Fields with least amount of geometry/topology?

  • Thread starter tgt
  • Start date
  • Tags
    Fields
In summary, The conversation discusses fields in mathematics, specifically in relation to topology and geometry. It is mentioned that abstract algebra is usually distinguished from topology/geometry, but other forms of mathematics may include elements of both. It is also noted that it is difficult to find a branch of mathematics completely unrelated to topology or geometry, with the suggestion of number theory or abstract probability theory as potential examples. Mathematical logic is also mentioned as a possible field that may be unrelated to topology and geometry.
  • #1
tgt
522
2
Which fields are they? Maybe a ranking if you can give one.
 
Mathematics news on Phys.org
  • #2
The simplest field I can think of consists of one number 0. The next simplest consists of two numbers (0 and 1) using modulo 2 for addition. After this things get more complicated.
 
  • #3
I had thought the question was about fields of work or professions! Veterinary medicine came to mind.
 
  • #4
fields (non mathematical term) in maths.
 
  • #5
tgt said:
fields (non mathematical term) in maths.

As far as I know, Sally Field has a very minimal amount of geometry/topology in her work. I think there was a scene of her doing some algebra in an episode of Gidget.
 
  • #6
A little bit more seriously, "Abstract Algebra" as a general field is usually distinguished form Topology/geometry. Other forms of mathematics typically include some algebra and some topology.
 
  • #7
HallsofIvy said:
A little bit more seriously, "Abstract Algebra" as a general field is usually distinguished form Topology/geometry. Other forms of mathematics typically include some algebra and some topology.

But still it's very related in a way since one can define geometry in terms of algebraic concepts. What is something that is so far from topology and geometry that there is not the slightest connection?
 
  • #8
What is something that is so far from topology and geometry that there is not the slightest connection?

It is very hard to find a branch of mathematics that has absolutely no connection to geometry or topology, particularly since you don't think abstract algebra is not far enough away. I could suggest number theory but then the pythagorean theorem might turn you off. Also abstract probability theory could qualify, as long as you don't use Borel fields for sigma fields.
 
  • #9
mathman said:
It is very hard to find a branch of mathematics that has absolutely no connection to geometry or topology, particularly since you don't think abstract algebra is not far enough away. I could suggest number theory but then the pythagorean theorem might turn you off. Also abstract probability theory could qualify, as long as you don't use Borel fields for sigma fields.

So maybe analysis related stuff? How about mathematical logic?
 

FAQ: Fields with least amount of geometry/topology?

What is topology and how does it relate to fields with the least amount of geometry?

Topology is a branch of mathematics that studies the properties of space and how they are preserved under continuous transformations. In fields with the least amount of geometry, topology is used to describe the underlying structure and relationships between objects.

How can fields with the least amount of geometry be applied in real-world situations?

Fields with the least amount of geometry are often used in fields such as physics, engineering, and computer science to model and understand complex systems. They can also be used to analyze data and make predictions about real-world phenomena.

What are some examples of fields with the least amount of geometry/topology?

Fields with the least amount of geometry/topology include topology, differential geometry, algebraic geometry, and differential topology. These fields are used to study the properties of space, shapes, and their transformations.

How does the study of fields with the least amount of geometry contribute to our understanding of the universe?

Fields with the least amount of geometry are crucial in understanding the fundamental laws of the universe, such as gravity and electromagnetism. They also help us understand the behavior of matter and energy on both the smallest and largest scales.

Are there any practical applications of fields with the least amount of geometry in everyday life?

While fields with the least amount of geometry are often used in theoretical and scientific research, they also have practical applications in everyday life. For example, they are used in computer graphics to create realistic 3D models and in medical imaging to understand the structure of the human body.

Similar threads

I What do applied mathematicians deal with?
Replies
4
Views
1K
I What is the name of this geometry theorem?
Replies
4
Views
894
B What is currently known about fields other than gravitation?
Replies
11
Views
2K
A What is the geometry of a gauge potential in the A-B experiment?
Replies
2
Views
975
I A way to comprehend the geometry of a hypercube
Replies
2
Views
1K
Undergraduate research topics in topology?
Replies
6
Views
518
B Notation for a "scalar absolute field"?
Replies
1
Views
1K
What is the difference between algebraic structure and space
Replies
2
Views
2K
How Can I Learn Seeding and Visualization Techniques for Vector Fields?
Replies
4
Views
1K
A Can Membrane Field Theory Elucidate M-Theory?
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top