## I hate math notation!

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Darryl
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### Re: I hate math notation!

Zach 739085133 wrote:One thing I would change if I had the power would be to do away with the symbol π, and use a single symbol to represent the ratio between a circle's circumference and its radius. (The number we call 2π.) For this post let me use ❖. That way when you are learning trigonometry in radians, a quarter of the way around the circle would be ❖/4, halfway around would be ❖/2, etc.

Actually, while it would make it slightly easier to relate to parts of a circle, it makes a lot of things far more complicated. Area becomes (❖/2) * r^2, and many other formulas become unnecessary fractions. With pi, most commonly used functions are whole multiples.
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Zach 739085133
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### Re: I hate math notation!

Cool. Sixth post. I can post links now. Michael Hartl has proposed τ for the constant, and I'll defer to his site, tauday.com, as well as the article π is Wrong! (pdf) for explaining the advantages of this symbol.

Last edited by Zach 739085133 on Thu Jan 27, 2011 3:25 am UTC, edited 1 time in total.

cjmcjmcjmcjm
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### Re: I hate math notation!

Zach 739085133 wrote:I agree that the inconsistency between [imath]sin^{-1}(x)[/imath] and [imath]sin^{2}(x)[/imath] is unfortunate. Even the name "inverse sine" is regrettable because the sine wave is not invertible. We work around that by inverting a small part of the curve. For those reasons I always use [imath]\arcsin(x)[/imath], even when scribbling notes on my own.
I always used [imath]sin^{-1}(x)[/imath] because that was what was on my calculator until I took calculus and my teacher would only accept [imath]\arcsin(x)[/imath]. Ever since, I've come to understand just why this is such better notation
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GenericAnimeBoy
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### Re: I hate math notation!

phlip wrote:
ImTestingSleeping wrote:3) Similar issues with [imath]f^{-1}(x)[/imath] being the notation for the inverse of [imath]f(x)[/imath]. I never liked that notation.

I think it's a reasonable notation along with functional powers, ie f2(x) = f(f(x)), etc... f-1(x) being an inverse fits well with that.

I'll agree that it doesn't fit well with sin2(x) = sin(x)2, which I always thought was odd... though I guess there's no real use for functional powers of trig functions (outside [imath]\lim_{n -> \infty} \cos^n(x) = 0.739...[/imath] of course). But I'll agree that when I was learning trig I did confuse sin-1 with csc and cos-1 with sec on more than one occasion...

The reason we write sin2(x) or (sin(x))2 rather than sin(x)2 is that the latter is too easy to mistake for sin(x2).

The notation for functional powers is all fine and good (if a bit rarely used), until you run into a Differential Equations prof who notates "the n-th derivative of f(x)" as [imath]f^{(n)}(x)[/imath] (only the parentheses distinguish it from functional power notation). That was a trip for awhile.

What really scared the crap out of me initially was my Calc 2 prof, who presented theorems in symbolic shorthand (like the backwards E for "there exists"). Of course, now that I know it, it's a lot faster to write one symbol than 12 letters.
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1fd5el
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### Re: I hate math notation!

hi there, my first post around here.

i hate math notations to
i hate the way math is taught

if you have only paper and pencil, or limited amount of writing space in a book, they are almost perfect.
but in the *-*-* century , notations should be dynamic &interactive, in a way that un-hide all possible(relevant) patterns.

the bandwidth ,for understanding math/info with this notations, it is small.

i believe understanding must be independent of a particular notation system.

cjmcjmcjmcjm
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### Re: I hate math notation!

1fd5el wrote:hi there, my first post around here.

i hate math notations to
i hate the way math is taught

if you have only paper and pencil, or limited amount of writing space in a book, they are almost perfect.
but in the *-*-* century , notations should be dynamic &interactive, in a way that un-hide all possible(relevant) patterns.

the bandwidth ,for understanding math/info with this notations, it is small.

i believe understanding must be independent of a particular notation system.

It says you have 0 posts. L.Q.T.M.
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Darryl
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### Re: I hate math notation!

1fd5el wrote:i believe understanding must be independent of a particular notation system.

That is the worst idea possible. You mean if I wanted to define addition to be written as a <Prince symbol> b, I could? And no one could tell me I was wrong to do so? That way lies madness.

The reason for math notation is that it is non-language dependent. So I could send what I'm working on to a collaborator in Japan, and not have to worry about the language barrier.
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archeleus
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### Re: I hate math notation!

cjmcjmcjmcjm wrote:
1fd5el wrote:hi there, my first post around here.

i hate math notations to
i hate the way math is taught

if you have only paper and pencil, or limited amount of writing space in a book, they are almost perfect.
but in the *-*-* century , notations should be dynamic &interactive, in a way that un-hide all possible(relevant) patterns.

the bandwidth ,for understanding math/info with this notations, it is small.

i believe understanding must be independent of a particular notation system.

It says you have 0 posts. L.Q.T.M.

Wonder why this happens? phpBB glitch?
I write a blog rant here.

Dason
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### Re: I hate math notation!

archeleus wrote:
Wonder why this happens? phpBB glitch?

double epsilon = -.0000001;

phlip
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### Re: I hate math notation!

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### Re: I hate math notation!

Welcome to Religious Wars. Where everything's made up and the points don't matter.
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capefeather
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### Re: I hate math notation!

Maybe what you perceive as "hard" in math isn't the notation but actually how math is taught in schools. The "math is too hard" aspect of our culture perpetuates itself in education and teachers helplessly indoctrinate their students with that idea. Students shouldn't get notation shoved into them like a cryptic language; they should understand the concepts and adopt the notation as a convenience. Making math notation itself more readable to computers than to humans is a terrible way to go...

(But yeah, some notation is just weird, like sin^2(x).)

GenericAnimeBoy
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### Re: I hate math notation!

In light of the impermanence and absurdity of existence, I surmise that nothing is better for us than to rejoice and to do good in our lives, and that everyone should eat and drink and enjoy the good of his/her labor. Such enjoyment is a gift from God.

benoitowns
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### Re: I hate math notation!

Darryl wrote:
Zach 739085133 wrote:One thing I would change if I had the power would be to do away with the symbol π, and use a single symbol to represent the ratio between a circle's circumference and its radius. (The number we call 2π.) For this post let me use ❖. That way when you are learning trigonometry in radians, a quarter of the way around the circle would be ❖/4, halfway around would be ❖/2, etc.

Actually, while it would make it slightly easier to relate to parts of a circle, it makes a lot of things far more complicated. Area becomes (❖/2) * r^2, and many other formulas become unnecessary fractions. With pi, most commonly used functions are whole multiples.

Although I will just stick with pi to make things easier, when using tau the equations look more consistent to me. That is, I know a lot of basic physics equations and when you derive them you will have them in the form of something like (u/2)*v^2
So I think using that their derivations become much more obvious.

thedufer
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### Re: I hate math notation!

Darryl wrote:
Zach 739085133 wrote:One thing I would change if I had the power would be to do away with the symbol π, and use a single symbol to represent the ratio between a circle's circumference and its radius. (The number we call 2π.) For this post let me use ❖. That way when you are learning trigonometry in radians, a quarter of the way around the circle would be ❖/4, halfway around would be ❖/2, etc.

Actually, while it would make it slightly easier to relate to parts of a circle, it makes a lot of things far more complicated. Area becomes (❖/2) * r^2, and many other formulas become unnecessary fractions. With pi, most commonly used functions are whole multiples.

Of course area becomes (❖/2) * r^2. That's the integral of circumference, ❖ * r (to a constant). Its actually much more obvious how the formulas relate when the circumference has as few constants as possible. Even beyond the relating formulas thing, I fail to understand why we should prefer the higher-order function have fewer symbols. Giving the lowest-order function as few symbols as possible seems to make the most sense - pi only makes sense if you're going to work with diameters, which basically no one does.

amit28it
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### Re: I hate math notation!

OK let me explain. I go to a charter school, so the school is 4 hours and mostly on computers

Before high school my math was horrible. When I got into high school i made a deterimation to get good grades in math. At first, I didn't succeed. But I studied, and eventually I was getting all A's in math. I got a award from the rotary club for the most improved grades.

However, the problem is this.
I have trouble with factoring, and i remember taking the SAT and having trouble on this problem to do with 'mirrors' in an xy graph of functions
i am good with algebra however

however

when i was a freshmen in high school, when most students take calculus, i was taking essienals. Basic math. I passed that with an A. Went onto pre algebra, passed that. Went onto algebra 1, passed that. Then BOOM, I am transfered to another school that doesnt have homework, and then from there I am lost

I had a teacher that couldnt help me because she was so busy. I couldnt ask questions like i always did, everyday, constantly i was very inquisitive with my old regular high school

so i never got past algebra 1

then guess what?

here comes the AIM test for math
What do I do? Well, I realize I don't have ANY CLUE how to do the problems because I NEVER GOT THAT FAR IN MATH. So i answered the questions i knew, and the ones i didnt i just guessed. Test results come back, "far below average'. What the heck?

I was so pissed. I am good in math, and here I get this grade. I want to be a physcist even

so here i have to take it again

i have no clue where to start
but if someone could help me with factoring or that mirror graph thing that would be great
get this though, i forgot EVERYTHING even BASIC MATH, except algebra
i cant even do percents anymore

reason is i finished my math credits and dont have to do math

so i'm not getting in the practice
now im really screwed
i dont even remember how to do fractions for Polynomials in XII Grade??

Proginoskes
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### Re: I hate math notation!

mister k wrote:one habit that does bug me, or did when I was still having to attend lectures, was the tendency for similar notation to crop up. x and y are fine- difficult to confuse. u and v... less so. n and m? p and [imath]\rho[/imath]? ARGH! I spent an entire day of revision realising I had confused pressure and density multiple times while writing.

My advisor once said that there aren't enough good letters in the alphabet. If you want to deal with functions, you have f(x), g(x), h(x), but now a fourth one requires i(x) (to continue the pattern), but i is either a square root of negative one, or an integer. Generic cartesian coordinates in 2, 3, and 4 dimensions are (x,y), (x,y,z), and ... (x,y,z,w) ... (WTF?)

As for [imath]\tau[/imath], it won't replace [imath]\pi[/imath] until someone comes up with a [imath]\tau[/imath]-joke like:

Teacher: What is the area of a circle?
Class: [imath]\pi r\,^2[/imath]!
Teacher: Wrong. Pie are round; cake are square.

exotica
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### Re: I hate math notation!

The short answer (to OP and anyone who thinks similarly) is yes, it's just you, and perhaps a few other people who have been similarly shortchanged by your math teachers and parents.

I can't fathom how anyone would find "math notation" difficult. Math software has always, when screen real estate is available, defaulted to showing expressions in "math notation". It does that for a reason: It's easier for almost everyone to read.

I don't understand how anyone could get through middle school math much less high school math without learning the few simple layout rules of "math notation": division is represented with the numerator over the denominator, with a line separating them. Exponents are indicated as superscripts. Subscript is usually an index for the accompanying variable. Radicals enclose their arguments under the upper extending line. There are more rules for higher math, starting with integrals and summation notation and matrices, but you have to define arbitrary syntax for those on a line-based input system anyway; there's no "natural" way to represent those things in line-based text.

Everyone suffers through one-line expressions because a keyboard does not make it easy to input "math notation". There are several commonly used standards for line-based math: Mathematica, TeX, MathML (though MathML is generally expected to be computer-generated and only minimally edited) None of those standards are easy to read and comprehend, which is why all graphical math software that I know of outputs expressions in "math notation" by default. I don't even know if you can have a program like mathematica display results in line-based text... I suppose they might have made it an option, but I've never seen it used.

You (OP, and anyone thinking of agreeing with the OP) claim you can match up parentheses with ease? You're either a savant or you're talking about simple expressions. However, even with simple expressions I often simply miss a parenthesis and everything gets unbalanced.

3/(1+3/(1+3/(1+3/(1+3/(1+3/(1-7/((3+z^k)^x)))))))

Tell me if that's balanced without scanning through the entire line keeping a running count of open parentheses. Lisp avoids this problem with auto-parentheses-completion and indentation. If it were trivial for people to keep parentheses balanced, Lisp-aware text editors, and code-aware editors in the case of other languages, wouldn't bother "helping".

Furthermore, looking at the above line you get an idea that there's a part of a continuing fraction with something interesting at the lowest level. However, change one of those / operators to a ^ and the whole thing from then on changes structure. Skimming it on one line, you might not notice that there's a break in the continuing-fraction pattern part way through. If it's represented in "math notation", the structure of the entire expression is obvious at a glance.

What "math notation" gives you is an overview of the structure of what's going on in the expression at a glance without reading through and parsing every single variable and operator and parenthesis in a line-based representation. It also drastically cuts down on parenthesis (and thus visual clutter) when lots of division is involved.

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