What course should I take for my fifth semester: Quantum, Analysis, or Lab?

[ahsanxr]

So I'm still in the process of deciding my schedule for this semester. So far I know I'm taking:

Introductory E&M
Classical Mechanics (junior level)
Advanced Linear Algebra
Introductory Differential Geometry.

I need a fifth course but can't decide which one to do this semester. I'm deciding between Quantum Physics I (Griffiths), Introduction to Real Analysis (Rudin), and an Elementary Physics Lab course. Eventually I'm going to have to go through all of these, but I need to decide which one to do now. The two I don't do, I'll do together in my fifth semester (in my third right now) The thing is I don't have the recommended prerequisites for Quantum (haven't had a modern physics class yet, but I do know the math) and neither for RA (don't have substantial proof experience), and lab in general is time consuming, so whichever I take, it's going to require me to work very hard and hence I can't take more than one out of these three. So which one would you recommend for someone with the following plans in mind:

- grad school in theoretical physics, or math
- wants to do an REU, preferably in math, in summer 2012.
- might graduate early
- might apply to programs such as Part III (Cambridge) or QFFF (Imperial) in the UK when I'm done.

My personal feeling is that lab seems the least interesting to me, while Analysis and Quantum seem extremely interesting but I'm afraid of the challenge they will pose in terms of hard work and that I might have to end up withdrawing or with a bad grade if it turns out to be too much.

(PS I'm sorry if you think I've been making too many threads lately, it's just that I'm in my second year now and I'm trying to set out a concrete plan, hence the need for advice)

 

[micromass]

I think quantum should be out. If you don't have the necessary prereqs, then this will probably be hard.
The same for real analysis. If you're struggling with proofs, then Rudin will be a hell for you. It's better to learn proofs while taking some easier classes first.
So that leaves us with the lab course.

Furthermore, you have four very theoretical courses already. Maybe a lab course could be a nice complement to all the theory?

 

[ahsanxr]

I think quantum should be out. If you don't have the necessary prereqs, then this will probably be hard.
The same for real analysis. If you're struggling with proofs, then Rudin will be a hell for you. It's better to learn proofs while taking some easier classes first.
So that leaves us with the lab course.

Furthermore, you have four very theoretical courses already. Maybe a lab course could be a nice complement to all the theory?

Well I'm willing to work very hard, as long as it's doable. So by "hard" what do you mean? I can devote up to 15 hours per week for Quantum or Analysis. The reason why I'm considering analysis is that the "Advanced Calculus" (the title doesn't make any sense whatsoever) class which I was thinking about taking, goes over Basic Linear Algebra (6 weeks), some Vector Analysis (2-3 weeks) and then some Complex Variables (4-5 weeks) which sounds like an easy class and can be skipped completely and I honestly don't want to be doing useless computation problems in Linear Algebra AGAIN (it's going to be my fourth time, honestly). I want a more challenging experience.

As for lab, I know I'm going to have to do this sometime in my undergrad (if I am to get a Physics BS) but writing 10 page lab reports every week just doesn't seem too appealing to me right now. And it might end up being useless if I decide to go into pure math or a very mathy side of physics, and this is the year where I'm trying to decide.

 

[micromass]

Well I'm willing to work very hard, as long as it's doable. So by "hard" what do you mean? I can devote up to 15 hours per week for Quantum or Analysis. The reason why I'm considering analysis is that the "Advanced Calculus" (the title doesn't make any sense whatsoever) class which I was thinking about taking, goes over Basic Linear Algebra (6 weeks), some Vector Analysis (2-3 weeks) and then some Complex Variables (4-5 weeks) which sounds like an easy class and can be skipped completely and I honestly don't want to be doing useless computation problems in Linear Algebra AGAIN (it's going to be my fourth time, honestly). I want a more challenging experience.

As for lab, I know I'm going to have to do this sometime in my undergrad (if I am to get a Physics BS) but writing 10 page lab reports every week just doesn't seem too appealing to me right now. And it might end up being useless if I decide to go into pure math or a very mathy side of physics, and this is the year where I'm trying to decide.

Well, if you're prepared to work very hard for real analysis, then it might work out. But it will still be difficult, though.
If you're deciding this year whether to go into math, then it might be best to take some real math courses. Real analysis and abstract algebra are real math courses, so they will show you what math is all about.

The thing with the lab is also that the classes you're taking now are relatively easy. So spending to to write a 10 page lab report is ok. But once the courses get difficult, you may want to spend time at those courses instead of just writing another silly report. So if you don't take the lab now, then you will have to do the lab during the upper-level courses. And you might lose some valuable time with it...

 

[inknit]

Unless you have some important lecture tomorrow in advanced calc, you might want to come to analysis and see what it's like.

 

[ahsanxr]

Well, if you're prepared to work very hard for real analysis, then it might work out. But it will still be difficult, though.
If you're deciding this year whether to go into math, then it might be best to take some real math courses. Real analysis and abstract algebra are real math courses, so they will show you what math is all about.

The thing with the lab is also that the classes you're taking now are relatively easy. So spending to to write a 10 page lab report is ok. But once the courses get difficult, you may want to spend time at those courses instead of just writing another silly report. So if you don't take the lab now, then you will have to do the lab during the upper-level courses. And you might lose some valuable time with it...

It would be great if you expand a bit on what "difficult" means. I'm willing to go through the text extensively, supplement it with others, and work on a proof book (Velleman) side by side (which I'm going to be going through for Advanced LA anyway).

Okay as for lab, well here are certain possibilities for which a lab might end up being completely useless to me:

1. If I decide to go into Math or Mathematical Physics
2. I'm highly considering entering Theoretical Physics through a mathematical program such as Part III at Cambridge.
3. I'm considering dropping the Physics major and just keep the upper division classes as it requires a lot of classes which take away a lot of time from my schedule (such as the above mentioned "Advanced Calculus", the second part of that course and 3 lab courses).

Is the lab something you eventually plan to take? And 10 page reports every week? Glad not to be a physics major

If I decide, to complete a Physics BS then yes.

And yes, I'll probably attend RA tomorrow.

 

[micromass]

It would be great if you expand a bit on what "difficult" means.

Rudin isn't easy because he doesn't do "pedagogical". He states his theorems and he proves them (often in a way that is not intuitive, but rather is elegant). He doesn't give any intuition... at all. It are only the results, he never talks about why we are doing a certain thing. So expect to get most intuition from other books or your lectures.

Furthermore, Rudin has exercises which often take a long time to think about. It may happen that you think about something for weeks. Rudin's exercises are not easy at all and can elude even the best students...

Rudin also deals with proofs as if it his natural language. Don't expect him to tell you how we prove something. He assumes that you know this already.

Complement Rudin with a book about proofs and an easier analysis book.

 

[hadsed]

I would do Quantum Mechanics. Griffith's is rather straightforward, and if you know a bit about differential equations, multi-variate calculus, linear algebra, and some of the basics of classical mechanics (the parts where you will need the advanced stuff will come if you take that class concurrently with quantum) you should be okay. To me, Analysis would be much harder than doing Quantum Mechanics, but of course that is up to the individual. And also, a physics lab might be more of a hindrance than a real class, which could be worse than having to actually take a class seriously. If your attitude isn't like that, then just ignore that bit (personally, that is my attitude as much as I realize that it is the wrong one).

 

[ahsanxr]

Rudin isn't easy because he doesn't do "pedagogical". He states his theorems and he proves them (often in a way that is not intuitive, but rather is elegant). He doesn't give any intuition... at all. It are only the results, he never talks about why we are doing a certain thing. So expect to get most intuition from other books or your lectures.

Furthermore, Rudin has exercises which often take a long time to think about. It may happen that you think about something for weeks. Rudin's exercises are not easy at all and can elude even the best students...

Rudin also deals with proofs as if it his natural language. Don't expect him to tell you how we prove something. He assumes that you know this already.

Complement Rudin with a book about proofs and an easier analysis book.

It certainly sounds like I'm ill-prepared for a class using this book. I think I might just end up delaying it til junior year. By then I'd have classes in Advanced LA and Abstract Algebra which will hopefully develop my mathematical maturity well enough to handle Rudin.

I would do Quantum Mechanics. Griffith's is rather straightforward, and if you know a bit about differential equations, multi-variate calculus, linear algebra, and some of the basics of classical mechanics (the parts where you will need the advanced stuff will come if you take that class concurrently with quantum) you should be okay. To me, Analysis would be much harder than doing Quantum Mechanics, but of course that is up to the individual. And also, a physics lab might be more of a hindrance than a real class, which could be worse than having to actually take a class seriously. If your attitude isn't like that, then just ignore that bit (personally, that is my attitude as much as I realize that it is the wrong one).

Would others agree that Quantum Mechanics would be easier than Analysis if a person doesn't have the necessary prerequisites (a modern physics class, and mathematical maturity respectively)?

Griffiths is intended to be an "introductory" book, isn't it?

 

[micromass]

Why not rent Griffiths and Rudin at the library and see what they look like. Read the first chapter and decide for yourself whether you are ready for the books.

 

[ahsanxr]

Why not rent Griffiths and Rudin at the library and see what they look like. Read the first chapter and decide for yourself whether you are ready for the books.

Yes, I've "acquired" both through other means and will be going through them. Quantum seems more likely as of right now.