Ask HN: What actually goes into learning math? I don't know where to start. | Hacker News Reader

Ask HN: What actually goes into learning math? I don't know where to start.

8 pointsrfnslyr8 comments

Grade 11 - Pre-calculus is where I last left off. All I remember where tons of graphs of parabolas going every which way and we had to identify them I think by -x/0, xx/+x or something, I legit have no idea.

I want to learn math, but whenever I googled I always had different answers.

Is there a Math road map? Like I'm having trouble understanding even the possible directions, let alone their existence.

I don't know where to start. I'm looking at open courseware on MIT and even the first undergraduate courses are far over my head.

Any help?

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Start with Khan Academy, work from the beginning until the calculus/precalculus sections. (it won't take long for you to blaze through the really early math and get to the point where you're reviewing highschool stuff) Then you'll be at a point to do early calculus and linear algebra courses online.

Thanks. Khan looks good.

I recently went through the stats courses... it was a great refresher from college.

I would definitely second Khan academy. I did this over a year ago and it was well worth the time and effort. I also supplemented with Purple Math. What was great about doing it was that it really filled in gaps in my own knowledge for things I didn't pick up in high school. For example, I know trig well from writing a lot of video games, but for some reason I had never learned about 30-60-90 or 45-45-90 triangles.

My experience is more with applied math (for physics and engineering), which is kind of another world from what mathematicians do. I'm not sure which you would prefer, but if it's the former I recommend checking out the table of contents from Mathematical Methods for Physics and Engineering by Riley, Hobson and Bence(can be viewed on amazon). It has a nice listing of all the topics, mostly in the order you'd want to study them (with a few exceptions). Doubt I'd recommend it as a first book in those subjects for an 11th grader, but it should give you an idea of what's out there.

http://www.amazon.com/Mathematical-Methods-Physics-Engineeri... (click to look inside -> table of contents)

The "other world" that I'm much less well read in more involves proofs and foundations, and would probably start with Euclidean Geometry and Set Theory, then topics like Abstract Algebra, Topology, Advanced Calculus, Real and Complex Analysis, Category Theory, and so on.

I'd also recommend j2kun's blog, which I've found great for a first intro to many topics, though it has a bit of a programming focus: http://jeremykun.com/ As mentioned above, Khan Academy, Coursera, Udacity, EdX and the others are good too, especially since they're free, so you don't have a lot to lose if you get in over your head.

Not sure if this will help, but it can't hurt.

There is plenty of math that does not lie on the academic beaten path (i.e. arithmetic -> algebra -> calculus --> etc.) I would recommend trying to figure out what area of math you are most interested in first, that way you will be enthusiastic about learning it. Once you have the mathematical momentum from that you will probably be able to learn whatever math you need to. A couple of books that helped me to find a direction were Mathematical Ideas[1] and Concepts of Modern Mathematics[2], which cover many different areas with just enough depth to give you a feel for each. If you are wanting to learn math solely for CS I would also recommend something like Schaum's Outline of Discrete Mathematics[3].

[1]http://www.amazon.com/Mathematical-Ideas-Edition-Charles-Mil...

[2]http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...

[3]http://www.amazon.com/Schaums-Outline-Discrete-Mathematics-R...

I suggest equipping yourself with some mathematical computation software. Mathematica is my favorite. There are some free, opensource alternatives like ipython which seems to be pretty popular lately. It helps to grasp things much more quickly by simply playing around with stuff. And you also get to write some code as a bonus. Say when I was learning economics I'd simply code all the concepts and charts in Mathematica and then play around with different input values to see what happens. mathworld.wolfram.com is a great resource for understanding mathematical concepts, very short, fairly formal descriptions with references. Helps to expose yourself to mathematical language even if you're confused at first. Wikipedia articles tend to be too long and all over the place.

Sounds like a startup opportunity. Like Kumon, but online and free. Or does it have to be free?

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