# A good place to find out the meaning of basic math terms

Hi

I have trying to study independently some fairly high level physics but I keep getting bogged down with simple (I imagine for other people) mathematics terms:

Here is a partial list of terms I don't get:

Operator
Argument
Mapping
Comutator

There are probably many others. My question is where can I find simple definition of these terms in everyday speak and not full-blown mathematical language?

For example to try to understand the term operator, I went to Wikipedia but unfortunately as is often the case I just go round in circles because each definition relies on using other terms like mapping and vector space and when I try to look up the meanings of those I end up back where I started. So I am looking for a source that gives everyday explanations of mathematics terms for real dummies. Thanks

micromass
Staff Emeritus
Homework Helper
I'm afraid you're just going to have to bite the bullet and study from math books.

Mark44
Mentor
Hi

I have trying to study independently some fairly high level physics but I keep getting bogged down with simple (I imagine for other people) mathematics terms:

Here is a partial list of terms I don't get:

Operator
Argument
Mapping
Comutator
Several of these are used with slightly different meanings in different fields, so context is important in defining them.
Let's start with "mapping". This represents a pairing of one set with another. It's roughly synonomous with "function" which also pairs objects in one set with objects in possibly another set. For example, the function given by ##f(x) = -\sqrt{x - 1}## maps the set [1, ∞) (the domain) to the set (-∞, 0] (the range or codomain).

"Argument" could mean the input to a function, as in f(3), where the argument to the function is 3. It could also mean the angle of a vector when the vector is expressed in polar form. For example, in the vector <1, 1>, the argument is ##\pi/4## or 45°. In programming languages, "argument" means an input to a function or subroutine.

"Operator" is another term that has different meanings in different disciplines. In the linear algebra subfield of mathematics, an operator is a linear transformation that maps a vector space to itself.

BTW, the last term on your list is commutator - two m's.
resurgance2001 said:
There are probably many others. My question is where can I find simple definition of these terms in everyday speak and not full-blown mathematical language?

For example to try to understand the term operator, I went to Wikipedia but unfortunately as is often the case I just go round in circles because each definition relies on using other terms like mapping and vector space and when I try to look up the meanings of those I end up back where I started. So I am looking for a source that gives everyday explanations of mathematics terms for real dummies. Thanks

SteamKing
Staff Emeritus
Homework Helper
If you want to get a general meaning without getting submerged in technical discussions, there are several dictionaries online which can be accessed to find the basic meaning of the term of interest or if there are possible multiple meanings. Often, a simple google search using the term can turn up the dictionary meanings.

Several of these are used with slightly different meanings in different fields, so context is important in defining them.
Let's start with "mapping". This represents a pairing of one set with another. It's roughly synonomous with "function" which also pairs objects in one set with objects in possibly another set. For example, the function given by ##f(x) = -\sqrt{x - 1}## maps the set [1, ∞) (the domain) to the set (-∞, 0] (the range or codomain).

"Argument" could mean the input to a function, as in f(3), where the argument to the function is 3. It could also mean the angle of a vector when the vector is expressed in polar form. For example, in the vector <1, 1>, the argument is ##\pi/4## or 45°. In programming languages, "argument" means an input to a function or subroutine.

"Operator" is another term that has different meanings in different disciplines. In the linear algebra subfield of mathematics, an operator is a linear transformation that maps a vector space to itself.

BTW, the last term on your list is commutator - two m's.
ks

Thanks - I have tried that but not with much success.

There is probably a pure maths course that I need to do but I can't afford it right now.

I do tend to get stuck on words. It took me ten years before I could say that I feel comfortable with the word 'tensor'

I probably just need to see more examples.

Cheers
If you want to get a general meaning without getting submerged in technical discussions, there are several dictionaries online which can be accessed to find the basic meaning of the term of interest or if there are possible multiple meanings. Often, a simple google search using the term can turn up the dictionary meanings.

Can you suggest any math books out there that are really readable?

I have been looking at a lot in various places but most of the time I find math books are written for people who already 'speak the language' - pretty much the same as reading Wikipedia.

As I have said in another post, it took me ten years before I could say I felt comfortable with the word 'tensor' as an example. Actually what helped me finally crack that one was an Open University undergraduate text book.

I think I could really sort out these problems by taking the OU's course in pure maths, but I just don't have the funds for that at the moment. That's why I am looking around to see if I can find a maths book that explains all these terms in simple plain English for people who are not already mathematically literate.

Thanks
I'm afraid you're just going to have to bite the bullet and study from math books.