*warning, long rant post*

Recently I have come to realize I am a poor student of mathematics, despite the grades I've made in my classes. I think this is due largely to the lousy instructive education I have received.

When I started high school, I took a geometry class. It was awful; in the entire class, I was not required to do a single proof. It was all memorization. Then in algebra the next year, the teacher started the class by saying, "you probably won't remember any of this material when you grow up, but what's important is exercising your brain." This was in the honors class! Who, with any job remotely related to mathematics, does not remember and apply algebra?! At the end of my sophomore high school year I took classes at a community college, including trigonometry and calculus. Compared to most of the students, I was very smart. I made A's without applying myself at all.

During all this time, I wanted to be an engineer, so I didn't think I actually needed to "understand" all the proofs and theorems I was being taught. But now I have changed majors to mathematics (actuarial science), because I am far more interested in math than engineering. So I currently have a lousy understanding of math. ex: I can quickly solve difficult integrals, but I cannot tell you why an integral is the area under a curve. It is pretty sad really...I wish I gave effort into the wonderful subject when I was younger. Truth be told, I think most students in the U.S. have a similar level of understanding. U.S. math education is pretty bad.

But now that I want to dedicate time and effort to truly learn math, I need to know where to begin. Could some helpful users give me book suggestions, or a "path" to follow? It is clear to me a lot of you are great mathematicians who truly understand the subject. That is what I hope to achieve for myself.

I would suggest picking up some books from the For Dummies Series, or even Schaum's Outlines; Textbooks are also good in explaining the theory. For online resources, if you need a brush up on Algebra and Calculus, Check out Paul's Online Notes.

Remember that MHF is a good place to ask your questions!! Whenever you get stuck, our dedicated staff and members will be willing to help you out!

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Pretty much what Chris said, the 'For Dummies' series are a good place to start, there is a wealth of information on the internet as well though, it's not always necessary to go out spending money on books.

And your a member of the best Mathematics on the web, so you've made a great step in the right direction

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Craig

Thanks for suggestions, I'm not sure that's quite what I'm looking for though. Let me summarize my knowledge a little better:

Geometry: Pretty terrible. I don't have any formal understanding of the subject, other than some knowledge of triangles/circles really.

Algebra: I understand very well. There isn't much "theory" to algebra (the type taught in high schools). So the subject is pretty intuitive to me.

Trigonometry: I understand the basic concepts well, but took shortcuts by memorizing identities and different facts. So it's the theory I'm bad at.

Calculus: I'm good at doing any textbook problem, taking tests, etc. It's just my understanding of the material/theorems that is bad.

So really...what I am looking for is books focused on theory. I have looked on Wikipedia, and it seems that "mathematical analysis" is actually the subject name of what I am looking for. Like a book that starts from basic properties of numbers and works up formally. And in addition, a good geometry book. Thanks again for your help.

For this I strongly suggest you to own a copy of "Calculus" by Spivak.
From wikipedia :

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Isaac

Thanks! I think that is what I'm looking for.