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

[diracy]

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.

 

[Intervenient]

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

 

[xdrgnh]

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

 

[Intervenient]

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.

 

[Matrix0]

As a scientist with a background in theoretical physics, I would recommend taking a variety of advanced math courses in preparation for a PhD in this field. In addition to the courses you have already taken in linear algebra, differential equations, and multivariable calculus, I would suggest taking courses in abstract algebra, real analysis, complex analysis, and topology. These courses will provide you with a strong foundation in mathematical concepts and techniques that are essential for understanding and solving complex problems in theoretical physics.

In terms of order, I would suggest taking abstract algebra and real analysis before complex analysis and topology. This will allow you to build upon the concepts and techniques learned in linear algebra and multivariable calculus to develop a deeper understanding of abstract mathematical structures and rigorous proofs. Complex analysis and topology are particularly important for theoretical physics as they provide powerful tools for solving problems in quantum mechanics and general relativity.

Additionally, I would recommend taking courses in numerical methods and computational techniques. In today's world, computational methods are becoming increasingly important in theoretical physics research, and having a strong background in these areas will make you a more competitive candidate for PhD programs.

Overall, the most important thing is to have a solid understanding of fundamental mathematical concepts and techniques, as well as the ability to think critically and creatively when applying them to solve problems in theoretical physics. I would also suggest seeking out opportunities for research or independent study projects in math and physics to further develop your skills and interests. Best of luck in your academic journey!