I want to understand Mathematics!

Cynic · Post by **Cynic** » Tue May 03, 2011 4:53 pm

Despite the fact that I'm able to addition/subtraction/multiplication/division in my head, I am still quite uneducated when it comes to math. If necessary, I can do some statistics after spending a day or two going over my old textbooks. But I still seem to have a problem with generic concepts.

I was wondering if there's a book or series of books that breaks mathematical concepts to the absolute basics and then slowly builds them up to explain more advanced concepts and ideas.

A primer isn't what I want as a primer basically necessitates that I already have a decent understanding of a lot of math. Any suggestions?

Ancient History · Post by **Ancient History** » Tue May 03, 2011 4:57 pm

You could try Bertrand Russel's The Principles of Mathematics, which is a good start.

Juton · Post by **Juton** » Tue May 03, 2011 6:47 pm

I learned a lot about math by working on projects that interest me. Learning about how to do simple things like calculate the probability curve of 3d6. It comes down to practice and you'll have an easier job remembering if you are doing questions that interest you instead of problems out of a book.

Doom · Post by **Doom** » Tue May 03, 2011 7:01 pm

Definitely, practice is key to 'learning' mathematics.

One way to get practice painlessly is to get motivation.

Since you're here, I'll bet games interest you. Pick up an electronic Yahtzee game ($10, give or take), and practice doing probability calculations as you play. When you start to get to problems that are tough for you (eg, chance of rolling a large straight when you need two particular numbers), that'll motivate you to get "Statistics for Dummies" or "Probability for Dummies", or an actual textbook. Keep at it until you know all there is to know about Yahtzee...or some other game that interests you.

When it comes to general learning of math, I favor textbooks (heavily biased, of course); you can often get very old textbooks in used bookstores fairly cheap--math doesn't change much over the years, old books are generally as good as new. Again, pick a topic that you have a specific interest in...if you're a gamer, I reckon that'll be probability.

If you're not sure, try getting a book called "Discrete Math" or "Finite Math". Books with titles like that usually cover half a dozen easily accessible topics. Basic math, basic probability, basic statistics, basic set theory, basic logic, and a few other things. They're good books for a dilettante who wants to learn math without necessarily going hog wild.

Lago PARANOIA · Post by **Lago PARANOIA** » Wed May 04, 2011 1:00 am

If you want to learn a math topic that's fairly difficult, impressive-looking, and only requires high-school algebra or precalculus to start with you can learn Linear Algebra. It's actually kind of fun for me before they started tossing differential equations into the mix because it's like learning a puzzle. Cramer's Rule and Gaussian elimination is also really useful in problem solving. If you learn it and some trigonometry then precalculus will be a breeze.

Granted, Linear Algebra does have a (very, very) steep wall after you've learned the basics of linear (in)dependence, determinants, orthogonality, span, basis, and eigenvalues/vectors where you will need to learn multi-variable calculus and differential equations to get any further.

Maj · Post by **Maj** » Wed May 04, 2011 5:48 am

What approach are you talking about?

Because people can always refer you to cool stuff that serves no apparently practical purpose like Donald in Mathmagic Land that talks about how math shows up in life. It's already on the indoctrination list of watching material for my son.

Or maybe you know about stuff like solving simultaneous equations in algebra or some other such topic and you just want to know what the hell you're gonna use that for and why on earth you should learn it.

It may behoove you to study math from a historical standpoint to learn what sort of situations required the invention of the various maths that we take for granted in modern schools.

Surgo · Post by **Surgo** » Wed May 04, 2011 6:05 pm

Cynic wrote: I was wondering if there's a book or series of books that breaks mathematical concepts to the absolute basics and then slowly builds them up to explain more advanced concepts and ideas.

Probably the best book for this is one written by one of the professors where I went to school, called Proofs and Fundamentals.

It's for a course that you're basically expected to take after Calculus, where the "actual" college math starts.

Disclaimer: That was the first course I took at Bard (though not with that professor), I was a math major for 2 years, and I'm pretty good at math.

DSMatticus · Post by **DSMatticus** » Wed May 04, 2011 6:43 pm

I personally went into computer science. I am horrible at anything beyond the scope of Taylor Series, but I've learned how to model behavior of systems and objects mathematically, and then analyze those models. Which I've always found more important than complex mathematics itself. Then again, that may be because I'm in computer science. That's sort of a tautology. "As a programmer, I find knowing the sort of math programmers have to do the most useful."

But yeah, I seriously have to recommend dabbling in computer science to everyone - just being able to structure high concepts in mathematical ways is a totally revolutionary skill you can use virtually everywhere.