reading math - refresher course needed

Discussion in 'Math' started by kokkie_d, Nov 1, 2011.

  1. kokkie_d

    Thread Starter Active Member

    Jan 12, 2009

    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
    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?

  2. someonesdad

    Senior Member

    Jul 7, 2009
    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.