Is Pure Mathematics required to be a top-tier Physics student?

[XcgsdV]

Hey y'all, I'm starting college as a Physics major this fall and I started working through Steve Warner's Pure Mathematics for Beginners in my downtime because I love the math courses I've had, wanted to learn more about proofs and how those things came to be, and most importantly had nothing better to do.

I got to Abstract Algebra (chapter 3, I'm a real go-getter...) and I'm fairly certain Pure Mathematics is just not something I'm going to enjoy. I can absolutely appreciate the beauty and insight gained from a rigorous logically sound proof, but all the talk about monoids and semigroups is just not in my wheelhouse. I can understand and appreciate them as algebraic structures that have some purpose I'm sure, it's just that I'd rather not prove that (Q*, • ) is a commutative group. I understand that there is a purpose in doing so, but I don't see that purpose aligning with my goals or interests. *To be fair, I also don't have much exposure to more math other than the very basics of Abstract Algebra, so I very well could just not like Abstract Algebra, and like different areas of pure math. It is midnight though, so more likely than anything I just want to go to bed or play the new Fire Emblem Warriors instead of dealing with proofs, which is the most realistic option here.*

I know it is more than possible to get through undergrad without a single pure math course, but if my goal is to be the best undergraduate physics student I can, and be the ideal candidate for graduate schools (this is not necessarily my goal, but for the sake of argument), what level of understanding would I want with pure mathematics, and would I be better served taking courses like Abstract Algebra and Real Analysis, or more advanced CS courses, or more statistics courses, or anything of that nature? More chemistry/bio if I find myself interested is biophysics? Lots of questions, I apologize. The general idea is in the post title, is a strong grasp of Pure Mathematics required to be an ideal candidate as a Physics student?

Also p.s. I know none of this actually matters right now and I have 4 years to deal with it, I am just nosy and like planning and would appreciate some opinions from those more experienced than I.

 

[PeroK]

I'd say real analysis and linear algebra are topics where you benefit from knowing the pure mathematics behind them. The first is the foundations of Calculus and the second is the basis of QM.

The problem with abstract algebra is that you take a long time to get to the applied group theory that underpins Noether's theorem and much of advanced modern physics.

With group theory you probably need to be prepared to jump in at a higher level without studying the subject from the ground up.

Note that being able to construct a logically consistent proof is definitely useful. Usually your first linear algebra course is where that becomes important.

 

[CrysPhys]

I know it is more than possible to get through undergrad without a single pure math course, but if my goal is to be the best undergraduate physics student I can, and be the ideal candidate for graduate schools (this is not necessarily my goal, but for the sake of argument), what level of understanding would I want with pure mathematics, and would I be better served taking courses like Abstract Algebra and Real Analysis, or more advanced CS courses, or more statistics courses, or anything of that nature? More chemistry/bio if I find myself interested is biophysics? Lots of questions, I apologize. The general idea is in the post title, is a strong grasp of Pure Mathematics required to be an ideal candidate as a Physics student?

Well, that depends on what you mean by a "top-tier" physics student, doesn't it?

From the above portion of your first post, it doesn't appear that you're dead set on becoming a theoretical physicist, period, and it does appear that you're at least inclined to explore various options. The ability to explore various options via electives is what I consider to be a great strength of US universities (with some exceptions, probably). So if your university offers you that flexibility, I would recommend that you take advantage of it. But, there's only so much you can cram into a 4-yr program. Unless you have a calling for pure math, I wouldn't use up all my electives in it.

Personally, I went through a rigorous undergrad and PhD program in physics at top schools and didn't take a single course in pure mathematics. As an undergrad, I took the math courses (in the math department) required for physics majors; as a grad student, I took courses in mathematical methods in physics (taught in the physics dept and required for physics grad students). But as an undergrad, I knew I wanted to pursue experimental solid-state physics. So I spent most of my electives in optional physics labs and elective courses and labs in materials science and engineering.

 

[malawi_glenn]

I give you my five cents regarding math for physics.

- Most crucial: What kind of physics are you interested in? Are you more into experimental or theoretical physics? Have you glanced on graduate level textbooks and research papers in that field to get an idea what kind of math is important to master?

- It is more important to know WHY a certain theorem is true, and under what conditions it is valid / not valid, than to actually perform the proof of the theorem.

- One can never learn too much about linear algebra and differential equations (ordinary and partial)

- Some Fourier analysis/transforms and complex analysis is always useful

- You need to be comfortable with some programming and computational/numerical methods, many problems are solved with computer aid these days. My PhD work was in theoretical particle physics, and I'd say ~30% of that was basically just how to figure out how to write code and match that code with other peoples code to perform the calculations needed for my research.

- Study from a mathematical methods for physics book like these
https://www.amazon.com/dp/3319011944/
https://www.amazon.com/dp/0521679710/
https://www.amazon.com/dp/1108471226/
and use books on these topics written for mathematics students if/when you need to know the background better. Remember to look at the table of contents, some of these books to not cover variational analysis or differential geometry methods which are required for most theoretical physics. I like the Atland book as an intro because it is just the very basics (linear algebra and calculus topics + it has answers to problems so good for self study) (Hassani and Riley books are much fatter and contain more topics, some of which you will never need!)

- You can always go back and study the foundations of the math later if desired / needed once you know what is important for you to know.

 

[CrysPhys]

I give you my five cents regarding math for physics.

<<Emphasis added>> Is that to cover inflation?

 

[malawi_glenn]

Is that to cover inflation?

I felt it was too much to just be worth two cents

 

[apostolosdt]

Math for physics is much closer to 'Applied Math' stuff. Depending on your physics concentration, you may have to be picky with the math topics. Calculus and Linear Algebra are a must, though.