10
votes
3answers
323 views

Applications of Banach Algebras and Operator Algebras

I am trying to learn operator algebra theory (I am tempted to start with Douglas' "Banach Algebra Techniques in Operator Theory"). One aspect that I am curious about is whether there are significant ...
78
votes
9answers
5k views

How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
2
votes
4answers
311 views

Applications of group theory to geometry

What are the applications of group theory to geometry? Where can I know more about these applications?
44
votes
8answers
3k views

Are there real world applications of finite group theory?

I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics. (Sufficiently applied mathematics such as ...
8
votes
3answers
553 views

What are applications of rings & groups?

I am following a course in basic algebra, and we have covered rings & groups in class, but I am having trouble visualising them. Are there applications of group &/or ring theory that can be ...
1
vote
2answers
131 views

An injective map where each value is mapped to many others?

I want "something" ("something" because maybe it is not really a mathematical function, called F in the above image) that can describe what is shown on the image. A given value from a domain Xi can ...
6
votes
3answers
2k views

Group theory applications along with a solved example

As I asked in previous question, I am very curious about applying Group theory. Still I have doubts about how I can apply group theory. I know about formal definitions and I can able to solve and ...
10
votes
3answers
2k views

Real-world uses of Algebraic Structures

I am a Computer science student, and in discrete mathematics, I am learning about algebraic structures. In that I am having concepts like Group,semi-Groups etc... Previously I studied Graphs. I ...
8
votes
4answers
346 views

Applications of Gröbner Bases

I would like to present an application of Gröbner bases. The audience is a class of first year graduate students who are taking first year algebra. Anyone have suggestions on a specific ...
2
votes
1answer
141 views

Are there any sets other than the usual in which we can apply Sturm's axioms?

As we all know, Sturm's axioms have completely solved the problem for finding the number of roots in an arbitrary interval $[a,b]$, using the derivative and forms a Sturm set. Now my question ...