Math is cool

Miscellaneous and Personal Stuff I Must Share
21

Thanks for the response, js_africanus. I sort of understand a little more what you’re talking about now. But perhaps I should restate my earlier post: the basic, everyday math I would like to become more proficient in I have trouble with because I’m not good with numbers. Seriously, I mean no offense by this, because I can tell it’s a subject you care deeply about, and I respect that, but what you told me there is not anything I really care about or have any interest in learning about. I’d like to become better at… you know, doing quick, slightly complicated division in my head, dealing with fractions and percentages quickly. That’s all. Stuff that’s probably pretty basic to you, but I was never really able to fully grasp. Everything else you talked about means nothing to me. And I do really mean ‘no offense’. I don’t want to come across as saying, “well, that’s just boring”, because it’s obviously not boring to you. Just nothing I care about, personally.

As far as me not being good at arithmetic for ‘no particularly good reason’, well, you may or may not be right there. I’m not sure, which is one of the reason I’d like to try and pick up some of the very basics again. All I know is, in high school, I did pretty well in every subject expect math. And it wasn’t something I just decided one day that I was no good at or that I didn’t need or that I didn’t care about. I really did struggle with it. Senior year, when I was really trying to get all my grades up in anticipation of college, I actually hired, out of my own pocket, an outside math tutor. I remember working with that woman a few times a week. Things would seem to make sense when she explained them, but then come test time… it was gone. Things just didn’t click. The concepts that seemed to have made sense in my head a few days prior were all jumbled again. As I said, I know I wasn’t a stupid person, so it was pretty frustrating. Thankfully, I majored in Creative Writing in college, and got my only math requirement out of the way by taking ‘Intro To Programming’! :smiley:

And today, really, the only reason I want to even relearn the basics is to become a better poker player. I know that probably kills you; you probably lump that in with the ‘poor attitude’ you speak of, and I can’t really argue with that. But the fact is, I just haven’t had the need or desire, other than to use it to play a game. Perhaps it’s hard for some people to understand, but it just simply hasn’t come up in my adult life.

22

Becoming a better poker player is just as good a reason as anything, if that’s what motivates you, Anamorphic. The only advice I can offer for division/fractions/percentages is find the techniques you need to master, then practice, practice, practice. I was a lot more naturally smart than my little sister in school, but she was the one on the Honor Roll. I just drifted thru school. She did it thru hard work and practice. Did I mention practice?

23

I agree with If6, there. Years ago, I picked up an old book filled with basic arithmetic exercises, meant to done mentally. Working through those exercises improved my mental math immensely.

Mental division gets a lot easier when you know lots of multiplication tables. You look at a big number, and you instantly REMEMBER that it divides by certain other numbers. Saves time.

Adding and subtracting fractions requires common denominators, which are also based on multiplication. 1/5 + 5/12 has to convert to 12/60 + 25/60 before you can work it, and it goes faster if you just KNOW that 5 times 12 is 60.

Percentages and decimals are just fractions written differently, and skill in these requires memorization of decimal equivalents of commonly-used fractions. A machinist, for example, might want to memorize all of the sixteenths. (1/16 = .0625, 5/16 = .4375, etc.)

Adding and subtracting anything is aided by the ability to instantly recognize the results of digit-groupings. 7 and 8 always add to 15, for example. I don’t add 7 to my total, then add 8… I see the two of them and just add 15 to my total.

It also helps to work from left to right… do the tens and hundreds first, then worry about the ones, contrary to the way it’s taught in the schools.

24

**All I know is, in high school, I did pretty well in every subject expect math. **

and perhaps spelling :wink:

:smiley:

25

You know what the names for the fourth, fifth, and sixth derivitives of displacement with respect to time are?

Snap, crackle and pop.

I am not making this up.

26

:p:D

27

I must agree, math is pretty darn spiffy. Personally, I am partial to mathematical ecology. It has a nice mix of fuzzy animals, cool pictures and snappy equations. Plus it’s great as a pick-up line (at say, math bio conferences).

Innumeracy is a problem in the US. But I have a bachelors degree in math and was counting on my fingers just today.

That’s snappy! Do you know where I could find a proof?

28

Yeah Short but the guys I’m talking about were in high school and couldn’t tell you what 3x3 is without using their fingers.

:frowning:

29

Does’n look so good cos it’s written in typewriter text instead of proper fractions.

Euler proved line one = line three much to the consternation of Leibniz and the Bernoulli brothers. It had baffled them for ages and euler’s solution was fairly simple. Although he did play pretty fast and loose with the rules.

Not sure when line two came in, but it is the beginning point for understanding Riemann’s Hypothesis and the zeta function. All I have really stated in lines one and two is a special case of the following: (ie, when s=2)

sum over all n (1/n^s) = sum over all primes (1-(1/p^s))^-1

both sides of the equation are statements of the zeta function, which is a fraction of a power of pi when s is even.

I was reading about all this just last wek. I wouldn’t have remembered the specifics otherwise.

proof of line one = line two or the more general statement I gave above is not too tricky, but I’m not sure I could type it easily. You might try www.mathworld.wolfram.com and look up the zeta function.
The above link works well for all of the numberphobes as well. There’s a whole chunk of maths there that I don’t understand, but if you go for the java aplets and animated graphics link then you find all manner of really cool stuff – particularly looking at polyhedra.

30

On the matter of coming to grips with numbers. As a maths teacher I concur wholeheartedy with Vlad Dracul. But even he has swwoshed glibly over the fine details. The whole thing about mathematics is that it is bewildering and bizarre when you don’t understand, and fun and obvious when you do understand. Which explains why people so often fall into the extreme camps of hate it / love it.

It is worthwhile getting familiar with your times tables and addition facts – and I mean really familiar. A little time invested will really pay off.

Another good thing to spend some time on is ways of splitting numbers to make whole tens. In NZ, this is called part/whole thinking. Here’s what I mean:

We know that 6+4=10. We can think of 4 as the compliment of 6. This fact can be used as follows:

6+7 equals 6+(4+3)
and this equals (6+4)+3
which is obviously 13.
Same trick but more involved:

67 + 55 = 67 + 33 + 22
=122

And this is where most of your mental short-cuts come from.

1298 = 12(100-2)
= 12100 - 122
= 1200-24
= 1176

264-192 = (564+8)-(192+8)
= 572 - 200
= 372

etc. With a bit of practice, this is easy to carry off in your head.

In the process of learning you will learn a few properties of some special numbers and then you will invent for yourself your own shortcuts. It will look impressive. And of course if you play rough and ready with the least significant digits you will produce some lightning fast estimates. Also useful.

Have fun.

31

Egads!

After 15+ years, I finally get the reason we played with the rulers and coloured plastic blocks in school! I had enough mental dexterty to do it longhand, so I glossed over that bit.

I didn’t find maths hard in school, but I saw it as rather mundane; I would rather do something more exciting.

32

A random variable is a measurable function from a probability space into a measurable space known as the state space.

A topological space is compact if every open cover of X has a finite subcover. In other words, if X is the union of a family of open sets, there is a finite subfamily whose union is X. A subset A of a topological space X is compact if it is compact as a topological space with the relative topology (i.e., every family of open sets of X whose union contains A has a finite subfamily whose union contains A).

(Music to my ears.)

33

I agree, but I would like to point out that the reason schools generally teach you to start from the lowest place value is that it saves you have to do a lot of unnecessary erasing. For mental arithmetic, it’s not a problem. If there’s a lesson in this, maybe it’s that there isn’t always one single solution that solves everything.

As far as examples of why math is cool, there are just too many. Right up there is the principle of induction.

34

It never happened for me, and it makes me sad. I envy you people who think math is cool, I really do. I wish I’d had some of you people as teachers.

I had a weird situation. When I was 7, we moved from a small city (where I’d been attending a bright, new, modern, highly-rated parochial school) to a farm in the country, just outside a tiny town, where I was dumped into a 2-room country school. This school was out of date even for 1963. The 1st, 2nd, 3rd and 4th grades were in one room, and the 5th, 6th, 7th and 8th grades were in the other. It was old, musty, rusty, drafty, and it even had an open pit, stinky outdoor john! I thought I’d gone to hell. My years there were miserable, and they forever damaged me academically. The biggest damage happened in the 4th grade.

For some reason, I was the only kid in 4th grade that year. The teacher did not want to teach me “special” so put me in the 3rd grade row and had me do what they did. (Aside: I was a voracious reader and was thrilled to find that, in the attic and basement of the farmhouse we moved into, there were dozens of boxes of books, including a complete set of the Book of Knowledge and several encyclopedia editions. I read and read and re-read everything. Lord, if I only had a tiny fraction of what I learned.) As a result of the books, I was way ahead of everyone else in reading, spelling and geography, so I was bored stiff. I’d sleep, or read books, she didn’t care. My parents didn’t know what was happening because I never thought to tell them. What I did miss out on, during that missing 4th grade year, was math, especially fractions and decimals. They tore that school down when I was in the 5th grade, and I jumped up and down in happiness. Even so, I got a reputation as the town idiot when a girl on the bus (who was going to the newly built town school, the one I would be going to the next year) asked me which was bigger, 1/2 or 1/4. Well, gee, duh, that was easy. 4 is bigger than 2, so of course 1/4 is bigger. A first grader wouldn’t know that. A fifth grader should. That officially made me the school Carrie for the next several years (aided by being poor, overweight and shy).

I never lived that down, and I never caught up. I rarely got anything over a D- in math after that 4th grade year and no teachers ever tried to figure out what was wrong, weird, since I was fairly advanced in everything else. In my freshman year, Algebra was required. The teacher just thought I was the most stupid thing in the universe (my Carrie rep was ingrained in teacher and student alike by then, did I mention that small towns suck?), and I never got anything over an F on any paper, quiz, test or report card that entire year in her class, while I was getting A’s and B’s everywhere else. Needless to say, college was out of the question for me, even though it would have been good for me.

I hope this isn’t taken as a thread fart. I just wanted to say that this is why I admire and envy you guys. I always thought it would be fun to think of math as fun, and instead I hate it and revert to feeling like a “stupid” gradeschooler when I even try to do something as simple as figure out fabric yardage. You’re so lucky.

35

Fun with eleven.

Take a three-digit number. When it’s first and third digits added together equal the 2nd digit, the number is divisible by 11.

Ex: 297

2 + 7 = 9 means 297 is divisible by 11.
297 = 11 × 27

In addition, If the first and thrid digits added together equals eleven plus the second digit, the number is divisible by 11.

Ex: 924

9 + 4 = 13 = 11 + 2. So, 924 is divisible by 11.
924 = 11 × 84

For 4-digit numbers, any number with a scheme of xxyy or xyyx is divisible by 11. 2277 and 2772 are divisible by 11.

37 is also a cool number.

Any 3-digit number where all the digits are the same is divisible by 37. 12321 is also divisible by 37.

36

For some reason, when I first encountered the concepts of open covers, finite subcovers, and the definition of compactness, I got this mental picture in my head of open manhole covers. Don’t ask me why. That mental image has never disentangled itself from these concepts, so when I read your post, there were the manhole covers again.

Fortunately, this mental imagery didn’t get in the way of my understanding about compactness. And it is a cool concept.

37

I understand Equipoise. A couple of comments.

  1. Maths was probably never going to be your brightest candle. Not everyone is going to be an arithmetic trapeze artist. (I wish I knew what RTFirefly and ccwaterback were on about!)

  2. Maths builds on itself. It is very hard to build the eighth storey of a building before the sixth is done. Someone stuffs up your fourth grade and it becomes near impossible to make forward progress.

  3. Maths is bewildering when you don’t understand – like a foreign language. And it is very intimidating. So it is easy to react negatively when you are being stretched too far or when someone wants you to make to large a leap. This can add to the difficulty of forward progress.

  4. You’re an adult now. There are no more tests. There are no insensitive bullies on buses. You can learn your own maths at your own pace for your own fun. You have already survived life with the level of maths you have at the moment. You can’t go backwards, but you can get a kick out of learning something new.

  5. I gotta learn some topology. Those donuts and knots and curved spaces have got me intrigued. And I understand that there is something strange about the linking of seven dimensional hyperspheres. It’s always fun to push the boundaries.

38

I know this is basic for most folks, but I was taught this long ago, and it has always stuck in my head.

Divisibility:

2 - the last digit is 2, 4, 6, 8, or 0.
3 - the sum of the digits is divisible by 3, and the summing can be repeated
4 - the last two digits are divisble by 4
5 - the last digit is 5 or 0
6 - the number is divisible by both 2 and 3
7 - see below
8 - the last three digits are divisble by 8
9 - the sum of the digits is divisble by 9, and the summing can be repeated

7 is trickier, but it works. Take the last digit of the number and remove it (so 2541 becomes 254). Now, for the digit that was removed, double it and subtract that from your number (doubling the 1 and subtracting it from 254 gives you 252). If that doesn’t help you, you can repeat the process (here you would have 25 - 4 = 21). At any point, once you have a value that is divisble by 7, like in the example, the whole number is divisible by 7 (2541/7=363).

39

Topology is a fun subject, but it’s also pretty advanced stuff. If you’re going to start, I suggest getting familiar with group theory and basic real analysis. Check out Dover for lots of cheap books.

40

I think around my 3rd grade I read a book Dad had that covered various ways to shortcut math problems. I don’t remember everything that came specifically from that book other then using dots to carry.

Whole/Part thinking was mentioned earlier. I may have learned it from that book or I may have figured it out for myself. I’m just surprised it is a “new” thing, it seems natural to do that.

I also never really learned to memorize my arithmatic tables. Unless I found the combination interesting I don’t have the result memorized. Bad thing is that at the Blackjack tables I tend to either miscount or I take a while to count up the total of the cards in my hand. The good thing is that most every math problem takes the same amount of time and I learned to actually think.