Get the book "Thinking Mathematically" (http://www.amazon.com/Thinking-Mathematically-J-Mason/dp/020... non affiliate link) which exposes the process of how mathematicians think, using simple problems. You can then adapt the process to your preferred level of problems. Also learn proof technique (Velleman's How to Prove it" is a good book for this) and doesn't make any assumptions of mathematical knowledge.
Ask HN: How can I discover math?
11–20 of 24 posts
Re: Ask HN: How can I discover math?
#12Find a problem that piques your interest, then learn the math that's relevant to the problem. You can choose a problem from most any subject, like math, physics, or economics. Having a problem that piques your interest--something to work toward--is a good motivator.
How would I go about finding said problem? Sorry if this seems stupid. There is no real problem that piques my interest right now perhaps because I don't really know the field all too well. I just want to enjoy learning math and get better at solving problems.
Actually, this is what the book "Who Is Fourier?: A Mathematical Adventure" is about. It's the adventure of a group of families who wanted to learn more about languages, which led them to sounds which led them to learn about Fourier transforms. It's a lot of fun and it actually has real math that you often get to learn in a signal processing class in college. While it is very focused, this book and the approach will pique your interest in other topics.
Re: Ask HN: How can I discover math?
#13You asked about beauty and history, with an idea on how to discover... personally, I started with "The Math Explorer: A Journey Through the Beauty of Mathematics": (http://www.amazon.com/gp/product/1591021375). That book got me hooked and from there I went on to pre-cal studies at university, eventually completing sequences in discrete structures, probability, up to and including calculus III, a level I never imagined I'd get to. That book was literally my starting point since I never took high school math seriously nor was I any good at that level. I think it'll serve you well considering the level at which you're at, as it did me. I've reread that book four times to date and still enjoy it.
Re: Ask HN: How can I discover math?
#14The one that made me truely see the beauty of maths:
Hallucinogenic drugs - due to the hallucinations basis in geometric shapes and patterns.
Not really useful for teaching yourself K-12 math however for the beauty of it nothing better
Re: Ask HN: How can I discover math?
#15Hijacking the thread here, but could someone quickly recommend a college-level calculus book?
Re: Ask HN: How can I discover math?
#16Hijacking the thread here, but could someone quickly recommend a college-level calculus book?
Spivak's Calculus, http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098... is a good bet. But it's very theory-involved.
Re: Ask HN: How can I discover math?
#17let's start with "how to solve it" (g. polya), if you love to learn the thinking of math.
Re: Ask HN: How can I discover math?
#18Find a problem that piques your interest, then learn the math that's relevant to the problem. You can choose a problem from most any subject, like math, physics, or economics. Having a problem that piques your interest--something to work toward--is a good motivator.
How would I go about finding said problem? Sorry if this seems stupid. There is no real problem that piques my interest right now perhaps because I don't really know the field all too well. I just want to enjoy learning math and get better at solving problems.
It depends on where your interests lie. Math is all around us and is involved in most everything we do, so any subject will work.
When was the last time something made you stop and think "that's cool--how does it work?" What was it and what about it caught your attention?
Just live your life and something will eventually catch your eye. Every "huh, that's interesting" moment is an opportunity to dissect it and learn the math that's involved.
Re: Ask HN: How can I discover math?
#19One book I'd recommend is "1089 and all that" (http://www.amazon.com/1089-All-That-Journey-Mathematics/dp/0...).
I've bought copies for friends and family whose maths backgrounds range from school to degree level and they've all enjoyed it.
It's not a textbook, more a conversational account of a few topics the author has found interesting through his life from a young boy to an Oxford don. It's very readable and the author's delight in maths and problem solving shine through
Re: Ask HN: How can I discover math?
#20It will only teach you a small bit of math (i.e. Trigonometry) but try programming a little 2D rocket ship game with some physics and movement etc. It can be fun and you will get a better feel for the maths involved. don't use libraries. Use javascript with canvas - easy as pie.