What is the study of higher dimensions?

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Discussion Overview

The discussion centers around the study of higher dimensions, particularly in the context of mathematical concepts such as hypercubes and the calculus applicable to these dimensions. Participants explore the existence of fields and methods related to higher-dimensional calculus and related mathematical disciplines.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the name of the study of higher dimensions, specifically mentioning hypercubes and expressing a desire to learn higher-dimensional calculus.
  • Another participant explains that the methods of calculus can be generalized to higher dimensions, allowing for the study of functions from ℝn to ℝ, and mentions the generalization of limits, differentials, and integrals.
  • A subsequent reply suggests that after mastering multi-variable calculus, one could progress to differential geometry.
  • Another contribution recommends looking into advanced abstract algebra courses, which may cover topics like reflection groups and Coxeter diagrams relevant to higher-dimensional spaces.

Areas of Agreement / Disagreement

Participants present various pathways and fields related to the study of higher dimensions, but there is no consensus on a singular approach or field that encompasses all aspects of higher-dimensional study.

Contextual Notes

The discussion does not resolve the specific definitions or boundaries of the fields mentioned, nor does it clarify the prerequisites or assumptions necessary for studying 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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