abstractmath.org

help with abstract math

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Last edited 4/16/2009 9:05:00 AM

 

Contents

Examples of functions  1

Specification and definition of function  3

Objects associated with a function  3

  The name of a function

       Domain and codomain                                 

       The value of a function

       The image of a function

       The quotient of a function

Properties of functions

Composition of functions

Inverses of functions  Error! Bookmark not defined.

Special kinds of functions  4

Images and metaphors for functions  4

Function Spaces

FUNCTIONS                       

The concept of function in mathematics is as important as any mathematical idea.   The mathematician’s concept of function includes the kinds of functions you studied in calculus but is much more abstract and general. 

If you are new to abstract math you need to know:

¨  The precise meaning of the word “function” and other concepts associated with functions.  (Specification and definition of functions, objects associated with functions).

¨   The many different kinds of functions there are.   (Examples of functions, properties of functions,  special kinds of functions.)

¨  The many ways mathematicians think about functions.  (Images and metaphors).

¨  Constructions:  Composition, inverses, function spaces