Struggling with Math: My Experience with Real Analysis

[bedi]

It has been a month now since I chose to study mathematics in college. In fact I want to do research in general relativity/cosmology so I think having a math degree first would be advantageous.
So I started with real analysis. I'm trying to understand the subject by myself. I read Rudin, covered the first 2 chapters and now I'm trying to do the proofs of all the theorems without looking at the book. I've asked several questions to you so far, and it looks like you all born with talent and knowledge... I'm not sure if I made any progress so far, could you tell me about your experience, how did you start and was the subject hard for you too or it's just me? It's hard to imagine all the steps while writing a proof...

 

[chiro]

Hey bedi and welcome to the forums.

There's been a lot of discussion about real analysis and a lot of people have commented on the difficulty especially when starting out.

My advice is to keep at it and soon enough things will get easier: it's like anything really.

Just don't think about it too much in the way that you expect things to fall into place straight away: if you chip away at something continually it will become clearer as time goes on.

Just remember though to interact with other people when you are stuck, or have a question, or want to talk about a particular issue or idea.

One thing you should remember is nowadays the amount of knowledge and advice you have access to is quite phenomenal and this website along I think is a testament to that, let alone the entire accessible internet content.

You wonder about talent and knowledge being born and while I agree that certainly a lot of people are talented at their particular things, I will say that these people are consumed by what they do and they work a lot and think a lot about these things, and most importantly they communicate with other like minded people.

It is a natural thing for like minded people to congregate with one another and this forum is a great example of this. Look at all the dialog that goes on and how ideas flow so readily, and how people debate with one another.

This is how you get good: you push yourself and you put yourself out there where other people can communicate with you, debate you on your ideas, and also discuss with you the intracacies of the topic.

Finally don't be worried about it being too hard: if you are always faced with a challenge you'll always have something to strive for and to work for.

 

[bedi]

Thank you for your advices, I would like to ask a lot of questions but they're mostly rather stupid...

 

[micromass]

In fact I want to do research in general relativity/cosmology so I think having a math degree first would be advantageous.

It won't be much of an advantage. Most courses will be a real waste of time for you. If you want to do research in physics, then you should major in physics.

 

[bedi]

It won't be much of an advantage. Most courses will be a real waste of time for you. If you want to do research in physics, then you should major in physics.

Well I obviously will need multivariable calculus. Topology, differential geometry and linear algebra are musts. However I'm not sure about measure theory and galois theory (I don't know anything about those two). All the analysis courses seem hard but fun and I think I must learn some set theory, group theory and ring theory to understand topology, I'm not sure about that too, though.

 

[Nabeshin]

Well I obviously will need multivariable calculus. Topology, differential geometry and linear algebra are musts. However I'm not sure about measure theory and galois theory (I don't know anything about those two). All the analysis courses seem hard but fun and I think I must learn some set theory, group theory and ring theory to understand topology, I'm not sure about that too, though.

It really depends on how you want to approach the subject of GR. From what you're saying, it sounds much more like you want to approach of from the mathematical standpoint than the physics standpoint. That's all fine and good, and there are people who do this, but just know that it's mathematics, not physics.

If you want to talk about physics, you can run a large spectrum in mathematics required. It really depends on what specific kinds of questions you want to ask. To get an idea, think of a specific problem, question, or research area and look up some papers on it on the arxiv. This should give you a decent sampling of the kind of math used.

 

[micromass]

Well I obviously will need multivariable calculus. Topology, differential geometry and linear algebra are musts.

Right, but that's hardly a reason to do a major in math. You could take most relevant math courses with a minor or just as optional courses.

However I'm not sure about measure theory and galois theory (I don't know anything about those two).

You won't need those. And if you ever do, you can always self-study them easily.

All the analysis courses seem hard but fun and I think I must learn some set theory, group theory and ring theory to understand topology, I'm not sure about that too, though.

You just need to be acquainted with set theory before doing topology. You won't need groups and rings. Unless you're going into algebraic topology. And even then, you can easily self-study whatever algebra you need.

 

[Hercuflea]

I have a complementary question that pertains to this thread...

If one's school does not offer a physics or engineering degree, would choosing math as a major be the best option aside from changing schools? I think I am kind of in the same situation as the OP because I am using my math degree more as a tool for graduate school than as the end goal.

 

[bedi]

I have a complementary question that pertains to this thread...

If one's school does not offer a physics or engineering degree, would choosing math as a major be the best option aside from changing schools? I think I am kind of in the same situation as the OP because I am using my math degree more as a tool for graduate school than as the end goal.

Actually I'm exactly in the same situation, but I will try to change my school in my sophomore year. I won't be upset if I can't though.

 

[jk]

If you're interested in physics, you should study physics