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

 

[Kirti_Vardhan_1]

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.

While most would say that applied math PhDs can work out without it, in reality one should be far above the normal abilities if one is going for a doctorate, that, from all my research and experience, means one should basically enjoy all his math subjects including group theory..so as to be able to contribute research that is original - I believe the entire point of the PhD including qualifiers. Most PhDs from serious places require GPAs above 3.3 to 3.5+..anyway, so I would normally tend to assume one should absolutely enjoy all his subjects and know them 'like the back of their hand'. While I am not a mathematician, Group theory is a core topic in any math degree but not considered core in applied mathematics at least for entry.

While the good score in the MATH GRE is also seemingly recommended. group theory underpins a lot of what’s going on in many engineering, physics, and computer science contexts.

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1. Symmetry and Transformations
- Group theory formalizes symmetry operations such as rotations, reflections, and translations.
- Example: In signals and systems, the Fourier transform is tied to the group structure of time shifts, and frequency analysis makes use of group representations.

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2. Coding Theory and Cryptography
- Error-correcting codes (Reed–Solomon, BCH) are constructed using finite groups and fields.
- Modern cryptographic schemes (RSA, elliptic curves) are explicitly based on group-theoretic structures.

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3. Control Theory and Dynamics
- In robotics and control systems, rigid-body motions are modeled using Lie groups such as **SO(3)** and **SE(3)**.
- Stability and controllability analyses often make use of Lie algebras and their properties.

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4. Physics and Engineering Applications
- Crystallography classifies lattice symmetries using point groups.
- In quantum mechanics, particle states are described by representations of groups such as SU(2) and SU(3).

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5. Computer Science
- Automata theory and formal languages employ group-theoretic concepts to analyze transformations on states.
- Algorithm design often uses symmetry reduction, which is grounded in group theory.

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[FactChecker]

You might want to look at the requirements for entering into the PhD program at the University and field of your choice. I would be surprised if Real Analysis was not required. Abstract Algebra might be, but I can think of others (like statistics) that are more likely. You might have to pass a test on those subjects to be accepted as a PhD candidate. I can tell you that if you have not had a class in those subjects, you will be at a great disadvantage to students who are reviewing subjects that they have already had.

 

[FactChecker]

I have a fondness for Abstract Algebra (but not much ability). It answers the question: "Given the most basic, minimal assumptions about a set and its mathematical operations, what can be proven?". Once that is addressed, it is surprising how many examples and applications it has in all fields because the assumptions were so minimal.

 

[hutchphd]

I would think that any afficionado of mathematics would be fascinated by the questions represented by Bertrand Russell and his Paradox. Does this not require some sure knowledge of groups and their foibles? (I am not a mathematics person)

 

[Muu9]

I would think that any afficionado of mathematics would be fascinated by the questions represented by Bertrand Russell and his Paradox. Does this not require some sure knowledge of groups and their foibles? (I am not a mathematics person)

Not really, no. At least I don't think that has anything to do with the operations on sets you see in group theory.