Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up.

EDIT: Could anyone suggest books for someone with a math education that just barely touches on high-school Algebra (got into parabolas, rationalizing, some graphing and functions). This is what I am currently doing: attending high school as a Junior.

Solution 1:

Be honest with yourself about what you do and don't understand. Don't fall victim to "proof by intimidation," where someone attempts to shame you into saying you understand something by implying that you're dumb if you don't. Always ask questions until you really get it. Similarly, don't let yourself move on before you understand something fully; pretty much everything will come back to bite you at some point down the line. If this seems like a pessimistic attitude, it's not - it is simply humility, and humility is the path to genuine knowledge.

EDIT: I just noticed your question about books. How To Prove It is a great transition to more advanced mathematics. After that, check out some of the Dover books, they are all very cheap and most are decent introductions to their respective subjects.

Solution 2:

Buy a huge whiteboard and think of math like a puzzle. Hours can pass by quick with space to scribble and self-motivation. Mathematics has to become a hobby for you to actually come to understand it. Know your basics well, even if it takes a while longer than expected to have a solid standing.

And in terms of books, check Amazon. I surf the web if I've got a specific topic in mind though.

Solution 3:

I would quote this excellent article by Peter Norvig.

It's about programming, but applies to all other domains as well.

Researchers have shown it takes about ten years to develop expertise in any of a wide variety of areas, including chess playing, music composition, telegraph operation, painting, piano playing, swimming, tennis, and research in neuropsychology and topology.

The key is deliberative practice: not just doing it again and again, but challenging yourself with a task that is just beyond your current ability, trying it, analyzing your performance while and after doing it, and correcting any mistakes. Then repeat. And repeat again.

Solution 4:

There is a nice book by Polya "How to solve it". It does not teach particular mathematics but rather "a way of mathematics". It's also quite elementary.

Solution 5:

Practice makes perfect!

Also ask for help from teachers, peers...even have a study group!