How do I prove to instructors that I taught myself prereqs?

[ElectroBurger]

I am in a happy but tough situation. I am paying for undergrad with a mix of 50% academic/50% music scholarships- but they are ALL through the music school. This means that I have to do a music major on top of my Physics major to pay for school. I have enough time in my schedule to do the regular physics curriculum and take graduate courses, but not to also take many math courses.

However, I am a successful self learner- I taught myself calculus and enrolled in a local college to take multivariable at a local college in year 12. When I got to school this past fall, I took the higher of the two linear algebra courses that my school offers and came out on top of my class. Now, I'm learning ODE, and I've already spoken to the physics department and received approval to take classes that would normally require a class in diffeq.

I do have space in my schedule to take 2 more math courses if I am to take the grad courses I want, and I'd like to take 2 upper level math courses to demonstrate my math abilities when I apply to grad school (in physics). In order to do so, I will have to have approval of the instructors of these courses.

How do I show the instructors (that I have never met) that I am capable?

My ideas so far:

1- as I learn ODE/PDE, I've kept every problem that I've done. I think dropping a stack of a zillion solved problems from the pertinent subject on the instructor's desk could be theatrical, at least

2- Take a final/midterm exam written by the previous instructor of the prerequisite course and getting an A on it.

3- I'd like to take Diff. Topology next spring, which requires general Topology (a fall course that doesn't fit my schedule) as a prereq. I went to the library and borrowed Greever's "Theory and examples of Point-Set Topology" because it is presented in a manner that allows for instruction by the "Moore method." Specifically, this means that the postulates are presented, but all but the very hard theorems are left for the students to prove. I feel like this would be ideal for self instruction of this subject. If I worked through it and proved all the theorems in a big notebook, I could show the professor my work in addition to offering to take a final to prove I've got it.

Any thoughts are appreciated

 

[ZombieFeynman]

So you're idea is to complete a music/physics double major (including graduate level physics classes) as well as a few upper division math courses? Good luck, but keep in mind graduate level courses are usually offered to students who have completed a full undergrad physics sequence and whose only obligations typically include 2-3 courses as well as a light teaching load. I think your plans are overly ambitious and perhaps reflect naive expectations.

Edit: And you've only taken (essentially) the intro undergrad math sequence and you want to take Differential Topology without having taken its prerequisite... I don't think you have realistic goals.

 

[jtbell]

How do I show the instructors (that I have never met) that I am capable?

Ask them. They might have ideas. If I were the instructor in question, I would want to talk to you in person about the prerequisite math topics, and have you do some exercises in my office. That way I could tailor them to the sorts of things that I expect students to be able to do in the class.

 

[ElectroBurger]

If I saw my own post online, I would be just as doubtful. However, I only posted here because it is a realistic goal. I'm not taking any grad courses until I've finished the undergrad curriculum, which will be in my junior year. Freshman year was griffths based E&M 1 and classical mech 1 for me and I got A's; hopefully that dispels some criticism. If you want to criticize the possibility of the possibility of my showing professors that I'm proficient in their courses' prereqs, then go ahead. That would be pertinent to this discussion. Please don't discuss whether you think what I am trying to do is possible. Self teaching is my jam.

Also... necessary effort to complete music classes<<physics classes. Its just the scheduling element that gets in the way.

 

[micromass]

Just send the prof an email and tell them you would like to take his class. Tell him you never took a topology class, but that you self-studied the material and that you think you know it well enough. It's then up to the prof to decide to allow you or not. Likely, he would have a little discussion with you to see how well you know your stuff.

 

[ElectroBurger]

Ask them. They might have ideas. If I were the instructor in question, I would want to talk to you in person about the prerequisite math topics, and have you do some exercises in my office. That way I could tailor them to the sorts of things that I expect students to be able to do in the class.

This seems like the safest route. However, since the class wouldn't be until next spring, I could email the professor today hypothetically to ask what type of specific skills he'd like to see. Do you think that would hurt my chances? Or would the proof of long term planning make him see me as more capable once my chance to meet with him finally comes?

 

[ZombieFeynman]

\ Please don't discuss whether you think what I am trying to do is possible. Self teaching is my jam.

I had classmates as an undergrad who were extremely ambitious (in perhaps different sorts of ways). Their ambition was the end of them and they did not make it into graduate school. I think they would have deserved fair warning and so do you. It's plausible that you will excel, but it's possible that you will crash and burn. You should be aware that one overly ambitious year can destroy your GPA. Spreading yourself too thin can also cause a dearth of available time for each class, causing holes in understanding to accumulate. I heartily believe I would be doing you a disservice not to point these things out to you.

 

[micromass]

This seems like the safest route. However, since the class wouldn't be until next spring, I could email the professor today hypothetically to ask what type of specific skills he'd like to see. Do you think that would hurt my chances? Or would the proof of long term planning make him see me as more capable once my chance to meet with him finally comes?

I don't see how that will possibly hurt your chances. It can only benefit you.
Not sure about the "hypothetical" part though. Just tell him what you're planning to do.

 

[ElectroBurger]

I heartily believe I would be doing you a disservice not to point these things out to you.

I completely agree with this. Your first post just seemed to come off with a critical feel as opposed to one of warning/caution.

 

[ElectroBurger]

Not sure about the "hypothetical" part though.

I meant that my emailing him today is a hypothetical situation. I'll only email him once I've started studying a bit and have my potential game plan set. And my only worry about contacting him now is that I have low credibility since I don't actually know the subject material yet. I don't want him to think that I'm making unrealizeable plans.

 

[WannabeNewton]

We can't answer this for you. It depends entirely on your department policy and the leniency of your undergraduate advising head. I personally know a handful of freshman who have already finished most of the physics curriculum and are taking mostly graduate classes starting their sophomore year. They did this through extensive self-study in HS and summer programs (e.g. the Columbia summer program) combined with the leniency of my physics department. So far they haven't had any trouble in their classes. That being said, it would be silly of you to think that self-studying is anywhere near equivalent to learning in an actual classroom. There is no doubt you will be missing out and will be at a disadvantage compared to kids who learned properly under a professor. You will be missing out on a lot of key insights-take it from someone who did self-study a lot and chose to skip all the lower-division physics and math classes before freshman year. The foundations are very important-if you self-study the foundations you will definitely feel the blow later on when you take classes like GR and QFT your sophomore year.

 

[IGU]

I'll only email him once I've started studying a bit and have my potential game plan set. And my only worry about contacting him now is that I have low credibility since I don't actually know the subject material yet. I don't want him to think that I'm making unrealizeable plans.

A reasonable worry. The only reason to contact your future professor before you've started is to tell him your plans and ask if he believes they are the best way to achieve what you are after. Let him know exactly how you have self-studied in the past and with what success.

There is no doubt that all of undergraduate math can be self-studied successfully if you are sufficiently awesome. But different paths work best depending on your existing skill set and predilections. Asking for advice won't hurt.

 

[TheKracken]

Hmm...This is very interesting to me and I would appreciate if you update us on how it goes!
Actually, not meaning to jump a thread, maybe the OP has experience. The University I intend to transfer to requires a intro to proof course and a intro to analysis course as a pre req to any other proof based course, the thing is, I will be self studying proofs and analysis with a professor at my community college, it would be most beneficial to me if I could skip those two courses.

 

[ElectroBurger]

Well, I got my answer. I actually resolved the issue several days ago, but I was paranoid that my the professor I talked with (a big guy in our physics department, the type who has a blog and writes a lot) would see me live-posting about the topic of my advising :tongue: .

As it turns out, I will be the first person at my university's music school to graduate with a with a major in physics . That was a big surprise to me- according to the professor, a bunch have tried and failed. However, because I already have taken the first bite of the meat of the physics core and got A's, he basically said that from here on out if I self study anything, it's the course instructors' jobs to decide if I have enough of a background for their courses.

On a side note about the math- I asked him whether I indeed need to have advanced math courses to put on grad school applications. His response was unequivocally no- that I only truly need to show that I have the math skills. I don't think he is incorrect- if there was a way to objectively show that I have skills in some area of advanced math without having a course in it, then why wouldn't it be fine? Of course, getting a good grade in a course would be the easiest and most incontrovertible way to do so.

 

[verty]

One thing you could do is to take an analysis course, I suppose complex analysis would be best, because advanced books, Cheng's "Field and Wave Electromagnetics" is one I can think of, pretty much need you to know analysis. And you just may find that grad school is like that.

-edit-
I've changed my mind slightly about this advice. I think complex analysis is not the way to go, it still has the value that it will convince people that you are serious but probably what value it has will be exhausted in the first few weeks of study. Then you'll be stuck learning things you aren't interested in.

 

[Gauss M.D.]

We use Cheng and that books has so far required zero experience in complex analysis. There's some harmonic functions, but on a very basic level, and I don't think it ever mentions conformal mapping techniques or anything like that.

Edit: I'd actually like to go even further and say that most of the math in that book is quite trivial once you know multi variable calc. I'm basically self studying the course and doing perfectly fine. Good book though.

 

[jesse73]

On a side note about the math- I asked him whether I indeed need to have advanced math courses to put on grad school applications. His response was unequivocally no- that I only truly need to show that I have the math skills. I don't think he is incorrect- if there was a way to objectively show that I have skills in some area of advanced math without having a course in it, then why wouldn't it be fine? Of course, getting a good grade in a course would be the easiest and most incontrovertible way to do so.

The point of grad school is to prepare you to become a contributor to research in your field. Grad schools use classes including grad classes as a measure of how likely you are to contribute to your field. A better and more indicative measure is to actually contribute in your field by doing research as an undergrad. I would try to focus on getting research experience because you seem very focused on the ideas of courses when you should focus on how you can show you can conribute to your field.

 

[ElectroBurger]

Im starting work in a condensed matter group at my school this summer, and I'd like to be able to make contributions as soon as possible. The PI I'm working with teaches the courses that I want to take, specifically higher level condensed matter and quantum mechanics. It's my hope that the coursework that I'll be taking will help me be able to be a more effective researcher.

Also, since this summer is the start of my research career, I don't want to lock out any other possible pathways. Another reason why in focusing on coursework right now.

 

[ElectroBurger]

It's kind of embarrassing to read all this old stuff of mine, but I thought I might as well let y'all know what happened.

I did not self study topology or take differential topology. Instead, I took the class formally (made it fit my schedule) and spent many, many hours studying and learning it. As a result, I went from having no idea of rigorous proofs to being pretty good. I did well enough for the professor to remember me. Then, this year, after spending time doing HEP ex, I reached out to my old topology professor and he remembered me and allowed me to work with him to study differentiable manifolds outside of my curriculum.

I'm using various books and literature for this, and have recently found John Baez's book "gauge fields, knots and gravity" and have included that too. Through all this, I have never heard the term "differential topology" mentioned once. The content of that area may cross over into what I'm learning, but the fact that I haven't even thought about that course in a year shows me how I was lacking in information whenever I wrote this.

The fact that I'm even studying on my own is a result of my learning that it's much important to do work and make contributions than it is to take classes. Also, I learned that reading a book doesn't mean you've grasped it's information. The most I've ever learned in college was during my late nights struggling with topology problem sets. My revised goal is to keep learning math and physics extra curricularly... But under the supervision of professors who I may do a senior thesis with.

 

[micromass]

Well, we definitely don't get much posts from people who give feedback a year later. But I love it when they do. So I really appreciate this message.

It seems you have worked very hard and you have reached a very high level now. I hope you enjoyed every bit of it. Well done and good luck!