Hello, I am a high school student with a strong drive to learn math. I've taken Calculus 1&2 from my school, but I'd like to learn more on my own. I would like to learn Multivariable Calculus, Differential Equations, Linear Algebra, and discrete mathematics. I looked for online notes and found Paul's Online Math Notes for Multivariable Calculus (tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx) and Differential Equations (tutorial.math.lamar.edu/Classes/DE/DE.aspx). Upon additional searching, I found notes for inear Algebra from Lamar University (cs.cornell.edu/courses/cs485/2006sp/LinAlg_Complete.pdf). Are these notes a good way to teach myself math, or is there a better way? How do I know that a set of notes is a quality comprehensive review of a subject?

Thanks in advance.

## Teaching myself math courses

**Moderators:** gmalivuk, Moderators General, Prelates

### Re: Teaching myself math courses

What ways work vary from person to person, so as long as you have reason to believe the source material is actually correct, you can pretty much try anything for awhile and if it's not clicking, then you can try a different resource. Use of multiple resources also helps to give you a sense for how comprehensive any particular resource is, although you should be aware that where one subject ends and another starts isn't always clear cut, so the same material might be considered a different subject from a different source. Reading the syllabus of the course for which the notes are from can give you an idea of what to expect, and you can compare with other syllabi to see how the scopes may compare (and note that a greater breadth of topics often comes at the cost of depth).

I didn't actually look at the particular sources you mentioned, but for online learning I'm a big fan of MITs OCW, which provides free course notes, tests, exams, lectures and more for a whole variety of topics (I linked math department stuff since that's what you were asking about, but they have stuff in other departments too). I believe Stanford has something similar as well as a few other institutions, and even searching youtube can lead to lots of helpful tutorials/lectures.

For math (and most subjects), be sure to actually try doing problems related to the notes though. It's easy to feel like you really grokked the notes or lecture or whatever, but when faced with actual problems to discover that you don't know how to proceed, so problem sets can be a good reality check (not to mention the more problems you do, the more likely that down the road you'll encounter a similar one where you'll be thankful to have had the experience).

Good luck with your learning.

I didn't actually look at the particular sources you mentioned, but for online learning I'm a big fan of MITs OCW, which provides free course notes, tests, exams, lectures and more for a whole variety of topics (I linked math department stuff since that's what you were asking about, but they have stuff in other departments too). I believe Stanford has something similar as well as a few other institutions, and even searching youtube can lead to lots of helpful tutorials/lectures.

For math (and most subjects), be sure to actually try doing problems related to the notes though. It's easy to feel like you really grokked the notes or lecture or whatever, but when faced with actual problems to discover that you don't know how to proceed, so problem sets can be a good reality check (not to mention the more problems you do, the more likely that down the road you'll encounter a similar one where you'll be thankful to have had the experience).

Good luck with your learning.

### Re: Teaching myself math courses

For university-level online learning, I'd suggest Coursera, which has a bunch of sign-up-able courses from a range of institutions. There's also Khan Academy which covers a huge range of topics.

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### Re: Teaching myself math courses

Hello Chill_Synesthete,

Of course only you will know exactly which areas you are interested in, but your description reminds me a lot of me when I was in high school. So if you're anything like I was, you probably don't know enough about the different kinds of math that exist to even know what kinds of math you should study. (If you think you have a pretty good grip on all the different kinds of math there are, it's a very sure sign that you don't, and I don't mean that in a bad way at all!)

One piece of advice I found extremely helpful (more recently) was a post from a Google programmer. The whole article is fun to read, but the part I specifically recommend you read (like right now) is the section headed "The Right Way To Learn Math".

There are a lot of free courses online. I particularly like the MIT open courseware materials, because you don't have to pay anything and you don't even have to log in or register, and also because you don't have to study all parts of the course if you are only interested in one specific aspect of it. I'm currently studying Mathematics for Computer Science and having a great time with it.

If you do study that particular course, feel free to PM me about it. I've kept all my notes and proofs and whatnot while working through it and wouldn't mind working together on some of it, or helping, or just chatting about the math you learn there.

Of course only you will know exactly which areas you are interested in, but your description reminds me a lot of me when I was in high school. So if you're anything like I was, you probably don't know enough about the different kinds of math that exist to even know what kinds of math you should study. (If you think you have a pretty good grip on all the different kinds of math there are, it's a very sure sign that you don't, and I don't mean that in a bad way at all!)

One piece of advice I found extremely helpful (more recently) was a post from a Google programmer. The whole article is fun to read, but the part I specifically recommend you read (like right now) is the section headed "The Right Way To Learn Math".

There are a lot of free courses online. I particularly like the MIT open courseware materials, because you don't have to pay anything and you don't even have to log in or register, and also because you don't have to study all parts of the course if you are only interested in one specific aspect of it. I'm currently studying Mathematics for Computer Science and having a great time with it.

If you do study that particular course, feel free to PM me about it. I've kept all my notes and proofs and whatnot while working through it and wouldn't mind working together on some of it, or helping, or just chatting about the math you learn there.

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