What is the study of higher dimensions?

[Nembrook]

What is the study of higher dimensions called? What I'm referring to are hyper cubes and such. I finished basic math this past year (calc123, ode and linear alg) and I really want to learn the calculus of higher dimensions. Does a field like this exist?

 

[Dr. Seafood]

The methods of calculus that you probably recently learned can be generalized to higher dimensions. This means to study functions from ℝⁿ to ℝ. As such, functions are of the form y = f(x₁, x₂, ..., x_n).

Ideas like limits, differentials, and integrals can be generalized to encompass functions of that form. In fact, considering higher dimensions allows us to use ideas we couldn't use with functions of a single real variable.

Look up multi-variable calculus.

 

[I like Serena]

After multi-variable calculus you can move on to differential geometry.

 

[micromass]

Also check out advanced abstract algebra courses. These courses sometimes study reflection groups and Coxeter diagrams and the like. These things are used to study higher dimensional spaces...