Do I Need a Math Minor for Quantum Mechanics in Physics?

[Jake4]

Heya folks!

So I had a question about mathematics requirements. In my current physics program, you are only required to go up to calculus 3. Some people choose to do a math minor, others choose other minors.

This same program, goes up to QM 1 + 2 as capstone classes.

My question is this, how can you handle QM if you are only to calculus 3? I truly don't know, and I'm wondering if they cover some necessary Mathematics in the QM classes themselves.

This extends to that if I don't HAVE to do a math minor, I would love to do an astronomy minor. This allows me some fundamental planetary and stellar astronomy classes, along with an astrophysics class that looks VERY interesting.

So essentially my question is this: Would I be missing out on key things to not take a math minor, and thus end my math studies at calculus 3? or will the necessary mathematics for QM be covered in the classes themselves?

With the math minor, I would be doing intro to linear algebra, and intro to differential equations. I could also do PDE's after that if I wanted.. beyond the requirement, but I could if I wanted to.

So that's really it, I'm done with general education classes, and would love to be able to do something interesting (astronomy) but not if it will hurt my physics goal.

If it helps, I plan to go to graduate school for physics after graduation, and would love to go into astrophysics or something similar.


Thanks!

 

[G01]

Heya folks!

So I had a question about mathematics requirements. In my current physics program, you are only required to go up to calculus 3. Some people choose to do a math minor, others choose other minors.

This same program, goes up to QM 1 + 2 as capstone classes.

My question is this, how can you handle QM if you are only to calculus 3? I truly don't know, and I'm wondering if they cover some necessary Mathematics in the QM classes themselves.

This extends to that if I don't HAVE to do a math minor, I would love to do an astronomy minor. This allows me some fundamental planetary and stellar astronomy classes, along with an astrophysics class that looks VERY interesting.

So essentially my question is this: Would I be missing out on key things to not take a math minor, and thus end my math studies at calculus 3? or will the necessary mathematics for QM be covered in the classes themselves?

With the math minor, I would be doing intro to linear algebra, and intro to differential equations. I could also do PDE's after that if I wanted.. beyond the requirement, but I could if I wanted to.

So that's really it, I'm done with general education classes, and would love to be able to do something interesting (astronomy) but not if it will hurt my physics goal.

If it helps, I plan to go to graduate school for physics after graduation, and would love to go into astrophysics or something similar.Thanks!

You need much more math beyond just the intro calculus sequence. The fact that that is all that is required sounds wrong to me. Do you have a mathematical physics course in your schedule?

Also, what do you mean by QM 1&2 are capstone courses? Are you not also supposed to take E&M (at 400 level), statistical mechanics, along with an advanced classical mechanics course?

To answer your question about math courses:

You should take a differential equations class. Also, I highly recommend taking a proof-based linear algebra class as well. Beyond that, any math will help.

 

[jtbell]

My question is this, how can you handle QM if you are only to calculus 3? I truly don't know, and I'm wondering if they cover some necessary Mathematics in the QM classes themselves.

They very likely do, if they don't specifically require a differentlal equations course or linear algebra course as prerequisite. Have you tried asking the professor(s) who teach the course? Different schools teach things differently.

It certainly would be helpful if you have had one or both of those courses before taking QM, so you don't have as many new concepts to learn, but I doubt it's necessary in your case. But ask your professors to make sure.

 

[Jake4]

I'm actually awaiting a reply from the department head, he just normally takes a few days to respond so I wanted to see if anyone else knew.

I may have used the wrong term when I said capstone, I simply meant those are the last classes we take in this program.

But jtbell, that's kind of what I was thinking, the only math classes they *require* are calc 1, 2, 3... so I figured that they have some sort of condensed version of the mathematics needed being discussed in the physics classes themselves.

we have no "mathematical physics" course. normal classical mechanics, optics, electronics, heat and thermo, electricity and magnetism, modern physics and then QM... I may have missed a thing or two, but that's basically it.

So you're saying it may help, but isn't necessary. To me, what that says is I should get a good text for linear algebra and a good text for DE and do some self study as needed... Does that sound like it would work? Using the books as a basic reference, seeing as they should offer some mathematics in the physics classes themselves?

Obviously I'll know more when the department head gets back to me, but I more wanted to ask if that is totally unheard of, or if that is the case sometimes. That is, that math is taught for physics, in physics classes.. at least in some condensed form.

 

[HeLiXe]

Heya folks!

So I had a question about mathematics requirements. In my current physics program, you are only required to go up to calculus 3. Some people choose to do a math minor, others choose other minors.

This same program, goes up to QM 1 + 2 as capstone classes.

My question is this, how can you handle QM if you are only to calculus 3? I truly don't know, and I'm wondering if they cover some necessary Mathematics in the QM classes themselves.

This extends to that if I don't HAVE to do a math minor, I would love to do an astronomy minor. This allows me some fundamental planetary and stellar astronomy classes, along with an astrophysics class that looks VERY interesting.

So essentially my question is this: Would I be missing out on key things to not take a math minor, and thus end my math studies at calculus 3? or will the necessary mathematics for QM be covered in the classes themselves?

With the math minor, I would be doing intro to linear algebra, and intro to differential equations. I could also do PDE's after that if I wanted.. beyond the requirement, but I could if I wanted to.

So that's really it, I'm done with general education classes, and would love to be able to do something interesting (astronomy) but not if it will hurt my physics goal.

If it helps, I plan to go to graduate school for physics after graduation, and would love to go into astrophysics or something similar.


Thanks!

Hi Jake,
It seems like we're pursuing similar courses of education. I working towards a BS in Physics with a concentration in astrophysics. I also intend to go to graduate school for astrophysics. The math courses required in my program of study are
CalcI-III
Differential Equations
Mathematical Physics (applying math to physics)
^^All of these would be done before QM.

I also intend to take a Linear Algebra class and at least two more math related classes just becoz . Mathematical physics is an upper level class, so I'm going to purchase "Mathematical Methods in the Physical Science" by Mary Boas (as recommended in the 'so you want to be a physicist thread) in the interim to get a head start. Good luck with everything!

 

[HeLiXe]

we have no "mathematical physics" course. normal classical mechanics, optics, electronics, heat and thermo, electricity and magnetism, modern physics and then QM... I may have missed a thing or two, but that's basically it.

Sorry just saw this after I posted

 

[Jake4]

Ahh no worries :D

that was actually really helpful. At my university linear algebra is a pre-requisite for DE, so it's interesting to know that it isn't necessary for DE... I'm most likely thinking of just purchasing the books and self teaching myself a little of both.

Our teacher (in calc based physics 1 (heheh)) already refrences linear algebra in class, so I'm thinking of grabbing a book on that soon. I've heard it's not very difficult, and is an interesting thing to have in your toolbelt, so I might as well get started with it.

DE I'll start when I'm done with that.. truthfully while this summer I'm taking classes, next summer I will have none, and that's the summer before QM. So I may just take the summer to learn about DEs to be prepared for QM... (unfortunately while my knowledge of the material I've learned so far is fairly good, my knowledge of the math application in higher level physics classes is quite horrible, so I wouldn't know if it would be useful to already know DEs for any other classes besides QM...

 

[HeLiXe]

lol I'll have calc based physics I in the summer, I was supposed to take it along with calcI, but their schedule did not fit mine...so here I am finishing up calcII and I still haven't taken a physics class. I'm taking DE this summer. I was apprehensive because I heard it is better to have calc III before it (because of vectors) and linear algebra, but my calc teacher said she's very confident I'll do well in it, so I'm taking the plunge :) QM is senior year stuff for us. Also DE is only a requirement for the astrophysics concentration...I'm not sure why it's not required for traditional physics.

 

[Jake4]

ahh I see..

Well I switched majors a year ago, I have all of my general eds done.. so next year IS senior year for me :)

just have all of the fun physics stuff to do :)

In my school they require calc 1 before calc based physics. I took calc 1 last semester, and calc 2 and cal based physics 1 this semester. Physics 2 in the summer, then onto mechanics in the fall :)

I'm excited because I get to take electricity and magnetism, and modern physics along with an astrophysics class next spring..

fun stuff :)

 

[PCSL]

I'm glad I saw this thread because I was having the exact same problem.

Question: What would be the ideal sequence of these three classes: Calc III, Diffy Q, Linear Algebra?

 

[HeLiXe]

ahh I see..

Well I switched majors a year ago, I have all of my general eds done.. so next year IS senior year for me :)

just have all of the fun physics stuff to do :)

In my school they require calc 1 before calc based physics. I took calc 1 last semester, and calc 2 and cal based physics 1 this semester. Physics 2 in the summer, then onto mechanics in the fall :)

I'm excited because I get to take electricity and magnetism, and modern physics along with an astrophysics class next spring..

fun stuff :)

So cool! Congrats :D I'll be finishing up my Sophmore year this fall and next Spring starts my Junior year. I'd love to hear which grad school you decide to go to and how you do on the GRE's (reading the comments about them here is putting fear into me lol).

I'm glad I saw this thread because I was having the exact same problem.

Question: What would be the ideal sequence of these three classes: Calc III, Diffy Q, Linear Algebra?

From what I've been reading, people say it should be Calc III ---> Linear Algebra ---> DE. My calculus professor says CalcIII and DE could be taken the same semester and then Linear Algebra the next. There are lots of mathematicians on this site though, so maybe some experienced person could give a better answer than me.

 

[clope023]

To answer the thread, I"m an EE but getting a math minor which consists of:

Calculus I, II, III
Linear Algebra
ODE
PDE w/ Fourier Analysis
Complex Analysis

I also want to take Numerical Analysis and wish I had to time to take Real Analysis, I'm also taking Probability and Statistics in the Engineering department, this seems to be most of the applied math scientists and engineers use unless they're theorists in which case I know they use Differential Geometry, Topology, and Group Theory on top of the ones I listed.

 

[QuarkCharmer]

It's strange to see different schools with such drastically different requirements. My university will let you take Linear Algebra after Calc I, DEQ after Calc II, and our PreCalc course covers what is basically the first 1/2 of Linear Algebra.

 

[Jake4]

Just checked out that book you recommended as well Helixe, it seems perfect!

From the reviews I'm seeing, it seems like if I do some self study from that, I won't need the extra math classes..

 

[HeLiXe]

To answer the thread, I"m an EE but getting a math minor which consists of:

Calculus I, II, III
Linear Algebra
ODE
PDE w/ Fourier Analysis
Complex Analysis

I also want to take Numerical Analysis and wish I had to time to take Real Analysis, I'm also taking Probability and Statistics in the Engineering department, this seems to be most of the applied math scientists and engineers use unless they're theorists in which case I know they use Differential Geometry, Topology, and Group Theory on top of the ones I listed.

Thanks Clope023, this was very interesting. What are the prereqs for topology at your institution? It is actually one of the courses I am interested in taking.

Just checked out that book you recommended as well Helixe, it seems perfect!

From the reviews I'm seeing, it seems like if I do some self study from that, I won't need the extra math classes..

Yes, it's designed to be very comprehensive. I plan on reading it over the summer (as I'm only taking three classes this summer), and I may not take linear algebra depending on my experience with it. Here is the link to the thread that I learned about the book from https://www.physicsforums.com/showthread.php?t=240792 It is like an academic guide written by a physicist at PF. I know you're about to graduate soon, but I think you still might find some useful things in there :) Or at the very least you will know you're on the right track.

 

[clope023]

Thanks Clope023, this was very interesting. What are the prereqs for topology at your institution? It is actually one of the courses I am interested in taking.

You need Calc III, Linear Algebra, and a first course in Real Analysis which deals with set theory and real number sequences and limits to take Topology at my school

 

[ZapperZ]

Since my "So You Want To Be A Physicist" essay was referred to on here, I'll point out the relevant discussion in Part III of the essay and my recommendation to get Mary Boas's "Mathematical Methods in the Physical Sciences".

Note also that this book was also discussed in a number of threads, including this one:

https://www.physicsforums.com/showthread.php?t=76454

Zz.

 

[AlexChandler]

If you plan to go to graduate school for physics, it would be very helpful to have some knowledge of higher math. If you really want to learn about space, you need to go quite far in math. Linear Algebra is absolutely essential. I would set my goal towards eventually trying to learn differential geometry.
By the way, self study will probably not be quite as good as really taking the courses. Higher math courses focus very much on proof. However proof is sort of a cultural thing in mathematics and it will be helpful to have the guidance of an experienced professor.

 

[HeLiXe]

Since my "So You Want To Be A Physicist" essay was referred to on here, I'll point out the relevant discussion in Part III of the essay and my recommendation to get Mary Boas's "Mathematical Methods in the Physical Sciences".

Note also that this book was also discussed in a number of threads, including this one:

https://www.physicsforums.com/showthread.php?t=76454

Zz.

Thanks so much for your essay ZapperZ! Actually I cannot thank you enough :) You should really write a book!

 

[Jake4]

Wow, well heard back from my department head.. and now I think I have things set :)

I'm going to go ahead and take linear algebra, and DE.. and possibly even PDE's my last semester. Essentially what was told to me, is that it's not necessary, because I can get through the classes with simply the information supplied in the classes, but if I'm planning to go onto any form of graduate work (which I am...) I would need to take at least linear algebra and DE's. Still sounds odd that I'm in the B.S. (non-teaching) program, yet they just wouldn't require something you would need for graduate school. Do many people go that route and not even attempt graduate school?

anyways, My schedule in the fall (feel like sharing because I'm super excited about it...) is:

Calculus 3
Mechanics 1
Planetary Astronomy (for funsies..)
Topics: General Relativity (just a random seminar course being given that looks really interesting)
Linear Algebra

any comments? Seem like a schedule that's manageable?

 

[HeLiXe]

I don't have any helpful comments, but it sounds like fun! :)

 

[AlexChandler]

My schedule in the fall (feel like sharing because I'm super excited about it...) is:

Calculus 3
Mechanics 1
Planetary Astronomy (for funsies..)
Topics: General Relativity (just a random seminar course being given that looks really interesting)
Linear Algebra

any comments? Seem like a schedule that's manageable?

Looks like a very nice schedule. It will be difficult, but every semester should be difficult from now on. My schedule this semester is somewhat similar:

Classical Mechanics I
Modern Physics
Linear Algebra
General Chemistry and Lab

This is my first semester schedule at a university (Michigan State University) and it has been quite difficult for me. At first, the courses seemed much too difficult, and I actually considered dropping Classical Mechanics. However, I just studied really hard, and I think I will end up with a 4.0 average. So if things seem overwhelming at first, don't worry too much. Just study as much as possible, and things will be good.

 

[HeLiXe]

I think I will end up with a 4.0 average. So if things seem overwhelming at first, don't worry too much. Just study as much as possible, and things will be good.

That's great Alex! Good job!

Well since we're talking about Fall schedules...I'm excited about mine too!
Calculus III
Chemistry II
Physics II
Speech comm for professions (last of general reqs)
C++

Also Jake thanks for starting this thread. I mentioned that I wanted to take two additional math classes. I was checking out the course descriptions and found that I will qualify for a math minor with all of the math I am taking :D