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Ask HN: How to learn math from zero for adults?

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Re: Ask HN: How to learn math from zero for adults?

#71
Pretty sure a lot of people in the comments have already suggested helpful online resources however I'd recommend you start right where you left from; your mid/high school textbooks. I'm kind of old-school and I think a pencil and paper approach w/o online distractions is how you really get closer to understanding math.

Of course you can use various tools (e.g. Wolfram Mathematica) for any fancy visualizations and maybe some tedious calculations. Just don't rely too much on them while learning the fundamentals (don't skip these boring "find the following indefinite integral" problems).

Re: Ask HN: How to learn math from zero for adults?

#72
post #70

I've done this and would echo the good advice you've already gotten about Khan Academy but I think the comments in this thread are skipping over the most important part: pace. Work slowly. Don't move on until you really "get" the concept you're working with. Some topics might "click" right away and others might take weeks of bashing your head against the wall until your brain makes sense of it. That's okay. It can de…

I'll just mention: From a scientific perspective, this is absolutely the wrong advice. If you couldn't understand something yesterday, that's very good evidence you won't make sense of it today. You should work hard, go deep, and try hard problems, but if you fail to understand something after putting in the effort, just move onto something else. Learn a few unrelated things, and come back. Much of the time, if you c…

To me, this has been the largest advantage of learning things at my own pace instead of in a classroom environment. Even as a student I recognized early on that topics that'd stump me would often click months later. By then it was too late for my grade, but I'd go back and realize that other things I'd learned in the interim made it easy.

So now when I find something blocking me, I just go learn something else instead. And what do you know, some combination of more wisdom, broader knowledge, or perhaps just a different mental state often works.

Re: Ask HN: How to learn math from zero for adults?

#74
The short answer: Go to https://www.khanacademy.org/. Click "Courses" on the top left. Start working your way through the pre-calculus course. Review Algebra if you're struggling with its prereqs. Continue down the course list (Jump around as required) until satisfied.

Re: Ask HN: How to learn math from zero for adults?

#75
Coincidentally I'm doing the same thing right now. The plan I'm pursuing is to design a multi-month course in a particular mathematical subject I feel I need to learn, as if I was going to teach it to someone else. I would need a course syllabus as a framework for the material (in my case, this is something called complex analysis, because I need to understand how it all works, and unfortunately neglected it in the past).

Step One: Find some good source material. Many people have suggested Khan Academy, in my particular case I've discovered this excellent Herb Gross lecture series, 'Calculus of Complex Variables' provided via MITOpenCourseWare. Then, review all the source material and make a list of the topics:

Part I: Complex Variables:

The Complex Numbers; Functions of a Complex Variable; Conformal Mappings; Sequences and Series; Integrating Complex Functions;

Part II: Differential Equations:

The Concept of a General Solution; Linear Differential Equations; Solving the Linear Equations L(y) = 0 with Constant Coefficients; Undetermined Coefficients; Variations of Parameters; Power Series Solutions; Laplace Transforms;

Part III: Linear Algebra:

Vectors Spaces; Spanning Vectors; Constructing Bases; Linear Transformations; Determinants; Eigenvectors; Dot Products; Orthogonal Functions;

Step Two: Plot a timeline. Here I'll give myself one week per lecture. I'll set aside 1-2 hours per day, at least four days a week, to work on the material. This might be inadequate. Staying motivated without having some external pressure will be a bit of a problem, but noting that from the beginning helps.

Step Three: Devise problem sets to test my understanding of the material. Here is where having a good teacher on hand would be invaluable, but that's not an option, so I'll have to find example problems. One option is to find a complex analysis textbook somewhere, and also find its solution manual, and use the problems provided there. Having the solutions around to check results can be very useful. A websearch like "complex analysis problems and solutions site:.edu" turns up a lot of results, just look for the simplest introductory ones (i.e. not the advanced proofs!).

So, I think this is the way to go for self-learning in math. If you have a more introductory level subject, say Linear Algebra (w/o complex), or Differential Calculus, just try to do the same thing.

P.S. I find Jan Gullberg's "Mathematics, From The Birth of Numbers" to be a great overview of the whole mathematical world, kind of like a guidebook: https://www.goodreads.com/book/show/383087.Mathematics

Re: Ask HN: How to learn math from zero for adults?

#77
Some good links have been posted. I'll post another, but it's just the first link I saw for what it is I think you should learn first: the Distributive, Associative, and Commutative Laws. They're taught in middle school, and easy to get. But you need to get them _deeply_. Spend hours internalizing them. Play around in a spreadsheet, making 2 or 3 formulas at a time that all do the same calculation but look different because you distributed, associated, and commuted the cell addresses differently in the formulas. Learn them so well you might forget the names but you can't forget the concepts, ever. Make them part of your being. https://www.mathsisfun.com/associative-commutative-distribut...

Re: Ask HN: How to learn math from zero for adults?

#79
post #28

I was a C student in high school. I never took a math class beyond basic algebra. I started from Khan Academy's first exercise when I was 33 years old. It seems silly looking back that I was solving problems on the number line as an adult. At that time, around 10 years ago, Khan Academy had excellent coverage through trigonometry and single variable calculus. Once I reached that point I went to my local community col…

What kind of job do you go into with a math degree?

Re: Ask HN: How to learn math from zero for adults?

#80
I'm studying math at Cambridge University right now, and a lot of resources for our courses are available for free online. I do think that learning on your own is just not the same as learning for a degree, but if you have the motivation then you may find it useful to follow along with parts of our course.

Dexter Chua was a Cambridge math student who started in 2014, TeXed all his notes and shared them on his website [0]. More people have followed in his footsteps, and you can find most of them by googling `Cambridge math notes site:srcf.net`. Many professors also put notes up on their websites, which can also be found by googling `Cambridge math notes`. I find that for many courses the notes are just as good as lectures, even notes written by students, and sometimes they're even better. They're certainly a lot faster.

You'll probably want to start with our first year courses, which are designed to take bright highschoolers and teach them how to think like mathematicians. If you're interested in the math of machine learning, you'll probably want to look at our courses on linear algebra, probability, optimization, and statistics.

[0] https://dec41.user.srcf.net/notes/

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