Enough Maths for Physics Grad School?

In summary, the speaker is currently in a theoretical astrophysics research group and plans to have completed three years there by the end of their undergraduate degree. They have recently considered pursuing theoretical physics instead of experimental, but they are concerned that they may not have completed enough math courses to be accepted into a graduate program. They have taken several math courses, including Calculus I, II, & III, Differential Equations, Matrix Algebra, and Methods of Theoretical Physics I & II. However, they are limited in their ability to take more math courses due to prerequisites. Despite this, they have been advised that for most theorists, a solid foundation in basic math is enough and they can learn more advanced math on their own. They also mention that
  • #1
Mike K
24
1
I am currently in a theoretical astrophysics research group. By the end of my undergrad, I plan to have done 3 years there. However, only recently did I consider doing theoretical, not experimental, physics. But I am worried that I won't have completed enough maths to be accepted anywhere. Right now, by the end of my undergrad, I should have taken:
Calculus I, II, & III
Differential Equations
Matrix Algebra
Engineering Mathematics
Methods of Theoretical Physics I & II (which focuses on PDEs and Group Theory)

Unfortunately, most math courses require a foundations in math prerequisite, so I don't have much room to take more maths. Is this enough to get into grad school to study theoretical physics? I could try to shuffle around my schedule to fit in the foundations course and another math like analysis or topology. I have taken many upper level physics electives already, so I guess I could reluctantly cut back a few.
 
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  • #2
Mike K said:
I am currently in a theoretical astrophysics research group. By the end of my undergrad, I plan to have done 3 years there. However, only recently did I consider doing theoretical, not experimental, physics. But I am worried that I won't have completed enough maths to be accepted anywhere. Right now, by the end of my undergrad, I should have taken:
Calculus I, II, & III
Differential Equations
Matrix Algebra
Engineering Mathematics
Methods of Theoretical Physics I & II (which focuses on PDEs and Group Theory)

Unfortunately, most math courses require a foundations in math prerequisite, so I don't have much room to take more maths. Is this enough to get into grad school to study theoretical physics? I could try to shuffle around my schedule to fit in the foundations course and another math like analysis or topology. I have taken many upper level physics electives already, so I guess I could reluctantly cut back a few.
It's not clear what 'Engineering Mathematics' covers that isn't already covered in the other courses you have listed. If it duplicates the material in the other courses, it would seem like a good course to drop and substitute something more relevant to your grad school work.
 
  • #3
For most theorists, if you have a solid foundation in basics (maybe have take a few more specialized courses), you can learn the rest you need ok your own. The way the average theorist thinks about math is a lot different than the way mathematicians do. This includes many theorists who use a lot of advanced math in their research.

For example, in my field there are a lot of people who use notions from topology, representation theory, differential geometry, projective symmetry groups, etc. but when you talk to many of them, they don't seem to think of themselves as very mathematical. This is because they are applying math to physical problems in a way which may not be rigorous. I've asked several of these people if I should take more math, but they all seem to say it is more useful to learn it on my own.

If you talk to mathematicians about things like path integrals, renormalization, or the AdS/CFT correspondence, for example, they will be very disturbed by the techniques used since from my understanding, many of these things have never been proven to work in a mathematically rigorous way, they just seem to work.
 
  • #4
SteamKing said:
It's not clear what 'Engineering Mathematics' covers that isn't already covered in the other courses you have listed. If it duplicates the material in the other courses, it would seem like a good course to drop and substitute something more relevant to your grad school work.

I agree. Conviently, I planned to take it next semester; instead I will the foundations course and maybe I will find time in my last semesters for a higher level math.
 
  • #5
radium said:
For most theorists, if you have a solid foundation in basics (maybe have take a few more specialized courses), you can learn the rest you need ok your own. The way the average theorist thinks about math is a lot different than the way mathematicians do. This includes many theorists who use a lot of advanced math in their research.

For example, in my field there are a lot of people who use notions from topology, representation theory, differential geometry, projective symmetry groups, etc. but when you talk to many of them, they don't seem to think of themselves as very mathematical. This is because they are applying math to physical problems in a way which may not be rigorous. I've asked several of these people if I should take more math, but they all seem to say it is more useful to learn it on my own.

If you talk to mathematicians about things like path integrals, renormalization, or the AdS/CFT correspondence, for example, they will be very disturbed by the techniques used since from my understanding, many of these things have never been proven to work in a mathematically rigorous way, they just seem to work.
Interesting; well I am certainly willing to learn such maths on my own.
Thank you, it is good to know that I will be able to still conduct theoretical research (and, less importantly, not be viewed as behind for lack of maths in admissions).
 

1. What level of math is required for physics graduate school?

The level of math required for physics graduate school varies depending on the specific program and research focus. Generally, a strong foundation in calculus, linear algebra, and differential equations is necessary. Some programs may also require advanced topics such as complex analysis, group theory, and partial differential equations.

2. Is it necessary to have a degree in math for physics graduate school?

No, it is not necessary to have a degree in math for physics graduate school. However, a strong understanding of mathematical concepts and techniques is crucial for success in physics graduate studies. Many physics programs offer math courses specifically tailored for their students.

3. What math skills are most important for physics graduate school?

The most important math skills for physics graduate school include problem-solving ability, critical thinking, and the ability to manipulate and apply mathematical concepts to physical problems. In addition, a strong understanding of calculus and linear algebra is crucial for success in most graduate-level physics courses.

4. Can I learn enough math for physics graduate school on my own?

While it is possible to learn some math on your own, it is highly recommended to take formal courses in math to prepare for graduate school. These courses not only provide a structured learning environment, but also allow for interaction with professors and peers, which can greatly enhance understanding and retention of mathematical concepts.

5. How can I improve my math skills for physics graduate school?

To improve your math skills for physics graduate school, it is important to practice regularly and seek help when needed. Taking additional math courses, participating in study groups, and working on challenging problems can also help strengthen your math skills. Additionally, reading and engaging with mathematical literature can help build intuition and deeper understanding of mathematical concepts.

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