Large Hardon Collider

[Woozie]

What are the differences between a Diff. EQ class and PDE? Seems like a lot of the same stuff.

Edit to your edit: Really don't think any of the probability stuff will be useful? I need 3 300+ level math classes for my minor anyways and I'm really not sure what to take besides PDE. I heard that the advanced calculus classes were a total waste of time at my school.

Edit 2: Also, the 300+ level statistics class at my school is this

Mathematical Statistics:

Continuation of MTH 331. Classical estimation methods and hypothesis testing are studied. This course also covers Chi square tests for goodness-of-fit and independence, regression and correlation analysis, and one-way and two-way analysis of variance including factorial designs and tests for the separation of means.

MTH331 (Probability) is the pre-req :\

No, probably certainly wont be at all useful in any way whatsoever, trust me. I only took it because it was a guaranteed A. I'm biased towards advanced calc since I'm a TA for it, but to be honest, you certainly wont need it during your undergrad as a physicists. I'm not so sure if it becomes useful later. It's really only useful if you need to learn Real Analysis for some reason (since you'll need to learn advanced calc before you can understand real analysis. Most physicists don't need to take Real Analysis, ever).

Oh, and speaking of bias, I'm writing my master's thesis on Partial Differential Equations, so I guess I'm a little biased towards that as well.

The Mathematical Statistics sounds like it would be useful if you're doing lab work. Honestly, I hate statistics. And so do you, you just don't know it yet.

PDEs on that level, in my opinion, isn't too different than DiffEQ in a sense. You're basically learning methods for solving different specific equations. The difference is that the equations you're dealing with here happen to be PDEs, which have some properties that makes them different than ODEs. For example, you'll learn about harmonic functions, which are very important. A function is harmonic iff it is a solution to laplace's equation. Some of it's properties can tell you a lot about a field whos potential energy is harmonic (e.g. electrostatic fields).

For the most part, you'll just break down equations into ODEs (this is especially true for the wave equation and, on that level of math, the heat equation). After doing so, you'll find that multiple solutions exist, and you'll write the general solution as an infinite sum or integral of every possible solution (e.g. as a fourier series). You probably learn a few tricks for solving PDEs which doesn't involve turning them into ODEs. The most important things you'll learn in that class are fourier series/integrals/transforms, Poisson's equation, and the sturm-liouville theory.

PDEs get a lot more fun after Real Analysis, but in this case they aren't very useful to physicists.

[Woozie]

One deals with multi-variables, the other does not.

Also would it be possible to wait on QM until after you've taken the PDE class? QM is hard enough as it is, I couldn't imagine going through it not knowing the math behind it. Except for the heat equation, you'll be using everything in that description in PDE for QM.

There's really no need for him to take PDEs before QM. Sure, it would be useful to be familiar with fourier analysis and/or sturm-liouville theory beforehand, but it's certainly not a requirement and not having this class isn't a huge handicap like not having linear algebra.

Change every d for a del
http://upload.wikimedia.org/math/a/5...a1073905e8.png to http://upload.wikimedia.org/math/3/f...4bafdae763.png
then pretend it's new mathematics you're dealing with.

This is basically all there is to the level of PDEs you'll be doing. Like I said, it doesn't get really fun/new/exciting until you're doing the really advanced stuff, which you'll probably never do as a physicists unless you go into theoretical physics and have to study real and functional analysis in detail.

Don't listen to future dropout. Every single mathematics and physics classes are incredibly useful, especially if you aim for theoretical physcics (stuff like astrophysics). Some might be more useful than other in the close future, but you will use all of them sooner or later.

I really can't see how advanced calc could be very useful unless he's going to need to take real analysis. And that's coming from a math major who TAs in advanced calc and is writing a thesis in the field of analysis. I'd like to convince everyone in the world to take this stuff because I think it's fun, but I have yet to see why it would be particularly useful, especially considering other things he could be doing with his time (like research).

Edit: My bad, you specifically said it would be useful for theoretical physics. I'm half asleep and my reading comprehension kind of sucks right now. But with that said, I'd still rather he take some research credits than advanced calc, even if he's 100% sure he'll be doing theoretical physics. Ideally, he would have time to do both, but from my experience, advanced calc takes up a LOT of students time - much more than calc II or DiffEQ. Unless it's going to be necessary for him or he has a ton of free time, he probably should just avoid it. Some students seem to just naturally love advanced calc and have to spend very little time on it, but most just really hate it and have a hard time on it. And it seems to have nothing to do with how smart you are or how good of a student or hard worker you are.

[Woozie]

Also, I've come to tell everyone that science is boring. I'm having a really hard time staying awake at work. I think the first time I stayed awake for an entire day was last Wednesday or Thursday. Yesterday we were doing something called Raman scattering, where you learn about a new material by shining a laser onto it, aiming the reflection into a device, and then taking a nap for 15 minutes (or at least that's how I did it). I also made a solar cell. Turns out, making a solar cell is 10% science and 90% standing around and/or taking a nap.

It should get less boring now that I'm about to have a specific project to work on. But first I have to read a 181 page thesis on "Photoluminescence and Extended X-ray Absorption Fine Structure Studies on CdTe Material". I don't know what half those words mean, so this could take a while...

[Eliseos]

Become an engineer! We get to nap AND do cool stuff.

[solanis]

your university offers an entire class on partial differentiation and its uses? that's really surprising to me, when I was doing the pre-reqs for my astrophysics degree all of that was contained within the general multivariate class. do they have econ majors take it too? PDE is really easy and pretty fun though, and a strong understanding of it will make your life significantly easier.

[Ferion]

I mean I wouldn't say probability is completely useless for math, but I'm extremely biased because all of the research/work I've done has dealt with probability/statistics.

Edit:

do they have econ majors take it too? PDE is really easy and pretty fun though, and a strong understanding of it will make your life significantly easier.

Honestly, as far as I've seen at most schools undergrad econ majors aren't required to to take beyond Calc I and a very simple probability course. Also, unless you go into financial economics where you study stocks/option pricing, differential equations are pretty much useless.

[Woozie]

your university offers an entire class on partial differentiation and its uses? that's really surprising to me, when I was doing the pre-reqs for my astrophysics degree all of that was contained within the general multivariate class. do they have econ majors take it too? PDE is really easy and pretty fun though, and a strong understanding of it will make your life significantly easier.

Your school may have had Advanced Engineering Math I and II or something similar, in which case, part II would be very similar to Sath's PDEs course.

Edit: Or are you saying you learned the heat equation, Fourier analysis, etc, in your multivariate calc class? If so, that's very unusual. The vast majority of schools wouldn't go over any of that in multivariate calc.

[Woozie]

I mean I wouldn't say probability is completely useless for math, but I'm extremely biased because all of the research/work I've done has dealt with probability/statistics.

The only probability and stats I've ever encountered were stuff most physicists would know (or could easily learn) without taking a stats course. And the useful stuff from stats are learned in a stats class, not in a probability class (or at least not at my school. My probability class was 100% totally useless in every way shape and form, and based on the posted description, it would seem that Sath's probability class is the same as mine).

[Kaylia]

Also, I've come to tell everyone that science is boring. I'm having a really hard time staying awake at work. I think the first time I stayed awake for an entire day was last Wednesday or Thursday. Yesterday we were doing something called Raman scattering, where you learn about a new material by shining a laser onto it, aiming the reflection into a device, and then taking a nap for 15 minutes (or at least that's how I did it). I also made a solar cell. Turns out, making a solar cell is 10% science and 90% standing around and/or taking a nap.

It should get less boring now that I'm about to have a specific project to work on. But first I have to read a 181 page thesis on "Photoluminescence and Extended X-ray Absorption Fine Structure Studies on CdTe Material". I don't know what half those words mean, so this could take a while...

Last time I went at the library to study, I fell asleep 2 hour, only to wake up with sleep paralysis in a pool of drool. That's how bad sciences is for you.

I really can't see how advanced calc could be very useful unless he's going to need to take real analysis. And that's coming from a math major who TAs in advanced calc and is writing a thesis in the field of analysis. I'd like to convince everyone in the world to take this stuff because I think it's fun, but I have yet to see why it would be particularly useful, especially considering other things he could be doing with his time (like research).

Edit: My bad, you specifically said it would be useful for theoretical physics. I'm half asleep and my reading comprehension kind of sucks right now. But with that said, I'd still rather he take some research credits than advanced calc, even if he's 100% sure he'll be doing theoretical physics. Ideally, he would have time to do both, but from my experience, advanced calc takes up a LOT of students time - much more than calc II or DiffEQ. Unless it's going to be necessary for him or he has a ton of free time, he probably should just avoid it. Some students seem to just naturally love advanced calc and have to spend very little time on it, but most just really hate it and have a hard time on it. And it seems to have nothing to do with how smart you are or how good of a student or hard worker you are.

There is no research credit for undergrade students here, so I don't know how it works. Since Sath was asking which one to pick between both options, that's all I considered.

Both classes are optional for sure, but sadly, I could say that about almost every classes. Truth is, the more times I'm forced to spend on various topics, the more I will think about it and integrate the concept in my way of thinking. The best example I could give is my real analysis classes. It was useless in every way for physics, but it's probably the classes that did the most to refine my approach toward mathematics and physics in general.

Stats and PDE are stuff you will come across a lot (pde more than stats early), and you can learn them on your own. However, becoming familiar with them will still be helpful. Solving the lagrangian of a pendulum or maxwell's equation for example. Fluid dynamics also have a bunch of PDE. You will come across that kind of mathematicals entities very often, and knowing what exactly it is will still help.

And even when you're not asked to solve the equation, I still think it's important to understand what you're dealing with exactly.

Edit: Or are you saying you learned the heat equation, Fourier analysis, etc, in your multivariate calc class? If so, that's very unusual. The vast majority of schools wouldn't go over any of that in multivariate calc.

Heat equation and wave equations were used in nearly every examples. The class was directed at engineer, but if you actually try, there was still a bunch of interesting crap to learn and link to makes.

[BerenTebogo]

I already have the max research credits I can take this semester. As far as Calc 2 goes, it was actually my favorite Calc thusfar. I actually ended up learning DEs pretty damn well once my life settled down a bit. I plan 100% to go into theoretical so I think the Adv. Calc is worth checking out. If probability isn't worth it though I can just drop it.

[Kaylia]

I plan 100% to go into theoretical

That's cute!

Spoiler: show

That's what we thought too!

[edit]
Don't feel too bad if you end up doing applied physics, you can still make fun of engineer and chemists.

[Cadsuane]

I'm wondering whether I should take a first year course on discrete math in the second year of my mathematics undergrad:

MATH 1805 [0.5 credit]
Discrete Structures I
An introduction to discrete mathematics and discrete structures. Topics include: propositional and predicate calculus, Boolean algebra, introduction to complexity of algorithms, mathematical reasoning, counting, recurrences, relations, introduction to graphs. (Also listed as COMP 1805.) This course is available to Science students only as a free option.

It seems a bit off the beaten track but I'm worried it'll be too easy and a waste of time. The advanced combinatorics, optimization, graph theory and algorithm courses in 3rd year, which I would think are where this sort of course is supposed to lead you, only list honours algebra II (which is largely concerned with group and ring theory and other abstract concepts, I believe). That leads me to believe this is more of a hobby course for computer science students.

But anyway I'm not too clear yet on how mathematical topics fan out as I progress through my undergrad. What do you guys think?

[Mizango]

Hey guys, been moving back home and finishing up my schooling situation since I was in TX for so long, so im in SC for the summer back in Gamecock country (GO COCKS!). Hope all is well, finally got internet access and will be around much more.

I love and miss you guys. Full blown nuclear homo <3

[Ferion]

That sounds like the description for a class called Math Reasoning at my school Cadsuane. The class was just a basic intro to proof writing and introduces the more theoretical side of functions and mathematical notation. Based on some of your posts I read it probably is too easy.

[Kaylia]

I'm wondering whether I should take a first year course on discrete math in the second year of my mathematics undergrad:

It seems a bit off the beaten track but I'm worried it'll be too easy and a waste of time. The advanced combinatorics, optimization, graph theory and algorithm courses in 3rd year, which I would think are where this sort of course is supposed to lead you, only list honours algebra II (which is largely concerned with group and ring theory and other abstract concepts, I believe). That leads me to believe this is more of a hobby course for computer science students.

But anyway I'm not too clear yet on how mathematical topics fan out as I progress through my undergrad. What do you guys think?

If it's the class they give to computer sciences student, it will probably be too simple for anyone majoring in physics/maths/sciences. There is still very important concepts in it, and it's not a bad thing for general educations, but you're probably better off learning it on your own using wikipedia.

What I learned over the years is that prerequisite are a big scam. If you want to take the class, don't let that stop you. You will probably end up doing better than the most anyway (since no one is going to be motivated). I'm not saying you will have an easy time, especially not first 4-5 weeks, but you can usually get away with it.

The safest way is to go chat with whoever is giving the class. They are the one that are in the best position to tell you if it's a good idea or not.

[Cadsuane]

Cool. I thought this might be an introduction to optimization/counting methods and the like, but from what you guys are saying, I can spend my time more effectively. Thanks guys.

[Eliseos]

If it's the class they give to computer sciences student, it will probably be too simple for anyone majoring in physics/maths/sciences. There is still very important concepts in it, and it's not a bad thing for general educations, but you're probably better off learning it on your own using wikipedia.

Yeah, this sounds like the CS class that only those (and maybe EEs? mostly for the Boolean algebra) have to take. It's ridiculously easy and I lost motivation within the first couple weeks due to how easy it was.

I think we used this book http://www.amazon.com/Discrete-Mathe...8117764&sr=8-1 and it was I'd really only suggest it if you were going into computational math or thinking of transferring to CS. The funny thing is I didn't really use much of the concepts in my later CS classes, only in my EE classes for truth tables, which are pretty easy to figure out on their own.

[Kaylia]

Cool. I thought this might be an introduction to optimization/counting methods and the like, but from what you guys are saying, I can spend my time more effectively. Thanks guys.

It kinda is an introduction to optimization, except you won't do anything like that. Optimization class that follow was also very easy if you have half a brain. It was more interesting on a technical standpoint though.

If you have to take a single mathematics class, I would vouch for a real analysis class. For me, it was one of the class that set the foundation for every other disciplines

It's ridiculously easy and I lost motivation within the first couple weeks due to how easy it was.

I actually managed to get a poor grade in that class despite that. I got cocky and never opened because I found the topic to be incredibly boring. Turn out i missed a few vocabulary and methods that were needed for the final...

[Cadsuane]

If you have to take a single mathematics class, I would vouch for a real analysis class. For me, it was one of the class that set the foundation for every other disciplines

Yeah that goes without saying in my program. First class devoted exclusively to Real Analysis is in third year (and it's a mandatory credit for me), but honours calculus introduces analysis concepts right from first year.

[Woozie]

Last time I went at the library to study, I fell asleep 2 hour, only to wake up with sleep paralysis in a pool of drool. That's how bad sciences is for you.







There is no research credit for undergrade students here, so I don't know how it works. Since Sath was asking which one to pick between both options, that's all I considered.

Both classes are optional for sure, but sadly, I could say that about almost every classes. Truth is, the more times I'm forced to spend on various topics, the more I will think about it and integrate the concept in my way of thinking. The best example I could give is my real analysis classes. It was useless in every way for physics, but it's probably the classes that did the most to refine my approach toward mathematics and physics in general.

Stats and PDE are stuff you will come across a lot (pde more than stats early), and you can learn them on your own. However, becoming familiar with them will still be helpful. Solving the lagrangian of a pendulum or maxwell's equation for example. Fluid dynamics also have a bunch of PDE. You will come across that kind of mathematicals entities very often, and knowing what exactly it is will still help.

And even when you're not asked to solve the equation, I still think it's important to understand what you're dealing with exactly.






Heat equation and wave equations were used in nearly every examples. The class was directed at engineer, but if you actually try, there was still a bunch of interesting crap to learn and link to makes.

These are all good points. I guess I just assumed his college was like mine where research credits is always an option for any semester. Since research doesn't seem to be an option for him, that changes things, unless there are other research options for him other than credits. The first few years of my research were for pay only, and some students do research without pay or credit. This would look good to grad schools.

I plan 100% to go into theoretical

lol, I'm pretty sure every single one of us said this at first. I used to be 100000000% certain that I'd do theoretical and vowed to never do an experiment because I hate them, and now I'm spending my summer building solar cells and doing laser scattering experiments. I'm even looking for grad schools for a condensed-matter PhD programs. The point I'm trying to make is that your mind still may change, so if there's any way you could possibly be involved in research now, you should go for it. Also, if you get the option to take a physics class that seems useful for experimental/applied physicists but useless to you, take the class anyways, just in case. I'm beginning to regret not taking solid state or optics.

But since you do plan to go to theoretical, you'll probably need every bit of math you can get you'll certainly need Advanced Calc before you take Real Analysis. Real Analysis is really useful, especially since it's the basics of every type of math that uses calculus, like advanced PDEs and Functional Analysis. What you should do is find a professor somewhere who does astrophysics and ask them what classes you'll need. I've done that before by emailing theoretical/particle physicists, and they always replied along the lines of "everything".