on mathematics

[coraa]

I have a lot of people on my friendslist who like math and appreciate the beauty of mathematics. I would like to appreciate the beauty of math too! This is a gradual change for me, because through high school I haaaaaaaaaated math, and I was positively gleeful when I got to college because my major and minor of choice required no math classes whatsoever. (I could fulfill that part of my general education requirements with either math or science GEs, and so I went with biology, mostly. Biology and paleontology.)

Anyway.

Here's my background in math, in case it helps. (I get long-winded.) The reason I haaaaaaaated math was that I was no good at arithmetic. (I can hear you all saying, as has been said to me before, 'but arithmetic isn't all there is to math!' I know. Bear with me.) This started all the way back in, like, first grade, and it started because while I have an excellent memory, I am bad at memorization. (They're not the same skill at all, in my opinion.) I remember, distinctly, being tested to find out what math group I should be in toward the beginning of first grade, and being asked 2+3, and then being penalized for counting on my fingers, because I should have had it memorized. I remember, a year later, being so bad at timed multiplication tests that they actually tested me to find out if I had a learning disability. (I didn't; I turned out to be gifted, with no learning disability in math and in fact a very good grasp of the theory behind multiplication and etc. I was just not good at memorizing multiplication tables.) That sort of set the tone for everything: I wasn't much good at memorizing multiplication tables, and I wasn't meticulous enough, and so even though I had no problem with the concepts, I struggled a lot with the arithmetic.

The problem is that if you're not so good at arithmetic, you'll have trouble in pre-algebra; if you're not so good at pre-algebra, you'll have trouble in algebra; and if you're not so good in algebra, you'll have trouble with... everything. By the time we were allowed to use calculators in Algebra II, it was too late: my association with math classes was that they were the classes in which I could totally understand the material and study for the test and still get not-so-good grades because I made arithmetical errors. And that's probably fair, because you actually do need to be able to calculate as well as understand the material, but it put me off the whole topic.

I actually got As in math in high school, partly because yay for graphic calculators, and I did trigonometry (I actually rather liked geometry and trig) and calculus, but I didn't enjoy it: because I had associations that math was the classes where I'd get poor grades without knowing why or how to fix it, they were the classes I liked the least and feared the most, even though by this point I did reliably well at them, and I was relieved to be done with the whole topic when I got to college.

However.

Reading the posts of mathy people on my flist, and having mathy friends in my discipline (being a technical writer means I spend time around lots of mathy types), makes it clear to me that I Missed Something in my desperate attempt to flee arithmetic and its descendants.

So. If you were to recommend a course of math study to an adult who still loathes arithmetic but wants to learn more about the rest of mathematics, what would you recommend? Any particular books? Where would you start?

I would love to learn more.

(Feel free to link your mathy friends to this post, if you think they might have ideas. although not if you think they will mock my lack of arithmetical prowess, because then I will a) ask how their medieval Welsh is these days, and b) bite their faces. ahem.)

Comments

[mindstalk.livejournal.com]

If you like logic and proofs, then yeah Raymond Smullyan books, Euclid, abstract algebra/group theory, or learning programming.

[coraa.livejournal.com]

Thank you!

I took a couple of programming classes in college (101 and 102, just for fun), and loved them and was pretty good at them, if I do say so myself. Perhaps I ought to leap back into my attempt to teach myself Java....

[mindstalk.livejournal.com]

Python's a more fun language in a lot of ways. I don't know Javascript much, but it's good for running lighter stuff in browsers, lighter than Java anyway. You might be bad at C/C++, which punishes not remembering key details.

Scheme and Haskell are less useful but might be a fun challenge; they specialize in functional programming, which is a pretty different mode of thought than Java's imperative and object-oriented programming. Smullyan's To Mock a Mockingbird is actually pretty related. Logic programming is another mode, though I don't know what's good for it these days -- Prolog or Mercury I guess, though spreadsheets are actually related.

[coraa.livejournal.com]

I actually learned on C/C++, and while some elements of it frustrated me a little (pointers! It took me a long time to understand pointers), it actually wasn't so bad because when it broke I could go back and fix it before submitting, which I was fine with. (I was pretty rigorous about self-testing, which of course was a lot of work, but which meant that I could be pretty well-assured of a working program and a decent grade by the time I submitted... which was the opposite of my junior high problem with math.)

But I've heard a lot of good things about Python, so that sounds like a good idea. Or Scheme, maybe.

[thegreatgonz.livejournal.com]

If you want to combine the two a little bit, check out Project Euclid- it's a collection of math problems of gradually escalating difficulty, intended to be solved by shortish computer programs (so you worry about the concepts and the computer does the arithmetic). It's great for teaching yourself a programming language.

[yhlee.livejournal.com]

If you are not concerned with immediate usefulness and want to try Scheme, I highly recommend The Little Schemer--the whole book is sort of in question-and-answer format, talks about common pitfalls, etc. It's funny and it's very accessible, all you'd need is a Scheme interpreter. (It has two sequels, The Seasoned Schemer and The Reasoned Schemer, but I haven't read them yet.)

[coraa.livejournal.com]

Oh, that sounds like fun!