Self-Study General Relativity: After Multivariate Calc in HS

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Discussion Overview

The discussion revolves around the prerequisites for understanding General Relativity (GR) after completing multivariate calculus. Participants explore the necessary mathematical fields and recommend resources suitable for someone with limited mathematical experience, particularly a high school student.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant inquires about the mathematical fields needed after multivariate calculus to grasp General Relativity.
  • Another participant suggests that familiarity with multivariable calculus may be sufficient to start learning GR, particularly through accessible resources like Carroll's online lecture notes.
  • There is an emphasis on the importance of having a solid understanding of Newtonian physics and classical electrodynamics as foundational knowledge before tackling GR.
  • Multiple resources, including textbooks and online materials, are proposed for studying GR and related topics, though specific recommendations vary.
  • One participant requests clarification on what it means to "understand GR," indicating a need for more specific goals in the learning process.

Areas of Agreement / Disagreement

Participants generally agree that a background in multivariable calculus is a good starting point for learning GR, but there is no consensus on the exact mathematical fields or textbooks that should follow. The discussion remains unresolved regarding the best approach and resources for a high school student.

Contextual Notes

Participants mention the necessity of a physical background in Newtonian physics and classical electrodynamics, but do not specify which aspects are most critical or how they relate to learning GR. There is also a lack of consensus on the best resources for someone with limited mathematical experience.

Who May Find This Useful

This discussion may be useful for high school students or self-learners interested in pursuing General Relativity and seeking guidance on the necessary mathematical and physical foundations.

SirMadame
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I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what corresponding textbooks I should get from those fields. Also, what General Relativity textbook would be best suited for me with my limited mathematical experience. I am still in high school, so I cannot reference any university material directly.
 
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SirMadame said:
what General Relativity textbook would be best suited for me with my limited mathematical experience

You might try Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019

These notes should be reasonably accessible if you are familiar with multi-variable calculus; they develop the key ideas of differential geometry from that base.
 
SirMadame said:
I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR

If you are familiar with multi-variable calculus, you probably have enough mathematical background to start learning GR (for example, from the notes I linked to in my previous post).

What you really need is the physical background. You need to be reasonably familiar with Newtonian physics (three laws of motion and gravity) and with classical electrodynamics (Maxwell's Equations and the Lorentz force law). Unfortunately I don't know of good introductory textbooks for these subjects, but many high schools have physics classes, so you might be able to take one, or to ask your school's physics teacher for suggestions.
 
Can you be more specific about the goal to "understand GR"?

https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20

http://www.eftaylor.com/download.html#special_relativity
http://www.eftaylor.com/spacetimephysics/
http://www.eftaylor.com/exploringblackholes/

http://www.gravityfromthegroundup.org/

http://pages.pomona.edu/~tmoore/grw/
http://pages.pomona.edu/~tmoore/grw/Resources/GRWC1.pdf
http://pages.pomona.edu/~tmoore/grw/Resources/GRWBook.pdf [sample]

https://www.youtube.com/user/eigenchris/playlists
looks pretty good, from what I have seenHere is my ancient website (relocated from its original location) that I made in 1995 when I was a grad student (and when the web was young). It was heavily based on Geroch's "General Relativity from A to B"
http://visualrelativity.com/LIGHTCONE/
 
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