How Can You Create Your Own Mathematical Space and Explore Embedding Techniques?

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SUMMARY

The discussion centers on creating a custom mathematical space and exploring embedding techniques. The user seeks to understand various mathematical concepts, specifically in topology and differential geometry, to achieve their goals. They have a foundational knowledge of partial differential equations (PDEs) and complex variables and are pursuing further education in graduate math physics. The conversation highlights the need for clarity in defining the type of mathematical space being referenced.

PREREQUISITES
  • Understanding of topology and its properties
  • Knowledge of differential geometry concepts
  • Familiarity with embedding techniques in mathematics
  • Background in partial differential equations (PDEs) and complex variables
NEXT STEPS
  • Research textbooks on topology, such as "Topology" by James Munkres
  • Explore differential geometry resources, including "Differential Geometry of Curves and Surfaces" by Manfredo P. do Carmo
  • Study embedding techniques in mathematics, focusing on "The Geometry of Geodesics" by Robert J. McEliece
  • Consider enrolling in graduate-level courses in mathematical physics to deepen understanding
USEFUL FOR

Mathematics students, researchers in theoretical physics, and anyone interested in advanced mathematical concepts related to custom spaces and embedding techniques.

Winzer
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I would like to really get to know the ins and outs of spaces in general.
I would also like knowledge in embedding.

My first goal is to make my own space with certain properties I need/want.
My second goal would be to take some equation and imbed it in my own space.
Unfortunately my math background goes up to PDE's and complex variables.
I will have graduate math physics under my belt in the future.

I am looking for advice in terms of textbooks and possible math courses I could take.
Thanks.
 
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Pretty Please!
 
I doubt that anyone has any idea what you are asking! There are a variety of different mathematical fields that use the term "space". Are you referring to topology? Are you referring to differential geometry? Or are you talking about "space" in the physics sense?
 

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