reading math - refresher course needed

Thread Starter

kokkie_d

Joined Jan 12, 2009
72
Hi,

Does anyone know about a good book (a dummies book for all I care) that can help with refreshing how to read maths (probably vague so I'll provide an example):

This is from a google book about poincare maps:

Consider the follwing ODE:
\(\dot{x}=f(x)\), \( x \in\Re^n\)
Where:
\(f:U \rightarrow \Re^n\) is \(C^r\)
First line would read as: the first derivative of x equals the output of the function f of x where x is an element of all real numbers something

The second line would then read as:
Where f something U then the real numbers something is part of a complex number set?.

As you might guess, my math "speak" is a bit rusty and I was wondering if people have some recommendations for books that handle with the "speak" problems?

Cheers,
 

someonesdad

Joined Jul 7, 2009
1,583
\(f:U \rightarrow \Re^n\) is \(C^r\)

The second line would then read as:
Where f something U then the real numbers something is part of a complex number set?.
That notation is standard and acknowledges that it's important when specifying a function to also specify the domain and range (also called the image) of that function. It also helps to look in the book for a glossary, index of symbols, notation page, etc. For example, the book's glossary explains what \(C^r\) is.

In this case, the "translation" is that the function f maps (that's what the arrow means) the open set U which is a subset of \(\Re^n\) into \(\Re^n\) and that f is also a member of \(C^r\).

A trip to a local university library will uncover lots of suitable books. With determination, you can also eventually figure out the notation by studying stuff on the web (this might be a starting place). Here are some books that I know to be pretty good that will probably get you going (I'm giving these solely because they happen to be on my bookshelves):

"Introductory Real Analysis" by Kolmogorov and Fomin (an inexpensive Dover book and one of the excellent translations of R. Silverman).

"Discrete and Combinatorial Mathematics" by Grimaldi.
 
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