Complex Analysis or Solid State Electronics?

[intelwanderer]

First post. Great to be here. :)


So, I'm stuck in deciding which of these courses to take next semester. I'm a current rising sophomore at UT Austin who has just switched from EE to physics-still nervous about that decision, but that's a separate topic. I've already got Waves(the first "real" physics course, or so I've been told), and intro Modern/Quantum, my GPA is already a wreck from my first year(so I NEED to start doing better. Last year was a mess for a lot of reasons-I'm considering getting tested for bipolar disorder as just ONE example-but I'm still not confident about my mental abilities/study skills), and I want to really get involved in a lab next semester, so I think I should only pick one. Any advice?

For the physics major, complex variables is recommended, and they say I will need it for quantum mechanics(it's recommended in EE too, probably would have taken it eventually), but I'm more interested in the solid state course, and I'm not sure if I'll get to take it again if I get out. Would I be able to take quantum mechanics though without complex?

My math ground is: Linear Algebra, DiffEQ, Calculus. Nothing proof based. I talked to a math senior yesterday and he said that engineering kids struggled a lot in his class because it wasn't mainly computational. Also available are Probability and PDE's(I'm sure there are other maths, but those are the ones I know), but the former the professor's said I'd pick up in my classes, and the latter requires real analysis as a prereq, and I've gone over the basics of PDE's already from ODE class, so I don't know if it would be a wise investment to devote a whole course to it. I could be wrong though-that's why I'm asking, heh heh. It uses Brown/Churchill, which from looking at other threads seems to be standard. http://www.math.utexas.edu/academics/archives/2010f/fall10syllabi/_files/55505.pdf

I'm the type that gets the concept but will typically make a little algebra mistake here or there on a test which ends up costing me dearly. So, how would I fare in a proof-like course? Complex analysis does seem really interesting looking at it-very beautiful, and it's applied toward stuff like signals which appeals, I'm still planning on taking various engineering courses-but I don't want to get into something that's I'm utterly unprepared for. I plan on going to the math department HQ today to see what they think. Again, I wish I could take both, but that's just a risk I can't take.

I'm on good terms with the Solid State professor if that counts for anything.

 

[chill_factor]

Go for Solid State Electronics. It helps you see the bigger picture of how to apply your knowledge and isn't as dry as complex analysis so you'll be more motivated. You don't need that much complex analysis for undergrad quantum. At least, I didn't use anything too complicated. You don't need to know complex integration and differentiation for sure. Never saw that on a single test I took nor saw it on the tests I downloaded for practice.

I just flipped through my graduate quantum book to make sure, and didn't see much of complex analysis besides knowing what the star sign means and switching from sine/cosine to exponential notation for Fourier transforms. There is a single derivation that utilizes contour integration in a late chapter but you'll be in good shape for Quantum 1. You can take complex analysis at the same time you take Quantum 1 so you'll be ready for Quantum 2 if you really aren't sure.

 

[Number Nine]

Do you have any background in complex variables? It's pretty essential stuff. Not only does QM use them all the time (path integrals, anyone?), even functions of a real variable can often require techniques from complex analysis to evaluate.

 

[chill_factor]

Do you have any background in complex variables? It's pretty essential stuff. Not only does QM use them all the time (path integrals, anyone?), even functions of a real variable can often require techniques from complex analysis to evaluate.

Does it really? Have I been learning the wrong quantum mechanics? The first half of Griffith doesn't really use any complex analysis. Never came up on a single test I took. Never came up on practice qualifiers I downloaded. What chapters of which books does it come up in?

 

[clope023]

Does it really? Have I been learning the wrong quantum mechanics? The first half of Griffith doesn't really use any complex analysis. Never came up on a single test I took. Never came up on practice qualifiers I downloaded. What chapters of which books does it come up in?

You can use residue calculus to solve improper integrals, to my knowledge griffith's text has a few such problems but they're few and far between.

 

[intelwanderer]

Well, I talked to one of the professors yesterday-I'm going to go to the math advising office tomorrow likely-and he said real analysis would be a good preperation for it, but I'll need discrete math to take that(the prereqs here are weird sometimes, you only need ODE's for complex. Unfortuantely the bureaucracy can be really annoying/strict as well. It's ridiculous, if someone wants to take a course and has the background, or thinks he does, it shouldn't matter what major or year they are. If he doesn't he pays the price, not the school. Part of the reason I'd like to take solid state is I expended a lot of energy getting into that class.) And the upperclassman I mentioned earlier told me to avoid it if I haven't done other proof based courses.

The physics advisor though-not the math one-said a lot of kids, probably physics or EE majors(I'd think that would be the engineering major that would take it) take it without proofs or anything and do OK on the other hand. So it looks like I'm getting different responses.I need another math course for the degree requirement(not that I will limit myself to that). I know basic complex variables(differentiation, Euler's, the like), but not analysis or anything. I'm capable of teaching myself though, and I'd imagine I'd do better in solid state. But if I don't take this course, will I be screwed in quantum?

 

[Number Nine]

Does it really? Have I been learning the wrong quantum mechanics? The first half of Griffith doesn't really use any complex analysis. Never came up on a single test I took. Never came up on practice qualifiers I downloaded. What chapters of which books does it come up in?

In Griffiths, no (though it does touch on a few topics, I think: the zeta function?), but it becomes increasingly important as you go on. Even when the physics itself doesn't require it, complex variables are such a profoundly important aspect of applied mathematics that everyone should have at least an introductory treatment (it makes other aspects of mathematics easier/possible).

 

[chill_factor]

In Griffiths, no (though it does touch on a few topics, I think: the zeta function?), but it becomes increasingly important as you go on. Even when the physics itself doesn't require it, complex variables are such a profoundly important aspect of applied mathematics that everyone should have at least an introductory treatment (it makes other aspects of mathematics easier/possible).

thanks for the advice, but is it 100% absolutely necessary to take an entire class on it, or would reading by itself be enough, and for the OP, would it be worth giving up a class that might not be offered again and is directly relevant to his interests?

 

[intelwanderer]

The question is not, "should I take complex analysis", it's should I take it this semester? Actually, it partly is that, but it's not the more prudent question.

However, if I put it off, I'm probably going to do so for a while, because of other coursework. I want to make sure I won't be clobbered in quantum-and other pieces of physics-in the meantime. But if a few concepts are all I need, I don't see a reason to take a whole class on it(one which I'd be very nervous of doing well in, considering my performance in lower division math). I can just pick up what I need to know from a book any day. Truth be told, I prefer learning from books on my own over lectures, but I'm not sure I'm doing it properly. Not that that has to do with anything.

This semester, I have the unofficial intro to quantum(which I strongly doubt uses any complex analysis), than I start the "official" quantum sequence for the next three semesters after that.

If it were up to preference, it would be solid state all day. But it might not be what I need for future physics, and I don't really trust my own judgement anymore.

 

[SteveL27]

The question is not, "should I take complex analysis", it's should I take it this semester? Actually, it partly is that, but it's not the more prudent question.

You said you don't have any proof background. And I assume you have not yet taken real analysis? I think you will find complex analysis pretty difficult under those conditions. They'll be talking about convergence and assuming you have an understanding of the topological properties of the plane. But everyone's different. You should talk to the prof who will be teaching the class.

 

[intelwanderer]

"M361 consists of a study of the properties of functions of a complex variable.
Topics to be covered include: complex numbers, functions on the complex plane, Cauchy's theorem and its applications, Laurent series, residue theory and the calculation of some improper and some de nite integrals. Rigorous proofs will be given for most results, with the intent to provide the student with a reliable grasp of the results and techniques."

The math prof said to take real analysis as preparation. I'm hearing different things from different people, but he'd know best.

 

[chill_factor]

"M361 consists of a study of the properties of functions of a complex variable.
Topics to be covered include: complex numbers, functions on the complex plane, Cauchy's theorem and its applications, Laurent series, residue theory and the calculation of some improper and some denite integrals. Rigorous proofs will be given for most results, with the intent to provide the student with a reliable grasp of the results and techniques."

The math prof said to take real analysis as preparation. I'm hearing different things from different people, but he'd know best.

this doesn't sound too hard. seems like you just need to know the results and techniques on tests. it seems more of a "math methods" class than a math class. why on Earth would you need to do a (probably proof based) real analysis class for that?

Complex analysis is a hard prereq for your major. However, it only requires linear algebra as a prereq.

I know there's a lot of math and theoretical physics guys that'd disagree with me but I think that taking a whole year of analysis, just to learn quantum, is way overkill. At most schools, you go straight to quantum after finishing CM and EM, or after a "math methods" class. Don't know why UT Austin is so strict and rigorous.

 

[intelwanderer]

First, let me note that I'm definitely more the applied/experimental physics type, at least for now. I can appreciate "beautiful" math, but I'm definitely not a guy who plans on doing string theory or anything like that. I would rather take courses in engineering/chemistry/extra physics than more math. And I am taking intro to quantum next semester, as I noted before.

The official name of the class is "Theory of a Complex Variable".

Complex analysis isn't a prerequisite for any of the physics courses. I take intro quantum/quantum I this year whether I take complex or not, after freshman physics and ODE's, so... I just need one more math course as a requirement, and this is the one that was recommended to me.Also, I just discovered that PDE's doesn't require(but it is recommended), real analysis. I think I was looking at an older site.

 

[intelwanderer]

this doesn't sound too hard. seems like you just need to know the results and techniques on tests. it seems more of a "math methods" class than a math class. why on Earth would you need to do a (probably proof based) real analysis class for that?

Complex analysis is a hard prereq for your major. However, it only requires linear algebra as a prereq.

I know there's a lot of math and theoretical physics guys that'd disagree with me but I think that taking a whole year of analysis, just to learn quantum, is way overkill. At most schools, you go straight to quantum after finishing CM and EM, or after a "math methods" class. Don't know why UT Austin is so strict and rigorous.

They don't make us. A lot of kids don't. I was just interested in doing the math requirement, and they said this is one they won't teach us in class but will be very useful.

Some say it is more "math methods", others say it's more proofy. I've heard conflicting things.

At this point, I'm leaning toward Solid State, but not sure yet. I dislike having to choose a "major" anyway. I'll learn what I want to. Not to mention that if grad school doesn't work out, this course might be marketable as well as interesting. And if not, at least I get some really cool knowledge this semester. I"m just worried that not taking complex will screw me in future courses. If it's absolutely critical to know all of it, than I'll take it, so I do well in upper level physics, which to have ANY realistic shot at a good-or really any-grad school, I'll need to do. But if a few things from it are all I need for undergrad quantum, I-or so I thought-can learn on my own online, and I will invest my time in a different course for now, and just take it later. Also remember that my semester is already filled-Waves includes a three hour lab above, and I want to get in research and actually do something this time-so, I need to budget my time, and I'm trying to keep it to three "hard" classes(Waves, Modern, and one of these) to try and get my GPA up, at least for this semester. If I can somehow crank out all or mostly A's this year(a longshot, I KNOW, but damn if I'm not going to try), I will be above the 3.0 limit, and then I'll be willing to take more "risks" with classes. I'm confident that Solid State I will do better in.

On the positive side, I've got REALLY good professors coming up for both physics classes(and a good thing, since these are supposed to be much harder than freshman physics), something I lacked as a freshman. I know the Solid State one is good(again, I've talked to him, he was one person who helped with the physics/EE decision), but I have no clue who teaches complex. According to people who have taken the course, some teachers are really proofy, others are applied, it depends on who is teaching it, so I'll be gambling on the professor with complex. Nevertheless, I don't have all the answers, and I'm looking from advice from people who've been in similar situations.

 

[jk]

You can also learn complex analysis on your own through self study. Electronics is harder to do on your own because of the labs

 

[intelwanderer]

All right, I think I decided on Solid State Electronics! Although until the semester starts I think I will stay registered in both, just in case I change my mind. Thanks everyone.

If anyone else has advice or wishes to comment, I'm still open for suggestions.