Preparing for General Relativity and Quantum Mechanics: A Summer Study Guide

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SUMMARY

To prepare for studying General Relativity (GR) and Quantum Mechanics (QM), foundational knowledge in vector calculus, multivariable calculus, and differential geometry is essential. The discussion emphasizes the importance of mastering linear algebra before tackling the complexities of GR, which involves tensors and differential geometry. MIT video lectures are recommended as a resource, but supplementary materials for practice are necessary to solidify understanding. A Dover book on linear algebra is suggested as a practical starting point.

PREREQUISITES
  • Vector calculus
  • Multivariable calculus
  • Differential geometry
  • Linear algebra
NEXT STEPS
  • Explore MIT OpenCourseWare for video lectures on calculus and physics
  • Study a Dover book on linear algebra for foundational concepts
  • Practice problems in differential geometry and tensor calculus
  • Research online resources for free physics and math practice materials
USEFUL FOR

Students preparing for advanced studies in physics, particularly those aiming to understand General Relativity and Quantum Mechanics, as well as anyone looking to strengthen their mathematical foundation in preparation for college-level physics courses.

Jonnyb42
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Ok so I was just hoping if I could get some learning material over the summer. I have currently finished first year calculus and am ready to learn vector calculus/multivariable calculus. I have also finished first year physics. I would like to know enough math to learn General Relativity and then Quantum Mechanics later on.

I am planning on watching as many MIT video lectures as possible, however there doesn't seem to be enough actual calculating and practicing with the math, so could anyone suggest some online material (free) that I could use to practice the math and physics I learn.

Anything I could use to get to GR and QM eventually would be great, thanks!

Jonny

(this is for the summertime, I am starting first year college afterwards, however I cannot wait!)
 
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The math you want to study is differential geometry/tensors for general relativity. With your current experience, you probably don't want to attack this just yet - it won't be very productive.

Maybe get a dover book on linear algebra and work though the material and all the problems?
 

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