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Old 2007-03-18, 20:26   #1
jasong
 
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"Jason Goatcher"
Mar 2005

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Default Need books about "crooked E"

I contracted a mental illness when I was 16, so my education was pretty much cut short at that point. From the 11th to the 17th of April, I'll be going to and returning from my brother's wedding. 48 of those hours will be spent in a van.

During that time, I'd like to increase my education by learning how to use the "crooked E" symbol. Apparently, I would've been learning about it a month or two after I became ill, because everything I've read is easy to understand up until that point.

Could someone advise me on some question and answer books(I'd prefer that the questions and answers be in the same book, everything has to fit in a backpack.) that I could use to teach myself? Something I could buy on Amazon preferably.

thanks in advance. :)
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Old 2007-03-18, 21:53   #2
sdbardwick
 
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Just for clarity, by "crooked E" did you mean this symbol?: \Sigma
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Old 2007-03-18, 22:05   #3
Wacky
 
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Quote:
Originally Posted by sdbardwick View Post
Just for clarity, by "crooked E" did you mean this symbol?: \Sigma
It's "Greek" to me. :)

There are many characters (typically from the Greek alphabet) that have a particular meaning in mathematics. (The one that you reference is the uppercase form of "Sigma" which is generally used to indicate a summation.)

It is unclear to me whether Jason is interested in the symbolic notation or in some characteristics behind the relationships that they are used to represent.

He could also be referring to some form of "epsilon".

On Google, the only reference that I found to "Crooked E" was a reference to the Energy trading company, Enron. (Disclaimer: I have a "vulture" interest in some of the obligations of that company)

Last fiddled with by Wacky on 2007-03-18 at 22:07 Reason: Speeling
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Old 2007-03-19, 01:15   #4
Xyzzy
 
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Quote:
He could also be referring to some form of "epsilon".
Epsilon, or epilepsy?

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Old 2007-03-19, 01:54   #5
jasong
 
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"Jason Goatcher"
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Quote:
Originally Posted by sdbardwick View Post
Just for clarity, by "crooked E" did you mean this symbol?: \Sigma
Just to clarify, yes, that is the symbol, and I'm interested in learning to do math with it.
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Old 2007-03-19, 04:36   #6
paulunderwood
 
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\Sigma means summation (in most contexts).
Rather than writing something like:
1+a+a^2+a^3+a^4+a^5+a^6+a^7+a^8+a^9+a^{10}+a^{11}+a^{12}+a^{13}+a^{14}+a^{15}+a^{16}+a^{17}+a^{18}+a^{19}+a^{20}+a^{21}
mathematicians express this as:
\Sigma_{i=0}^{i=21}a^i
or sometimes something like this:
\Sigma_{i=0}^{21}a^i

Assuming the distributive law: C*(A+B)==C*A+C*B and by repeatedly using it, you can see that:
C\times\Sigma_{i=0}^{i=21}a^i=\Sigma_{i=0}^{i=21}C\times a^i

An interesting sum is:
\Sigma_{n=1}^{n=\infty}{\frac{1}{n^2}}
(Hint: Euler's zeta function )

Things get hairy when you start nesting one \Sigma inside another.

Last fiddled with by paulunderwood on 2007-03-19 at 05:01
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Old 2007-03-19, 04:49   #7
jasong
 
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"Jason Goatcher"
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If it's so simple, maybe you could recommend a textbook to help me learn it? :)
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Old 2007-03-19, 10:30   #8
cheesehead
 
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"Richard B. Woods"
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Quote:
Originally Posted by jasong View Post
During that time, I'd like to increase my education by learning how to use the "crooked E" symbol.
For future symbol references:

Switching your display font to some Unicode font (http://en.wikipedia.org/wiki/List_of...#Unicode_fonts) may help when viewing the following.

http://www.maths.tcd.ie/~dwilkins/La.../MathSymb.html

http://whatis.techtarget.com/definit...803019,00.html (warning: contains so many images they may not all load in IE until you clear cache)

http://en.wikipedia.org/wiki/Table_o...atical_symbols

Last fiddled with by cheesehead on 2007-03-19 at 10:33
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Old 2007-03-19, 12:36   #9
m_f_h
 
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Indeed the "crooked E" is the greek letter Sigma (i.e. it's a crooked S and not an E...), for "Sum".
I learned it with that one:
Walter, Wolfgang: Analysis 1.. Springer-Lehrbuch. Berlin: Springer, 398 S. (2004).

I liked his style: concise for the mathematics, very rich in historical comments.
However, since it's in German, I don't know if it will help you.

But I think any 1st year "analysis" (=calculus) book will deal with that,
it's a question of personal preference which one you like better than another.
Searching amazon.com for "calculus I" gives you the following as #1,
I don't know it, but you can have a look inside the book ;
searching for "infinite sum" takes you to p.203 where the "Sigma" is introduced.
(It's over 300 pp but you can buy it used for $13 - just the right thing for your travel...)

http://www.amazon.com/Calculus-I-Und...4307268&sr=1-1
("calculus I" by Mardsen,Mardsen & Weinstein, if the link does not work).

Last fiddled with by m_f_h on 2007-03-19 at 12:37 Reason: but>buy
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Old 2007-03-19, 14:13   #10
davieddy
 
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"Lucan"
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Jasong. If you know what a "loop" is in a computer program,
that should help your understanding of this notation.

David
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Old 2007-03-19, 16:13   #11
philmoore
 
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Most textbooks on "College Algebra" or "Precalculus" also have introductory sections on sequences and series, including the sigma notation. This might be a good place to start, as these descriptions will not assume that the reader has any previous exposure to this material.
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