Thread: What is Topology and Analysis?

1. What is Topology and Analysis?

Hi,

What is Analysis? What is Topology? What is Differential Equations with Linear Algebra? What is it used for? Besides teaching, what are the jobs someone can do with an BS and AS degrees in mathematics?

2. Originally Posted by php111
What is Analysis?
Have you ever studied Calculus? Calculus is part of an area of math (huge absolutely huge) called "Analyis". Basically, Analysis is the foundation of Calculus. You might have noticed you do not do proofs in Calculus rather you learn formulas. Once you master them you can start to understand why these formulas and ideas work mathematically.

There are many different types of Analysis'. Calculus is usually called "Real Analysis" because you use real (i.e. non imaginary) numbers.

There is another one called Complex Analysis. That one does Calculus with complex (imaginary) numbers.

What is Topology?
The Greek translation is "study of space". That is basically what it is. It studies objects in space in a mathematical way. For example, what does it means a "region" how do you define that. And what does it means "inside of a circle". How do you define that? And similar related things. It is also very very huge.

Analysis and Topology are seperate areas of mathematics.

Now the funny thing is that out of all the places you could have placed this thread you placed it in "Algebra", which is a totally different area from Analysis and Topology. (Algebra is my favorite).

3. Originally Posted by ThePerfectHacker
Have you ever studied Calculus? Calculus is part of an area of math (huge absolutely huge) called "Analyis". Basically, Analysis is the foundation of Calculus. You might have noticed you do not do proofs in Calculus rather you learn formulas. Once you master them you can start to understand why these formulas and ideas work mathematically.

There are many different types of Analysis'. Calculus is usually called "Real Analysis" because you use real (i.e. non imaginary) numbers.

There is another one called Complex Analysis. That one does Calculus with complex (imaginary) numbers.

The Greek translation is "study of space". That is basically what it is. It studies objects in space in a mathematical way. For example, what does it means a "region" how do you define that. And what does it means "inside of a circle". How do you define that? And similar related things. It is also very very huge.

Analysis and Topology are seperate areas of mathematics.

Now the funny thing is that out of all the places you could have placed this thread you placed it in "Algebra", which is a totally different area from Analysis and Topology. (Algebra is my favorite).
Thank you but under Algebra the description says Topology. That is Advanced Algebra it says. What is Princples of Analysis? What is Differential Equations with Linear Algebra that i asked? I also asked what i can do with an AS and a BS degree in mathematics? No never studied calculus.

4. Originally Posted by php111
Thank you but under Algebra the description says Topology. That is Advanced Algebra it says. What is Princples of Analysis? What is Differential Equations with Linear Algebra that i asked? I also asked what i can do with an AS and a BS degree in mathematics? No never studied calculus.
You need to get an idea of what mathematics is about, so you need to read something like Tim Gowers' book "Mathematics, A Very Short Introduction"

RonL

5. Originally Posted by php111
Thank you but under Algebra the description says Topology.
It means "Algebraic Topology". Not ordinary (pointwise) Topology.

6. Besides teaching, what are the jobs someone can do with an BS and AS degrees in mathematics?
Serving coffee.

7. Originally Posted by php111
Hi,

What is Analysis? What is Topology? What is Differential Equations with Linear Algebra? What is it used for? Besides teaching, what are the jobs someone can do with an BS and AS degrees in mathematics?
Well I know what BS is but what is an AS degree?

RonL

8. Originally Posted by CaptainBlack
Well I know what BS is but what is an AS degree?

RonL
associate (of science) degree, it's a 2-year degree offered by community colleges in the US

9. Yes an AS is offered at a community college and BS degrees and up are offered at universities. What are the different jobs that are with them degrees in mathematics besides serving coffee? lol

10. Originally Posted by php111
Yes an AS is offered at a community college and BS degrees and up are offered at universities. What are the different jobs that are with them degrees in mathematics besides serving coffee? lol
i just remembered a user asked this not so long ago. see here, i give websites that give a (big) list of career option for math people in the second post. other users, such as JakeD, made suggestions as well