Applied Math PhD candidate but I hate group theory

[ansabs]

TL;DR Summary: I want to do a PhD in applied math but I hate group theory, is this a big problem?

Hello, I am a second-year math and physics double major with a minor in data science. I just finished group theory (today actually), and it was my least favorite class in all of university so far. It doesn't interest me, and I am also very bad at it compared to other math courses I have done. The other courses I have done are calculus I-III, ODEs, Linear Algebra, and Prob/Stats. Is it a problem that I really dislike group theory? I am planning on doing a PhD in applied mathematics after I graduate, focusing on mathematical/computational modeling, dynamical systems, and scientific computing. All of my undergrad research has been computational physics, machine learning, and mathematical modeling.

I know this may sound a little ridiculous, but let me know if you have any advice.

 

[Hornbein]

TL;DR Summary: I want to do a PhD in applied math but I hate group theory, is this a big problem?

Hello, I am a second-year math and physics double major with a minor in data science. I just finished group theory (today actually), and it was my least favorite class in all of university so far. It doesn't interest me, and I am also very bad at it compared to other math courses I have done. The other courses I have done are calculus I-III, ODEs, Linear Algebra, and Prob/Stats. Is it a problem that I really dislike group theory? I am planning on doing a PhD in applied mathematics after I graduate, focusing on mathematical/computational modeling, dynamical systems, and scientific computing. All of my undergrad research has been computational physics, machine learning, and mathematical modeling.

I know this may sound a little ridiculous, but let me know if you have any advice.

I'd say that group theory has little to do with applied mathematics.

 

[FactChecker]

For PhD research, you may have to deal with a lot of things that are not your strength. It's not a question of whether you like group theory on its own, but rather if you can handle parts of group theory that are relevant to your field. The fact that you disliked it initially should not be a show stopper. A lot of people don't like it initially.

FYI, Emmy Noether is often credited with the development of abstract algebra (of which group theory is a part). She also proved Noether's Theorem, which is one of the most profound theorems in physics.

 

[hutchphd]

I know this may sound a little ridiculous, but let me know if you have any advice.

In my experience, the subjects that I "hate" are those that I do not truly understand. Likely this is because their approach is, on some level, antithetical to my own. Understanding such subjects is both very difficult and very important. This is more a psychological than a strictly logical exercise and so you need to find a mentor who can help you. A mentor is someone who knows you and group theory.
Incidentally group theory is pretty good stuff. Not really all that complicated, yet very powerful.

 

[Klystron]

Is it a problem that I really dislike group theory?

NIMO (Not in my opinion.) I found a firm grounding in set theory served me well in mathematics/CS academia, though I also enjoyed studying and solving abstract algebra. IMO set theory permits one to think geometrically while also providing a framework for learning mathematics.

I discussed these ideas with Calculus III classmates who laughed and stated that they liked calculus in order to avoid solving so much (tedious) algebra. This was ~50 years ago when group theory was probably not as formalized as today.

Since I also like what I have learned of group theory, perhaps you just had an incompatible instructor or a difficult schedule.

 

[hutchphd]

I like to think of group theory as set theory with verbs added . With the addition of these few rules it becomes a much more useful tool. The O.P. must have had a really bad prof.

 

[mathwonk]

If you think a group is a set of symbols with a binary operation having identities, inverses, and associativity, they can be abstract and boring. But if you think of them as invertible transformations of a space, with properties such as isometry, smoothness, or linearity, they can have lots of geometric content. Here is a relevant course description:
https://mastermath.datanose.nl/Summary/418

 

[Muu9]

Try taking some proof-based courses in a different field, like analysis.

 

[bryantcl]

Assuming you're applying to programs in the United States, I concur with the poster that said, in the course of your Ph.D studies you may be required to take a course that you dislike. This could be to fulfill some course requirement of your program or your advisor may encourage you to take it as it may has some relation to your research.

However, hope is not lost. When applying to programs take a look at their research foci and course requirements. This should tell you if a course in group theory in particular or abstract algebra in general is required.

Hope this helps,
CLB