Author Topic: My Math Book (Read 5714 times)

ruler501 · « **on:** February 22, 2011, 09:21:39 pm »

I am writing a book on learning math. I taught myself from an advanced 6th grader to a seventh grader who can (kindof) do Calculus and I want to help others do this. I want this book to be simple enough to understand, but include proofs for most things it does. I also partially wrote this book because I'm tired of everyone around me complaining because math is so hard so I am going to show them how easy it is. I plan on posting excerpts from it here for review so I can see how I'm doing I'm sure you guys can understand why I don't post the whole book so far. I have only been working on this for about a week and even then this is on/off work for me so currently I am 7 pages in. thank you for any feedback and I will be sure to mention everyone who gives me help in the acknowledgments.
At this time I do not plan to ever have this published It will just be something I distribute to friends or use to help me teach others math.

The first excerpt is here it is the first page from my book please comment or tell me what I can do better(i will also gladly take any praise you have to give

)

Spoiler For "First Page":

The first and most important thing for you to learn about Algebra is variables. Variables are any placeholders for something else. In regular Algebra you will learn to use variables to represent numbers in a specific scenario. In early algebra you will mainly use two variables. One will be the independent variable which you change to modify the dependent variable. The most common name or symbol for the independent variable is x, and the most common one for the dependent variable is y. You might change the name of these variables to fit your scenario better. In most textbooks and other practice problems you will see x and y.
A function is anything where combinations of independent variables equal one specific dependent variable. You can prove if it is a function by looking at the inputs (independent variables) and the outputs (dependent variables) If there is more than one output for each input you do not have a function. A function can apply to many things through life, but in this book we will try to focus purely on algebraic functions. You express a function by replacing the dependent variable by f(x) where x is whatever you independent variable is.
Functions can be viewed in many ways the first way you should learn to view functions with is tables. In the table you have one column to tell you what the independent variable is then in the column directly across from that you should have a column telling you what the dependent variable is. To check to see if the values in the table are from a function you would check to see if there is only one dependent variable for each instance of the independent variable. It is not a function if it has more than one dependent value for each instance of the independent variable
Another way to view functions which you will probably use much more is graphs. The easiest way to do this is to use a graphing calculator. If you have a TI-84, a TI-83, or a TI-82 I will explain how to do that here. If you have a TI-Nspire it is explained in the appendix B. If you have any other kinds of calculator check your manual which probably came with it to see how to graph functions. From here on out when I say calculator I am referring to one of the aforementioned TI-80’s. To view a function on a calculator you would turn the calculator on and enter the equation into the space given when you press the Y= button. Once you have done that press the graph button and the function should be displayed. You can get a table on a calculator by pressing 2nd and then pressing graph. Graphs are the easiest things to check to see if they are displaying functions. You just look at it and see if a vertical or straight up and down line would pass through it in more than one place. If that happens then you do not have a function.

I have a title on top of that in a nice graphical header. It is chapter one of my book. Functions and Variables is the chapter name. the book has a currently undecided name

EDIT: I have posted a preview of chapter one as a Word 2003 document the password to access it is saftey. I will be happy to hear any feedback you have.

(I'm sorry if this is in the wrong forum)

Munchor · « **Reply #1 on:** February 26, 2011, 02:27:38 am »

I see what you did there

This is the right forum.

I also have to note that it looks cool, but I never learnt variables in school, at least not like you talk about them. But you're the one who's right, I'm sure.

ruler501 · « **Reply #2 on:** February 26, 2011, 08:42:36 am »

I'm trying to immediately show people how you can apply it to real life. I believe that is a wonderful way to show real life scenarios. If you want to look at it I will temporarily post a copy of my nearly completed first chapter. I am just working on examples and checking for errors. here and PM you the password to it. You will need Microsoft Office 2010 to open it though.

aeTIos · « **Reply #3 on:** February 26, 2011, 08:43:44 am »

Wow nice Ruler!

ruler501 · « **Reply #4 on:** February 26, 2011, 08:48:28 am »

Thank you, I hope to be able to do something with this when I'm done, but currently I don't know what.

EDIT: I've attached an early version of chapter 1 to my first post. I have password protected it since I am running this off of a flash drive. The password is safety. I would love to hear any comments/corrections you have for me.

Munchor · « **Reply #5 on:** February 26, 2011, 08:50:49 am »

Quote from: ruler501 on February 26, 2011, 08:42:36 am

I'm trying to immediately show people how you can apply it to real life. I believe that is a wonderful way to show real life scenarios. If you want to look at it I will temporarily post a copy of my nearly completed first chapter. I am just working on examples and checking for errors. here and PM you the password to it. You will need Microsoft Office 2010 to open it though.

I believe you should 'Export to PDF' it, but still nice

ruler501 · « **Reply #6 on:** February 26, 2011, 08:58:15 am »

I don't know how to password protect pdfs. I don't want people to be able to steal my work if I lose my flash drive. I did decide to save it as a 2003 just in case someone didn't have office 2007+. I'm thinking of using this chapter as a preview for now and probably will not post any of my other ones. I might send it to someone who helps me a lot for editing/revision because I know I'm going to make mistakes if this book gets as large as I want it to be.

This is slightly off-topic but does anyone know a proof for the distributive property. how do you prove that (x+y)(x+z)=x^2+yx+zx+yz? this is for proofs I want to put in later in my book.

EDIT: should I describe the differences between functions and equations in the first chapter. I ask this because I am now in the second chapter on Linear Algebra and I keep saying there is a difference. but I am not sure of where to write what that difference is.

Munchor · « **Reply #7 on:** February 26, 2011, 01:02:16 pm »

ruler501, I'm a programmer so my way to proof stuff is by making a program with a for loop that tests all numbers, so here is my way of proofing that 2x=3x-x:

Code: [Select]

for x in range(-100000,100000):
    if 2x != 3x-x:
        print "ERROR"

It will never print ERROR (I think).

Maybe this will help you.

EDIT:

Code: [Select]

>>> def proofTeory():
	for x in range(-100000,100000):
		if 2*x != 3*x-x:
			print "ERROR"

			
>>> proofTeory()
>>> #Nothing Happened
>>>

ruler501 · « **Reply #8 on:** February 26, 2011, 08:41:11 pm »

I need to be able to prove it for all numbers even if I prove it for the first trillion there are still an infinite more. Is there any way you could prove this in a different way?

EDIT: I could really use comments on this I want to know what to improve

jnesselr · « **Reply #9 on:** February 26, 2011, 09:53:40 pm »

Quote from: ruler501 on February 26, 2011, 08:41:11 pm

I need to be able to prove it for all numbers even if I prove it for the first trillion there are still an infinite more. Is there any way you could prove this in a different way?

Sure, easily. Let's try it with 1 and 2. (1)(2)=2, correct? Okay, how about 2 and 3? (2)(3)=6. So, we could say (N)(N+1)=N²+N. Now, is this true? 1²+1=2. 2²+2=6. Actually, because this works for (N)(N+1), we can try and replace N with N+1. So that gives (N+1)(N+1+1) or (N+1)(N+2). Whoa, that looks familiar. (N+1)(N+2)=N²+3N+2. And, this works for all N, since we tested it for N and N+1. This is because every time we do N+1 as N, it still works.

Now then, let's try mixing it up a little bit. How about (N+X)(N+1). Whoa, that's interesting. (N+X)(N+1) = N²+NX+N+X. Now, since X is just some number as well, and we already proved (N+1)(N+2) = N²+3N+2, and that it can work for any N, obviously this must work as well. The same could be said about (N+1)(N+Y) = N²+N+NY+Y.

Now, for the interesting part. (N+X)(N+Y)=N²+XN+YN+XY for any N (as we proved), any X (as we proved), and any Y (as we proved). Wait, we just proved the entire thing. In fact, to go backwards, check this out:
Given N²+XN+YN+XY, if we take N out of the first two terms, we get N(N+X)+YN+XY. And Y out of the last two terms gives N(N+X)+Y(N+X). And since you have (N+X) for both the N and the Y, you can do (N+Y)(N+X). And you can do that, because of being able to distribute it.

EDIT: If you liked it, a thumbs up would be nice.

* King Graphmastur hopes this is useful either way

ruler501 · « **Reply #10 on:** February 26, 2011, 10:20:14 pm »

Thank you this proves exactly what I've been working on

I still would like feedback from what I've written so I can fix any problems/make it better

Author Topic: My Math Book (Read 5714 times)

ruler501

My Math Book

Munchor

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aeTIos

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Munchor

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Munchor

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jnesselr

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