The Math thread

[Bobtheduck]

Because I am struggling so badly with my Intermediate algebra (a great deal of that being presentation... I forget to write out every step, I forget to box my answers, I forget to label my lesson, etc...)

If any of our resident Engineers and mathematicians have time, could you offer us some Tutoring? I'm sure I'm not the only person here struggling with Math, and so maybe let this thread be a place to ask math questions and have someone try to anwer them. To help us out with our struggles. So, anyone else up for this?

[Omega Amen]

*Sighs*

Well, we engineers are busy people, but I would like to see my fellow CAA members perform better in math. I am not sure how will we address problems that requires a graphical reference, like drawing out equations on graph paper. Plus, I am not sure this forum system has the text tools to properly show math equations.

But if you post with specific questions on a subject (not your assigned homework problems, of course) with enough time for us to look at with our spare time. We might be able to do something.

Maybe my fellow engineers and mathematicians can add more to this discussion... anyone?

[Technomancer]

Another engineer eh (I'm an electrical myself). I'll help out when I can, although I have my own mathematical studies to pursue at the moment.

[Omega Amen]

some esoterical language that uses creepy Greek symbols and no numbers.

*gives a friendly, warm chuckle*

Well, first fear to debunk. Those greek symbols can be replaced with the alphabetical letters that you should be comfortable with in algebra. Those alphabetical letters can be replaced with stars or boxes or question marks which I have seen when I was in second grade.

They are all variables, and we have to represent variables (unknown values) with some type of symbol, it doesn't matter whether it is Greek, english alphabet, whatever. Also, these Greek symbols are to represent a number that we have yet to figure out or to represent a value to you might have to put in yourself.

I am speculating that Greek is traditionally used because of the Ancient Greek mathematicians, and it is sort of like a universal academic language meaning any mathematician from any country can read it.... Reading it in the sense that these greek letters just represent some variables (values). It is just a standardization and is not even followed strictly.

Symbols are just symbols. This fear is completely unwarranted. For example:

5 + a = 8, therefore, a = 3.

5 + alpha = 8, therefore, alpha = 3.

5 + squiggle = 8, therefore, squiggle = 3.

See? No mathematical rule changes. Relax.

[Icarus]

I'd be happy to help as able.

[Fsiphskilm]

OH! OH! You shal

[Azier the Swordsman]

OH! OH! You shall love me and pet me for this. *sits on floor*

http://www.thebeehive.org/school/high/subjects.asp?subject=35
http://www.webmath.com/

*pets Volt and gives him a bone*

Good boy!

[Technomancer]

Okay on to the work.

Bob, what areas specifically are you having trouble with? Perhaps you could give us an example.

[Omega Amen]

I just thought of this. Technomancer and whoever else is joining me in trying to tutor this thread will need some standards for mathematical notation and guidelines for posts.

First, we are not the only math tutors in the world. Make some friends (that includes your teachers and teaching assistants) who are comfortable with math. You will probably get better and faster help. You should first consult with them before asking help from members in this thread.

Second, please put a title to your posts briefly describing your problem.

Third, to tutors/helpers, please indicate which member and problem you are replying/addressing to in your post (maybe in the title of the post too).

EDIT: 2-15-2004: Please use a "monospaced" font like Courier New to express your equations. (This rule was inspired by one of Cephas's posts.)

= is equals, for equality

< is less than

> is greater than

<= is less than or equals to

>= is greater than or equals to

!= is "not equal" or unequal (opposite of equality)

+ is plus, for addition

- is minus, for subtraction

* is times or "multiply by", for multiplication (do not use the letter x or X for multiplication, please.)

/ is "divide by", for division. Example: a divided by b should be written a/b. This operator can be used to express fractions (which really is a division operation) such as one-half can be written as 1/2.

^ is the exponent operator. Example: "10 to the 3rd power" is 10^3 which equals 1000 by the way.

() are parentheses used to denote order of operation. For example 10^(1 + 2) should first turn into 10^3 which then equals 1000.

Use alphabetic letters for variables. We do not want to see emoticons for variables. They are cute for forum messages. They are annoying in your equations.

Upper and lower case letters will be considered different variables. For example, x and X will be considered different variables. They will not be assumed to be equal or the same variable.

EDIT: 2-15-2004: There are famous constants such as PI (ratio of a circumference to a diameter of a circle) that are often used in math. Define any constants with your equations.

EDIT: 2-15-2004: Unit imaginary numbers and unit vectors: The unit imaginary number (square root of -1) should be noted either as i or j. Unit vectors should also be noted with other alphabetic letters in bold and italic and in a monospaced font like Courier New.

Make sure you put spaces in your equation to make it easy to read. Also give a line of space before your equation and afterwards. This will make analyzing your equations easier and quicker. We also expect to use the preview and edit functions in posts to correct any sloppy presentation. This is to not clutter the thread with posts of essentially the same question or equation over and over again.

If you have a scanner and you want to scan in your equations on paper, use white paper without lines and write neatly in a dark ink (black or blue) or in dark pencil lead. Write neatly with organization and purpose. We will not try to decipher scribbles.

I am particularly busy and I cannot and will not answer math questions at the last minute. I expect it will be the same way for the other tutors.

Be patient and respectful... you should be anyway when you are in the CAA.

We will also not be responsible for whatever grades you get because of our advice. It is your grade and your responsibility. We are doing this from the kindness of our hearts.

That's all I can think of for now. Alright? Good.

[Saint Kevin]

I'll be glad to help if I can. Does anyone know a better way of doing math notation than Omega Amen's way? I mean there's gotta be some free program out there with all kinds of mathematical symbols we can just cut and paste into a text box right?

[Icarus]

I have a few things to add concerning notation.

PI is to be used only to denote 3.141592654... Unless you mean that, please use other variables.

Also, if your equation contains i, please tell us if you mean some random number or if it means the square root of -1.

[Pepper Kittie]

I'd love to help in any way that I can ^^ I'm not particularly fond of math, but I'm pretty good at it for my age. *smiles* I'll try my best to help if anyone needs it.

[Omega Amen]

Hello,

I want to thank Icarus, Cephas and anybody else with their suggestions for the standards of notation.

Probably the biggest change to this post is that I am asking people to type out their equations in a "monospaced" font like Courier New. (These type of fonts are called monospaced, right?)

Cephas, since your derivative explanation post is the source of inspiration for this change, I would like you to edit that post using this Courier New font. I think you will get a "neater" result.

Saint Kevin, I would like to think that there is software that can help us in typing equations as you described, but honestly, I do not think such software exists. However, if anyone else can find what Saint Kevin is asking for, please let us know.

That is all. I need to get back to my work.

[Saint Kevin]

I do know that mathematics software, such as Maple, exists. The thing that I do not know is whether or not free, easy-to-use mathematics software exists. I will check into it.

[andyroo]

You mean OpenOffice Math?

[Bobtheduck]

sorry I left this thread for so long. I actually seem to be doing fine now, but I think it would be good to explain how there can be equations

Omega said to use Monospaced fonts, but for smaller equations (anything you'd get in Algebra 2) you could use one line and extra parenthesis, just like when you use a scientific calculator. so, bucket is directly related to riggomortis and inversely related to trout could be shown as b=(kr)/t (k being the relation constant)

My main problem in math was forgetting to work steps, forgetting to check, forgetting to write down the answer in sentance form for word problems, or forgetting to organize myself... I did have problems with a few questions I would have brought here, but as the homework turn-in time for those problems has allready passed, I'll come as I need help later on.

Thanks for making the tutorials section... I plan on making good use of this forum!

EDIT: That could be another reason why I wasn't doing well... I don't read everything...

[Technomancer]

I'll be glad to help if I can. Does anyone know a better way of doing math notation than Omega Amen's way? I mean there's gotta be some free program out there with all kinds of mathematical symbols we can just cut and paste into a text box right?

There is, although I doubt that they'll work here, at least not with some effort. I've used MS Equation Editor quite a bit in my writing, and that would probably be the one with the most support in terms of web-display tools. Some people swear by LaTex however. MathCAD allows mst of the usual sorts of symbols as well, as does Mathematica (at least for report writing).

[Bobtheduck]

It's official... I'm dropping this class, and I'm going to study independently for a year instead of in a class for a semester. I just can't deal with the workload. I seem to be getting it all, but always a day late. If I would have realized this, I would have taken the class that was broken up into two semesters... I was thinking with impatience, and impatience has impeded me this entire time... I think God's telling me to slow down and so that's what I'm going to do. I do plan on continuing this on my own, but I'll do it a bit more slowly.

In the mean time, I need help with something...

No matter how many times I've done this problem, I keep getting the arithmetic wrong. Simple arithmetic... At least, I think that's what I'm getting wrong. Anyhow, I'm to discover the point of intersection in 3 equations with 3 variables.


*GRR!!! Piece o malarky sent the post instead of doing a new line when I pressed enter... That's the first time that's ever happened...*

The equations are
2x-5y +3z= -1
x +4y - 2z= 9
x - 2y - 4z= -5

I am using elimination, so I took the second equation and the third equation and eliminated the z vatiable

-2x - 4y +4z= -18
x - 2y -4z= -5

from that I came up with

-x - 12y = 23 as the 4th equation (I just noticed my mistake... I copied the sign wrong on the right side of the equation... I put a +23 instead of a -23)

Well... I just noticed my problem... A mistake with signs... Well... Hopefully I can notice my mistakes so I won't make them anymore, and with the decision to drop the class I can do that without threat of the time constraints. I think this is the best thing for me to do. Anyhow, any suggestions on how to keep my signs in order?

RE: Omega Amen's No Emoticons for variables

That's funny... The reason why is because my teacher used a flower for substitutions...

|s-3|>=4

|:)| >=4

>=4
or
-:)<=-4

In fact, we HAD to use the flower to get full credit because she said it's easier to remember to switch back to the real expression if we knew that the variable wasn't really the flower (or for that matter)

My study partner, who dropped out before the first full exam, dropped because of little quirks like that... I don't think he'll have much luck elsewhere! Math teachers are all crazy! It's just what thinking of raw numbers all day will do to you, hehehe... Speaking of thinking about raw numbers all day, I wonder what cooked numbers taste like...

I may take the full year course starting next semester, pushing back my entrance into full sail that much more... But... I know God wants me working in video games... I just don't know if he wants me working in programming. I'm praying about that one a lot. (you can read up about that in my LJ)

[Omega Amen]

Bobtheduck, you worked on a system of three equations that I believe are independent and linear. Hence, the key is just to figure out what each variable is... one at a time. You said that you figured out your mistake. Good job.

It's official... I'm dropping this class, and I'm going to study independently for a year instead of in a class for a semester. I just can't deal with the workload.

Well, don't kill yourself over this. Mastering math requires patience, practice, concentration, and time. It sounds like you made the wise move. However, don't give up.

Well... I just noticed my problem... A mistake with signs... Well... Hopefully I can notice my mistakes so I won't make them anymore, and with the decision to drop the class I can do that without threat of the time constraints. I think this is the best thing for me to do. Anyhow, any suggestions on how to keep my signs in order?

I had the same problem when I was very young. The only solution I know is that you must practice diligently. It is like practicing a dance/sports move or learning a musical instrument. The practice reinforces self-discipline and concentration, which is what you need to avoid these mistakes. First focus on simple problems that clearly illustrate the concept. Then work on more complex problems, which in reality just have more simple computations to make. (You will see what I mean.) In order to increase your speed and proficiency, you have to practice even more. Your mind will adapt to the general process of solving a type of problem, and naturally, your speed will increase.

Mistakes like these are also made by brilliant mathematicians. We are not perfect, but we can practice to the point where they rarely occur.

As general advice, you can say you "mastered" the material when you don't feel like you are "learning" anything during a test. If you are still "learning" things during the test, you haven't practiced or prepared enough.

RE: Omega Amen's No Emoticons for variables

That's funny... The reason why is because my teacher used a flower for substitutions...

<snipped the emoticons>

In fact, we HAD to use the flower to get full credit because she said it's easier to remember to switch back to the real expression if we knew that the variable wasn't really the flower (or for that matter)

Math is an exercise in abstract thought, and she was attempting to reinforce this fact to you.

I do not want to see emoticons because they interfere with the spacing of lines of text and some of them are too animated or have several "smileys"/objects interacting, which could create confusion. This slows down interpreting the equations, annoys me (which means I might not give help at all), and serves no worthy purpose in this tutoring thread. Letters are just fine, and that's what professional mathematicians use. I am not trying to be cruel. I am trying to help people by making things easier to manage. I thought I should clear that up.

Making less mistakes and increasing your speed will only come through practice, Bobtheduck. If there was a trick to it, I would gladly tell you, but that is not the case here.

These type of mistakes become even more annoying in programming. They are often the "bugs" that sometimes take hours to find. I felt that I should share that with you.

[Bobtheduck]

What's the pattern to doing factorials and... Whatever those things are called that are like factorials only they're addition instead of multiplication. How do you figure those out without doing it by hand?

[Technomancer]

If you mean factorials as in say 5!=1x2x3x4x5 then it's just as written. It's fairly straightforward to write a program to compute this. Manipulating factorials is fairly easy, at least if you're able to divide (e.g. n!/(n-1)!=n). Do this whereever possible before computing your final answer.

Summations (Series) are a more general topic. There are ways of manipulating series to simplify them, however this depends on the type that you're working with (e.g. power series, Taylor, Cauchy etc). Different series will allow different manipulations (I'm sorry if that sounds vague, but so is the question), but there is no general technique that will solve all types.

If you can't immediately recognize the type of series, remember that the summation operation is linear. You may find that there is some transformation (integration, differention, splitting, etc) that will give you one or more series that can be simplified into an easier expression. Of course, there are those series that can only be computed by repeated summations, so you'll have to settle on acceptable approximation if you need numerical results.

[LorentzForce]

Today, I did my math exam. I studied enough, did all the questions, but I don't know if I got them all right or not. I hope did alright, all my previous math exams were pretty much all failures. But that was back when marks didn't go anywhere; now it does. So, wish me luck that I did alright

In the end it'll only be worth like, 12.5% of HSC result, which is like LONG time away. The BIG HSC is worth 50%, so I better do real good in that one.

Hmm, all these questions about locus, finding equations for parabolas, Simpson's rule... there's another math test soon which will be much, much harder. So, off I go again to study.

Now you all know why I don't post often these days.

[ice122985]

hey, guys, i am majoring in math, but barely up to precal. so if i can help, just let me know. i'll do my best to help.