplement to a textbook.  I think he has one for calculus as well, plus individual primers on a myriad of topics from Fourier analysis to blockchain technology.  Many of them help whet the appetite for rather advanced topics while still being surprisingly accessible to someone with little formal mathematics education. Others, like KhanAcademy, have a wider selection, especially for earlier mathematics.  Search around!
Some reasons I recommend YouTube channels are as follows:


*

*I have a tendency to get bogged down by notation, and unfortunately this notation is rather unavoidable in a pure-text format.  At least for me, seeing a lot of ink on a page can be intimidating, and often it's not even that difficult of a concept.  Being able to watch computer-generated animations or someone drawing diagrams or even just listening to an expert's informal stream-of-consciousness can do wonders cutting through the notational barrier. 

*There are a number of subjects where it's absolutely essential to have lots of visual representations of the mathematics you're seeing; imagine trying to go through vector calculus without seeing many pictures.  This is just one instance where having a professor in an actual classroom can be really useful, but even a professor can't animate drawings on a chalkboard, and some have limited drawing skills.

*It offers yet another perspective on the material being learned.  One should never confine themselves to a single source when learning new concepts.  Often, there are vastly different approaches to presenting a concept, and seeing as many as possible affords richer understanding. Plus, if you get stuck in one source, another might help clear things up.

*Coupled with Math.SE as a resource, one can link directly to the very moment one gets stuck or a question arises.  
Watching YouTube videos, of course, comes with a few caveats.  First, they should be a supplement, not a substitute, for actual textbooks.  And second, it's easy to become too passive.  Don't just watch.  Work problems.  Put pen to paper.  Doing exercises yourself is the only way you're going to internalize what you're trying to learn.  You may think you've mastered something, but all-too-often, holes in your understanding aren't going to become apparent until you're actively doing the mathematics.
A: Maybe you can show him  some good sites for it, for example 3Blue1Brown or Mathologer,these channels mainly focus on the intuition and understanding of mathematical concepts . Khan Academy is also a good site I'd recommend as this also focuses on the way one can solve problems.
Books and  other resources are also a good place to start.
I'll leave some links to sites which are really good and can help improve mathematical understanding .(1)PBS Infinite Series  (2) standupmaths  (3) Numberphile. 
Also, he can always opt for online courses in mathematics , also I'd recommend this Paul's Online Math Notes if he is interested in some good notes.
A: Here are 2 very good resources
http://math.wikia.com/wiki/Introductory_mathematics
http://math.wikia.com/wiki/Outline_of_mathematics
