Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Discussions About The Formulas

You can discuss general matters about the formulas here.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

I think that once a formula is submitted, a moderator should copy and paste it into the first post of the topic, and in doing so, we are able to organize these into sections to make it easier to read.

Furthermore, I suggest some sort of formatting, such as always use latex, so that if we wish to transfer these to say a web page, it will be much easier.  If you guys agree, I'm willing to repost all the formulas which aren't in latex, in latex.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: Discussions About The Formulas

I totally agree! I was actually going to post this suggestion myself..

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mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Discussions About The Formulas

Great new forum, MathsIsFun!

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A logarithm is just a misspelled algorithm.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

I think that once a formula is submitted, a moderator should copy and paste it into the first post of the topic, and in doing so, we are able to organize these into sections to make it easier to read.

Do you mean that each topic will have only one post?

Or nicely organized posts like the first two by ganesh in Integrals here http://www.mathsisfun.com/forum/viewtopic.php?id=3299. To me that looks nice - the bold heading is easy to see, and you can quickly scroll to the next post to see if its heading is relevant. The latex also looks nice there.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

I would say they should all go within in post.  But that's just an opinion, nothing more.  I don't have any real reasoning as to why one post rather than many.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Discussions About The Formulas

What's the difference between Caculus formulas and Differencial Calculus formulas?

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

Differencial Calculus has equations that involve to different derivatives of y such as:

5y' + 6ty'' = cos(e^t)

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Discussions About The Formulas

So do you mean Differential Calculus consists of Differential Equations and Partial Differential Equations?

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

That would be my guess, yes.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

Should set theory contain on that which would be given in an introduction to sets?  Or should it also contain things about the real numbers?

Normally, when on is first introduced to sets, you always deal with countable sets.  They are nice and neat.  When one gets to more advanced "set theory", which is really under real analysis (analysis of the reals), you start dealing with uncountable sets, density, and other exciting things of that nature.

Or maybe there should just be a real analysis section?  What do you guys think?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Discussions About The Formulas

But that won't be too much help.
It's like proposing a Euclid post. Can you imagine a bunch of formulas or theorems can express the whole system, or at least the majority of?

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

Yea, I guess so.  There aren't any real formulas in real analysis, only definitions and theorms.  Which brings me to my next point.  Formulas are computational things.  That's only half of math.  How about theoretical?  Could we have a theory section where there would be things like definitions and theorms as well as a formula section?

Some examples:

Geometry: Two triangles are similar when...
Calculus: Defintion of continuous, fundamental theorm of calculus
Set theory: If there exists a bijection between two sets, then those sets have equal size

And so on.

What do you think?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Discussions About The Formulas

I totally agree with your idea. Sometimes it's really difficult to apply math by just referring to a formula (Or else everybody could escape from math lessons through keeping a handbook). Yet introducing the whole system would be like authoring a new book and unrealistic.

So my idea is to set a Theory Piece Section, to allow people to explain and dig difficult, fundamental  ideas or whatever he/she thinks important to a math learner, in Existing math theories.

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X'(y-Xβ)=0

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

The Formulas are developing into a really wonderful resource, but don't seem to be the right place to talk theory.

So how can we best deal with theory? The forum itself may not be good enough. Wikipedia has its strengths, but being an encyclopedia it concentrates on documenting things, not teaching.

In my experience you need a wide range of "tools" to explain something well. You mentiond "Geometry: Similar", well here is my page on Similar.

As you would see, I use lots of diagrams, colors, and interesting layouts - then on downstream pages I have flash animations to show the concepts - basically I use any method I can lay my hands on

So possibly the best way to explain theory would be a full-blown web page.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

The formula section is to be used as a reference, not a teaching manual.  For example, d/dx sin(x) = cos(x) makes no sense unless you already understand derivatives.  That's the sense I was talking about formula.  Start making another reference manual.  So if you want to look up the what it means to be a Cauchy sequence or the definition of an injective mapping, that would be the place.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

But wouldn't it be nice if it were also educational? With a few extra sentences and some illustrations or whatever we could clear away the cobwebs of confusion for lots of people!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

WARNING: I am going to be doing some "behind the scenes" restructuring of the latex images, which may result in some "down time".

Reason: we now have over 3000 latex images all in the one directory and the server is not handling it efficiently, so I have been working on a new structure. I have tested it on dummy data, but now need to test it on live data.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: Discussions About The Formulas

I've started submitting some equations to this section, but I am beginning to have trouble. To be specific, the vector formula thread is not allowing me to post (or even preview my post, which is strange because it let me do that until recently). I get a 403 Forbidden error. Is there any explanation for this?

Also, I was wondering if it would be alright for me to start new formula threads, if there are topics that I feel don't fit in any other thread.

One last thing. I noticed that the first few replys on the "Differential Calculus" thread pertained to differential equations, but then the rest addressed plain old derivatives. Should differential equations get their own thread, or should I feel free to submit any formula relating to differential equations to the "Differential Calculus" thread?

Edit: The first small section of my vector formula post seems to submit, but I still get 403 Forbidden for the other material. I have no idea why.

Edit 2: I've managed to pinpoint the problem down to my "curl" section. Everytime I try to post it in any form I am given the 403 Forbidden error. My formulas with ∇ are incomplete without the curl! I won't be able to sleep tonight.

Edit 3: It appears that for some reason the forum doesn't like the word curl. If nothing immediately follows the word's last letter, I am unable to post (note the period immediately after the "evil word" in the previous sentence). I had to perform a little trickery to get the word "curl" alone in my vector post. Does anyone have an idea why this is so?

Last edited by Zhylliolom (2006-08-05 16:54:44)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

I can use the word curl

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: Discussions About The Formulas

That's very odd. I can do it now too. Anyway, would it be alright for me to make new topics as needed on this forum? Right now I'm wanting to make a topic on inequalities.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discussions About The Formulas

That is weird, then! Maybe something to do with your browser, its cache or something. Let me know if you have other problems like it.

You are fully welcome to create new topics, Zhy!

Differential: we could split it up if other people agree.

And one other comment - this formulas section is a success - I notice some topics have around 2,000 page views, and we haven't even let other websites know about this!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: Discussions About The Formulas

Yeah, I noticed the amount of views and was pretty impressed. I'll post some differential equation stuff in the "Differential Calculus" thread for now, I guess. About people agreeing on the splitting of that thread, I vote for it, because I view differential calculus as the part of calculus I where you learn how to take derivatives of functions and apply them to other problems. Differential equations are something you do further down the line, and it might confuse someone just looking for a formula for a derivative when they run into things like integrating factors and hypergeometric functions.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Discussions About The Formulas

I am going to start moderating this section more heavily, so post whatever you think is right, and I'll clear up any leftover things (like the diff eq posts in the differential calc section).

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

Re: Discussions About The Formulas

Any progress, Ricky?

I have a suggestion, once that is done, we may request the Admin to consider having a link from the homepage of the website. Certainly, only after double-checking each and every formula. What do you have to say, Ricky?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.