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Shameless plug, but I try to explain math concepts on my blog. Here's an example for e, which eluded me for a while:

http://betterexplained.com/articles/an-intuitive-guide-to-ex...

My goal is to explain ideas as I wish they were shared with me: informally, with the primary focus on intuition (there are plenty of places to practice the mechanics). Hopefully it can come in useful for you.

I just wanted to say that your explanation for e is excellently done. I found it incredibly helpful - it was exactly the kind of intuitive, step-by-step explanation I was looking for. I hope that you're planning on releasing more content.

Thanks, really glad it was helpful. I'm planning on going back and covering all the math I thought I'd learned in school :).

This was true for me, and partly out of frustration of this I picked up a major in math in addition to comp sci so I could get through more math heavy computer science books.

It depends what you are reading, but a good discrete math textbook provides a lot of groundwork for mathematics commonly used in computer science, but expects little in terms of prerequisites, so notation is usually explained.

At some level, learning the fundamentals is just necessary, but for computer science discrete mathematics and linear algebra (the basics of which are easy and also don't have much in terms of prerequisites) will get you far.

On the other hand higher math is ruthlessly cumulative. If you find that you need to understand Lagrange multipliers, for instance, you'll see they relate to the gradient, which has its own symbol, which is defined in terms of partial derivatives, which have their own symbol, which relates to limits of vectors, which have their own symbols and notations, etc.

I wouldn't say that it is just higher math. As a high school student, here is my path of e^ix.

Physics 1 Advanced, Simple Harmonic Motion is being taught. When told to find a case where the second derivative of a function is a negative constant times the function, I think e^ix. The answer is sin(x), but Euler's equation now makes sense. The most beautiful equation now makes sense.

A month later, glancing in a book of useful mathematical equations, I see sin(x) = (e^ix - e^-ix)/2i. Hyperbolic trig suddenly makes sense, which is useful over a year after finishing it. The weird equation for the normal curve from statistics starts to make more sense, because e^(-xx)=(e^(ix))^ix, which helps explain the 1/sqrt(2pi) weirdness. I start to understand why the most beautiful equation has its name.

I think that most math is cumulative, but only some parts are hard enough to make you notice it.

The best resources for learning math are textbooks. Learning math from pages on the internet is difficult. Mathematicians don't have quite the strong online presence that programmers do so the online literature suffers.

Textbooks are fantastic, though. They are written to be self contained and will start at the beginning (usually with an introduction to fundamental subjects such as set theory). If you're serious about learning math, they are the way to go.

This is a good place to start when you see a symbol that you don't know.

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

I really like "Concrete Mathematics". It has nice, interesting problems, a very readable style, and introduces all notation used. It also has well written solutions to all of the problems.

That said, I read the book after I had a math degree, so while it seems very accessible (more so than most undergrad discrete math books), perhaps someone who read it as an undergrad can comment.

I got my BS in engineering (electrical), managed to scrape my way through all the hard math classes, but never really had a firm grasp on any of it. A bit later on in the real world, doing some signal processing work, some of it started to snap together. But then I read the Structure and Interpretation of Computer Programs. Which I found to be more math heavy than any other prob books I'd read previously. But the way everything was describe, and laid out in the context of programming, all my past math just came streaming back, and suddenly made sense. It was like that "a-ha" moment, times 1000.

I don't know what the point of my ramblings are. I guess math finally made sense after learning programming first, much like yegge proposes in his post. But I had the basics down first, and I was at least familiar with the concepts.

Amen.

Mathematical notation is optimized for symbol manipulation using a pen and paper, not communication of information. Even to us programmers, it's a slew of one-letter variable names that very rarely seem to have the same meaning.

Furthermore, those single-letters are not from a character set that has been stuffed into our heads since we were 3 years old, so there's an amount of translation going on, similar to the process of learning a foreign language (hear spanish -> translation to english -> process thought -> generate response in english -> translate to spanish -> speak spanish vs. hear spanish -> process throughout -> speak spanish).

Bret Victor's project seems to be attempting this a little bit: http://worrydream.com/KillMath/

Wikipedia is a fantastic resource, but it is first and foremost an Encyclopedia, a reference. It has many times helped me refresh my memory or helped explain something I read first in another context. But it is not a good place to learn a brand new subject.

There are many good resources to learn math, most in the form of books (some of which have digital versions). Personally, I find it best to find a subtopic that interests me and dive in. Though I will say that I would recommend "Chapter Zero" to most people wanting to get back into math after a long break.

Yes, Wikipedia has it's advantages as an encyclopedia.

I simply mentioned it here since Steve advocates just diving in and following links on wikipedia as a way to learn a subject.

This might be a great way to find out what stuff is out there to learn or for somebody more familiar with Math to get a synopsis of a topic but as a learning resource for a newcomer to any particular field it seems likely to reduce you to a jibbering wreck very quickly.

Completely agree.