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

[yhlee]

If unhappy associations are likely to be a problem, I recommend looking at something like discrete math. I used to have a textbook around here on loan but darned if I know where it is.

Are you looking to learn to do the math or to learn about the math?

For a general overview of what-it-is-that-mathematicians-do that's aimed toward the layperson, Philip J. Davis & Reuben Hersh's The Mathematical Experience is pretty good, if dated. A couple other pop math things that don't teach you how to do the math: Ivars Peterson's The Mathematical Tourist is exactly that (with lots of pictures), along with its sequel, Islands of Truth. James Gleick's Chaos is about the birth of chaos theory and is very fun in its own right. The Diagram Group's Images of Infinity is a very cool children's book about transfinite numbers.

For learning-to-do-math, you may have some luck with books on problem-solving--you can do a lot of interesting math without having a deep background. I have not finished reading either of these books because my attention span sucks like whoa, but Ian Stewart's Concepts of Modern Mathematics is fairly user-friendly, and it's a Dover paperback for $13, which sort of recommends it to me all by itself. You might also enjoy Thinking Mathematically (focus on problem-solving) by John Mason with Leone Burton & Kaye Stacey, which...actually, I now feel like working through this and making comments as I go, if that would at all be helpful to you. (Although I might do it anyway.)

I will point to this post because I do know some people mathier than I am who might have things to say. :-)

[coraa]

I think at this point I have enough distance from my junior high frustration that I don't think unhappy associations will kill it for me, but discrete math still sounds like a good idea.

And I'm interested in both learning about the math and learning to do the math, although I will probably start with learning-about-the-math because that will give me an idea of why learning-to-do-the-math is cool, hopefully!

Thank you for the recs; they look very good (and the library has several of them, hurrah!). And I would love to see you work through Thinking Mathematically; it'd be fun to work through it myself and then see what your comments were as well.

And thank you for the signal boost. :)

[jazzfish]

Ditto on The Mathematical Tourist.

You also may be interested in (warning: pdf) A Mathematician's Lament, on the deplorable state of math class. The part that really struck me, that made me think "i /like/ math!", was from the bottom of page 3 ("For example, if I’m in the mood to think about shapes") through the top of page 5. That's exactly the sort of pattern-matching and -finding that I adore, and that got squashed out of math for me ages ago.

[coraa]

Ooooooh yes. Thank you for the link. That's painfully accurate as to my experience of junior high/high school math.

reposted to cut the personal details...

[cathexys]

I concur on the discrete math. That was my first thought as well. You might actually try formal logic, which gives you a nice intro into the beauty of math aspects but is often taught in philosophy departments, so... :)

Re: reposted to cut the personal details...

[coraa]

Thank you!

I actually had a formal logic class in junior high and loved it to pieces. I ought to pick that up again.....

[viridian]

I have no suggestions, but I wandered over here from someone on my flist and will be stealing recs from people because your math experience sounds exactly like mine.

I've often wondered if I have discalculia, and they just hadn't really discovered it when I was in grade school/early jr. high & having the most difficulty. I was also at the top of my class in every other subject, my grades only really suffering slightly when I had to work with mathy concepts, like in chemistry and physics. The result is that I'm kind of phobic about math. It makes me anxious and I literally had the same problem as you, where I would understand the concept as it was being taught, think that I understood it well enough to take a test, and then get wrong answers and have no real idea why. I could often do the same problem twice without getting the same answer, and then have to try a third time to figure out which one was correct. It sucked.

[telophase]

I had problems with math, and as my mom was a math teacher, it was more annoying. than usual. :) I think my big problem was that I don't learn well unless I have a thing I want to do with this knowledge: I never thought I was a programming-type person until I had a pressing need to create a database-driven dynamic website, and then it turned out that I'm a perfectly fine programming person. So learning math was hard because I never saw the point of doing this thing, and the vague "but you'll need it later!" never really fit, because even though I could conceptualize needing math as an astronomer (or one of the other things I wanted to be as a kid), I couldn't grok the reality of it.

Later on in college, when a friend learned I was majoring in a field that didn't require me to take calculus, he was aghast at the concept that I wasn't taking it anyway. I said "When will I ever need it?" He said "Well, if you wanted to fill the fountain in front of the student center with Jell-O, then you'd need to be able to calculate how many boxes of Jell-O you'd need."

I stared at him for a while, then solemnly promised that if I ever wanted to fill the fountain with Jell-O, I'd pick up the phone and ask him how many boxes I should buy.

[coraa]

Yeah, I think a lot of my trouble in high school was math anxiety: by that point, with the help of a calculator, I could do the work, but the anxiety of 'I may get this wrong and not know why' made me hate the subject.

I also remember doing the same problem several times, in that 'if I get the same answer twice, that's probably the right one' way.

[djkittycat]

My wall in math came in statistics and calculus. I could do computation, but I could not do all the graphing shapes and such very well. I was bad at econ for the same reason. I could not for the life of me figure out how and when to move the graph of supply and demand. Maybe I wasn't meticulous enough, I don't know. But I can't do statistical analysis using a graph. It gives me a headache.

You can have a learning disability and also be gifted at the same time. They are not mutually exclusive categories. In fact, people with learning disabilities are also often gifted in some other way.

I am wondering what you do when you have to half or double a recipe. To me, cooking is about math. I guess you have a calculator in the kitchen, right? I have seen pastry chefs using calculators on tv.

Anyhow, for math books, I'd recommend Flatland. It's about geometry and largely philosophical.

[coraa]

Sorry, I was unclear: I was tested as gifted in mathematics, as well as in language. (That sounds like bragging, and I don't mean it that way [I may have technically been gifted but I still sucked], but I think it's important to note that this kind of difficulty with calculation and so on isn't just restricted to people with learning disabilities; it's possible to put someone with plenty of aptitude off math that way, too.) My problems were all skill-based, not aptitude-based.

EDIT: Although, now you mention it, while I did peachy on the math-and-logic problem-solving sections, my weakest part was always visual/spatial intelligence, which might be related. Dunno. I did always do okay in geometry despite that, but I think that was just because I got on well with proofs.

When baking, yeah, I use conversion tables and a calculator. When cooking, I eyeball most things anyway (I cook by ear, mostly), so the math of it doesn't matter.

And thank you for the rec!

[ursula]

William Byers' book How Mathematicians Think is interesting & readable. It talks about the role of ambiguity & paradox in creating mathematics. And sexy things like infinity.

[coraa]

Yay, thank you for the rec!

[rho]

I'm not entirely sure who to suggest, and mainly wanted to comment to cheer you on. I think it's fantastic that you're willing to give maths another shot, and I really hope that you enjoy it as much as I do.

That said, I will offer a tentative recommendation for Ian Stewart's books, particularly Professor Stewart's Cabinet of Mathematical Curiosities. It certainly won't teach you how to do maths, and it won't even teach you a whole lot about maths, but it just may teach you how to embrace and appreciate maths.

[zeborah]

I've recently come across the "Manga Guide to..." series, which includes Statistics and Calculus. I haven't looked at those ones myself but have been browsing through the physics one which is set at a basic level and explains Newton's laws with tennis balls and roller skates. Might be worth a look at if you think you'd like that sort of thing?

[madduckdes.livejournal.com]

My little bro is actually pretty fun to talk to, and very into "eh, and the rest is just arithmetic" summaries once the conversation stops being theoretical. Maybe we can have a hang out next time he comes to visit.

I've been meaning to read this book
http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach
forever and keep failing to make the time. Maybe we could read it at the same time and talk about it.

[coraa.livejournal.com]

Ooh, that sounds fun! Both halves of that, I mean.

[tedeisenstein.livejournal.com]

1) Jerry Pournelle (s-f writer) said he became a psych major in college rather than physics because every time he did the problems, he always got the wrong answer. Years later, when good calculators came out on the market, he went back and did more physics-textbook questions - and got every one right. Turns out he understood the concepts perfectly but that he couldn't add or multiply worth a damn.

2) If you want a gentle introduction to various mathematical concepts, try Fantasia Mathematica (Clifton Fadiman, ed.); it's full of short stories and poems all with a mathematical backgroud. I'm sure Isaac Asimov has something, too, if you want a nice, gentle approach. George Gamow, back in the 1950's (give or take a decade) wrote a decent broad-concept book called (if memory serves), One, Two, Three, Infinity...

More recommendations will have to wait until I get back home and can look at the maths-and-sciences section of my library.

Mind you, my father was a math major as an undergrad and physics as a grad student, and I was the only one in my high school class ever to get hundreds on algebra tests, so I may find the above books somewhat easier to read than you, but they're also ones I recommend to friends as good reads even if they're not reading them for the math.

[coraa.livejournal.com]

1) That's me, pretty much. I'm perfectly capable, I just don't memorize lists of things well, and I'm not meticulous enough to calculate right every time. Things got so much better with a calculator.

2) Thanks for the recs!

[avani.livejournal.com]

This may seem silly, but we've been having a lot of fun reading Euclid's Elements lately. It is basic, but still requires thought.

Discrete math is fun and good for parlor tricks :P This is the book used at Mudd, which is a pretty awesome intro and something I'm sure some Mudder (maybe Pava?) up there is likely to have handy.

[coraa.livejournal.com]

Doesn't sound silly at all! Of course, I do love really old books. ;)

I've gotten a few suggestions for discrete math, so I'll definitely look into that. Thanks for the rec. :)

[sidhebaap.livejournal.com]

There's two menus to select from. 'Learning about math', and 'learning math'. (But you can order from both!)

For learning about, you might look at Nahin's An Imaginary Tale, or Havil's Gamma, or Wilson's Four Colors Suffice. You probably can't go wrong with Martin Gardner, either. Garden path from those, and see what catches your interest. Perhaps To Mock A Mockingbird by Smullyan, too. If you want to edge sideways into things, maybe look at something like The Physics of Birdsong.

For learning, there's a quote I like, but can't pull up. I think it was Paul Halmos who said the way to learn a lot of math is to read the first chapters of a lot of different books. :)

But the key to everything else is a little bit of set theory, and a little bit of basic logic. 'Enough' is in the first chapter of any junior/senior math text, probably. Enderton's books on logic and set theory are fun/good, too.

Another thing to look at would be an 'intro to proofs' book - something like Schumacher's Chapter Zero or Rotman's Journey into Mathematics. They use little pieces of a bunch of different topics as a playground to learn about doing proofs.

If you want something specific, I'd recommend abstract algebra. Gallian is an easy/common textbook. It would probably be okay to start with, even without the previous mentioned stuff.

Good luck, and have fun!

[coraa.livejournal.com]

Thank you! This is a great set of recs. (I do want to do both 'learning about' and 'learning to,' but I think I'll start with 'learning about' in order to find out cool things and motivate myself. :) )

Yay!

[sartorias.livejournal.com]

You might enjoy the phenomenology of physics.

[coraa.livejournal.com]

Oh, good idea, thank you!

[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....

[porfinn.livejournal.com]

This is a delightful post! Thank you.

[triath.livejournal.com]

Most people here are recommending fairly rigorous math books. If you want to enjoy the beauty of math, I highly recommend the book "The Joy of Mathematics" and "More Joy of Mathematics". They're pop mathematics books that will introduce you to mathematical concepts that will knock your socks off. Short, sections that will make you think enough to put the book down in wonder for awhile. At least I remember loving this book when I was younger and it made me want to study math. I really hope that it isn't written at too low of a level, I haven't looked at it again and not every book holds up.