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...

 

[CellCoree]

The study of higher dimensions is a branch of mathematics known as topology. It involves the study of geometric properties and relationships that are preserved under continuous deformations, including those in higher dimensional spaces. The specific topic you mentioned, hypercubes, falls under the category of polytopes, which are higher dimensional analogues of polygons and polyhedra.

The study of higher dimensions is a very active and important field in mathematics, with applications in various fields such as physics, computer science, and engineering. The calculus of higher dimensions, also known as multivariable calculus, is an essential tool for understanding and solving problems in these fields.

There are many resources available for learning about higher dimensions and multivariable calculus, including textbooks, online courses, and research papers. I recommend starting with a solid foundation in basic multivariable calculus before delving into more advanced topics. With your background in calculus and linear algebra, you have a strong foundation to build upon. I encourage you to explore this fascinating and challenging field further and see where it takes you.