Math Levels for different Physics Courses

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Discussion Overview

The discussion revolves around the mathematical prerequisites necessary for studying advanced topics in physics, specifically Quantum Mechanics, Relativity, and String Theory. Participants explore the relevance of various mathematical fields, including calculus, linear algebra, and differential equations, in relation to these subjects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to understand the level of mathematics needed for Quantum Mechanics, Relativity, and String Theory, mentioning differential equations and partial differential equations.
  • Several participants emphasize the importance of linear algebra for Quantum Mechanics, with one stating it is fundamental to the theory.
  • A participant lists various topics covered in their linear algebra course, highlighting its depth and relevance to physics.
  • There is a question raised about the relative importance of linear algebra compared to differential equations, with one participant suggesting they are equally important.

Areas of Agreement / Disagreement

Participants generally agree on the significance of linear algebra for Quantum Mechanics, but there is a debate regarding the comparative importance of linear algebra and differential equations, with differing opinions expressed.

Contextual Notes

The discussion reflects varying levels of familiarity with the mathematical concepts and their applications in physics, and does not resolve the question of which mathematical discipline is more critical.

sr6622
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I am currently in Cal AB and will hopefully study through Cal BC this year. I am raelly interested in Quantum Mechanics, Relativity, and String theory.

I just wanted to know what level of math I will need to study Quantum, relativity, and string theory in depth.

Like Diff Q's, Partial Diff Q's?

I just want to know so I have some mathematical direction...

BTW, Cal BC is like Cal I.5, i think...
 
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I think linear algebra is pretty important for QM.
 
Nothing000 said:
I think linear algebra is pretty important for QM.

I think Linear Algebra would benefit any Physicists.
 
Nothing000 said:
I think linear algebra is pretty important for QM.

SURE IT IS.

Linear Algebra is the fundamental mathematical formalism behind the theory of QM.

Any physicist who gets a "respectable" education will have passed some heavy courses on linear algebra. In college i studied many aspects of linear algebra in the very first year like :

1) all the stuff on vectors like linear combinations, linear dependence, etc etc (we already saw this in high school)
2) linear transformations
3) affine algebra (incidence geometry and parallel classes)
4) projective geometry (angle of Laguerre )
5) homogeneous coordinates
6) eigenvalues and eigenvectors
7) 3-D geometry (also covered in high school)
8) intro to group theory (Cayley tables, cosets, equivalent classes)

This was, together with the calculus course, one of the biggest courses in my first year of college. Lot's of theorems and proofs and exercises...

regards
marlon

Here is http://aivwww.ugent.be/Studentenadministratie/Studiegids/2005/EN/FACULTY/WE/COURSE/CBNAST/01000009/INDEX.HTM
 
Last edited by a moderator:
Would you guys say that linear algebra is more important than differential equations, or is Diff E just as important? I am not majoring in physics, I am just wondering.
 
Nothing000 said:
Would you guys say that linear algebra is more important than differential equations, or is Diff E just as important? I am not majoring in physics, I am just wondering.

No, they are most certainly equally important.

marlon
 

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