Math Levels for different Physics Courses

[sr6622]

I didn't really know which thread to post this in...

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...

 

[Jelfish]

There is a forum called "Academic and Career Guidance" that might be more appropriate.

In regard to your question, I would say that if you plan on taking these courses in college, you won't have to worry about what to study as they will definitely be prerequisites.

Here's a rough guideline for quantum mechanics and general relativity:

Quantum mechanics deals with the Schrödinger Equation, so you definitely need a course in differential equations, specifically ones that will teach you methods in variable separation for partial differential equations. Also, you'll be going into spherical potentials, which will require you to be comfortable with multivariable integration (often called Calculus 3 in college). It would also be helpful to know some linear algebra and vector calculus when dealing with eigenfunctions and eigenvalues.

For general relativity, I would say that vector calculus and linear algebra are important. I haven't actually taken a course in it myself yet, but I looked over some of the math and those topics seem to stand out.

Keep in mind that in many college level classes, you'll learn some of the math as you learn the physics.

If you're in high school, you shouldn't have too much to worry about, especially if you're in calc BC. Most colleges have calc I & II courses so you'd be able to survive even if you went in with no math credit.

String Theory is something that you'd go into after your undergraduate career (meaning I have no idea what the pre-reqs are), but by then, you'll have a much clearer path on what courses you'll need to take.

If you're going to college, it would be much more helpful to talk with the advisor in the physics department, since every school is a little different.

Good luck!

 

[Curious3141]

There is a forum called "Academic and Career Guidance" that might be more appropriate.

In regard to your question, I would say that if you plan on taking these courses in college, you won't have to worry about what to study as they will definitely be prerequisites.

Here's a rough guideline for quantum mechanics and general relativity:

Quantum mechanics deals with the Schrödinger Equation, so you definitely need a course in differential equations, specifically ones that will teach you methods in variable separation for partial differential equations. Also, you'll be going into spherical potentials, which will require you to be comfortable with multivariable integration (often called Calculus 3 in college). It would also be helpful to know some linear algebra and vector calculus when dealing with eigenfunctions and eigenvalues.

For general relativity, I would say that vector calculus and linear algebra are important. I haven't actually taken a course in it myself yet, but I looked over some of the math and those topics seem to stand out.

Keep in mind that in many college level classes, you'll learn some of the math as you learn the physics.

If you're in high school, you shouldn't have too much to worry about, especially if you're in calc BC. Most colleges have calc I & II courses so you'd be able to survive even if you went in with no math credit.

String Theory is something that you'd go into after your undergraduate career (meaning I have no idea what the pre-reqs are), but by then, you'll have a much clearer path on what courses you'll need to take.

If you're going to college, it would be much more helpful to talk with the advisor in the physics department, since every school is a little different.

Good luck!

GR involves a good deal of tensor analysis. I remember that the math in GR (as opposed to SR) was very heavygoing.

 

[benorin]

As for http://superstringtheory.com/math/index.html, click on the link and browse through what the "Official String Theory Website" considers pertinent study material.

Study hard for your AP exams, I once TA'd for that class [AP clac BC]: but study the material, know it rather than the exams.