Math Courses for Theoretical Physics PhD - Linear Alg., Diff Eq, Calc & More

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Discussion Overview

The discussion centers on the appropriate mathematics courses for undergraduate students intending to pursue a PhD in theoretical physics. Participants share their experiences and suggest various courses that may be beneficial, focusing on the order and necessity of these courses.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant inquires about the necessary math courses for a theoretical physics PhD, noting their completion of linear algebra, differential equations, and multivariable calculus.
  • Another participant outlines a typical sequence of math courses at UCSB, including two quarters each of calculus, linear algebra, and differential equations, followed by vector calculus.
  • A different participant agrees with the UCSB sequence but argues that additional math courses are essential, suggesting complex variables, abstract algebra, mathematical physics, and differential geometry, among others.
  • One participant emphasizes that they are merely reporting the mathematics prerequisites at their school and expresses uncertainty about the content of upper division physics classes.

Areas of Agreement / Disagreement

Participants express differing views on the sufficiency of the suggested math courses, with some advocating for a more extensive curriculum while others provide a standard sequence without consensus on the necessity of additional courses.

Contextual Notes

There are varying assumptions about the prerequisites for upper division physics classes and the extent to which they cover mathematical concepts. The discussion does not resolve these uncertainties.

diracy
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If I'm interested in pursuing a theoretical physics PhD, what math courses should I be taking in undergrad and in what order should they be done? I've already taken linear algebra, differential equations, and multivariable calculus, so at a level more advanced than that. I appreciate the help.
 
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At my school (UCSB), it's done

1. Two quarters of Calculus
2. Two quarters of linear algebra and differential equations
3. Two quarters of vector calculus

After that, it's just loads of physics classes
 
Intervenient said:
At my school (UCSB), it's done

1. Two quarters of Calculus
2. Two quarters of linear algebra and differential equations
3. Two quarters of vector calculus

After that, it's just loads of physics classes

You need way more math then that. Take complex variables, abstract Algebra, a class in mathematical physics, differential geometry plus others. Here is my math schedule for undergrad. https://www.physicsforums.com/showthread.php?t=524112
 
xdrgnh said:
You need way more math then that. Take complex variables, abstract Algebra, a class in mathematical physics, differential geometry plus others. Here is my math schedule for undergrad. https://www.physicsforums.com/showthread.php?t=524112


I'm just reporting what the mathematics prereqs are at the school. I have no idea if the upper division physics classes don't learn those, I'm not a physics major.
 

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