# reading math - refresher course needed

#### 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):

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,

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.