What do Greek symbols in math represent and how do you decipher them?

[Newtons Apple]

Ok... if there's one thing that really rustles my jimmies...is when I look at an equation an it's chock filled of greek letters, in a big swirl of greek alphabet soup...

I have a question, when you approach a new equation, do you automatically know what the symbols mean? Is it relative to the type of equation? I was looking at this, in regards to

and

Are the two greek letters here, epsilon and sigma(?), always to refer to the same thing for every problem? How do you know then what they refer to? I see a lot of problems where they don't specify what the symbols mean? I look online and I get varying answers.

Is there a set way that one should "read" a statement like the one below? And more specifically what on Earth does epsilon stand for here, and how do you know?

 

[micromass]

Some Greek letters are standard, other differ in use. For example, $\sigma$ (=sigma) might stand for different things depending on the text. For example, in statistics texts, it might stand for the standard deviation. But in other texts, like group theory, it might be a function. It really depends.

The "epsilon" symbol is usually written as $\epsilon$ or $\varepsilon$. The symbol you wrote above is $\in$ and it denote set membership. This is standard over all of mathematics. You won't meet a math text where $\in$ means something entirely different. You might meet texts where $\sigma$ or $\varepsilon$ is different though.

How do you know? Experience. If you study a lot of math texts, you will start to know such things. The $\in$ for set membership is usually taught in intro proofs books or set theory.

 

[Newtons Apple]

Okay... that actually helps. A lot. How do you pronouce(and type)..ehh that E character?
Is there anyway to tell which characters are constant and which can change depending on the context? Or do I just have to gain experience?

Lastly, when you have something like,

(yes I"m studying proofs...vainly attempting to study proofs)

Can you just look at it with no prior knowledge to what it is and know what is means? It seems like people can just post a formula or equation such as this.. with all sorts of greek letters and variables mixed in and they just know what it means...

 

[micromass]

Okay... that actually helps. A lot. How do you pronouce(and type)..ehh that E character?

"Element of" or "in".

Is there anyway to tell which characters are constant and which can change depending on the context? Or do I just have to gain experience?

It comes down to experience. But see this: http://en.wikipedia.org/wiki/List_of_mathematical_symbols

Lastly, when you have something like,

(yes I"m studying proofs...vainly attempting to study proofs)

Can you just look at it with no prior knowledge to what it is and know what is means? It seems like people can just post a formula or equation such as this.. with all sorts of greek letters and variables mixed in and they just know what it means...

No. Without previous knowledge, I have no idea what it's about. I might figure out some parts though. But certainly not the entire thing.

 

[Newtons Apple]

No. Without previous knowledge, I have no idea what it's about. I might figure out some parts though. But certainly not the entire thing.

Ah, I see. Lastly, do the normal rules of algebra, order of operations, and simple algebraic rules even apply to these huge and more complex equations, or formulas?

And thanks for the list of math symbols!

 

[micromass]

Ah, I see. Lastly, do the normal rules of algebra, order of operations, and simple algebraic rules even apply to these huge and more complex equations, or formulas?

Yes, they should still apply. However, there might be some instances where they don't apply, but this should always be clear from context.