What is the study of higher dimensions?

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SUMMARY

The study of higher dimensions is primarily referred to as multi-variable calculus, which generalizes traditional calculus concepts to functions of the form y = f(x1, x2, ..., xn). This field encompasses limits, differentials, and integrals in higher dimensions, allowing for a deeper understanding of complex functions. Following multi-variable calculus, students should explore differential geometry and advanced abstract algebra, which includes topics such as reflection groups and Coxeter diagrams relevant to higher-dimensional spaces.

PREREQUISITES
  • Basic calculus knowledge (Calc 123)
  • Understanding of ordinary differential equations (ODE)
  • Familiarity with linear algebra
  • Concepts of limits, differentials, and integrals
NEXT STEPS
  • Study multi-variable calculus to grasp functions of multiple variables
  • Explore differential geometry for insights into the properties of higher-dimensional spaces
  • Investigate advanced abstract algebra, focusing on reflection groups
  • Learn about Coxeter diagrams and their applications in higher dimensions
USEFUL FOR

Students and professionals in mathematics, particularly those interested in calculus, geometry, and abstract algebra, will benefit from this discussion on higher dimensions.

Nembrook
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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?
 
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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, ..., xn).

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

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