The incidence matrix of a graph is a way to represent the graph. Why go through the trouble of creating this representation of a graph? In other words what are the applications of the incidence matrix or some interesting properties it reveals about its graph?

Knot theory was likely originally motivated by the study of real-world knots such as these: Indeed, mathematical knot tables to this day look not too dissimilar from the familiar “age of sail”-style knot collections that decorate the walls of countless homes and restaurants around the world: So, has knot theory as a purely topological discipline […]

I am reading the book Introduction to Smooth Manifolds by John Lee. In his book he proves a theorem called the Whitney’s Approximation theorem which essentially states that any continuous map can be approximated by a smooth map. In the end he gives an application where he proves that any homotopy between smooth manifolds is […]

People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers? In another word, what is a pratical gambling game that involving some distributions that is relating to variance other than the normal distribution?

This question already has an answer here: Fourier transform for dummies 14 answers

Is there an application of graph theory (or group theory) in astronomy. If there is, refer me some references.

I’m carious to see applications of tensor product. Is there any set of things that if they happen or we encounter them then we use tensor product, tensor algebra, …? I will be happy if it be explained beside an example.

Does somebody know any application of the dual space in physics, chemistry, biology, computer science or economics? (I would like to add that to the german wikipedia article about the dual space.)

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 prove problems related to Group theory. But when comes to applications, I don’t know where to start. I […]

Let $G$ be a simple graph and denote by $\tau(G)$ the number of spanning trees of $G$. There are many results related to $\tau(G)$ for certain types of graphs. For example one of the prettiest (to me) is that if $C_n^2$ denotes the square of a cycle, then $$\tau(G) = n^2 f_n$$ where $f_n$ is […]

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