In Mathematics, a set is denoted by a capital letter and is represented by writing it in the roster form, set builder form and descriptive form.
In Physics, a vector is denoted by a letter of the alphabet or the end points of the directed line segment which is representing it with an arrow(half or full) or a bar above or a tilde(~) below and is represented by a directed line segment drawn to scale whose length represents the magnitude of the vector and whose direction represents the direction of the vector.
The dictionary says:
Denote - verb (used with object)
1.to be a mark or sign of; indicate: A fever often denotes an infection.
2.to be a name or designation for; mean.
3.to represent by a symbol; stand as a symbol for.
Represent - verb (used with object)
1.To serve to express, designate, stand for, or denote, as a word, symbol, or the like does; symbolize: In this painting the cat represents evil and the bird, good.
2.To express or designate by some term, character, symbol, or the like:
The meaning of both the words seem similar to me
What is the difference between denotation and representation (denote and represent) and their usage? I guess that representation is some what related to description.