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This is going to be long as I believe that the context is important.

I have always been fairly good at maths and physics (won state wide prizes in the math contests and even won a gold medal in the national physics olympiad.) I live in USA/UK/AUS (trying to hide my identity).

However, after going through grade 12 I got a spot in medicine and happily went along with it because most of my friends were high achievers and I thought why not? I got a fair bit of recognition for getting into medicine (I admit I enjoyed the ego stroking) but luckily medical school is a graduate course (M.D), so I still had undergrad to go. I initially enrolled as a double major - math and physics but within the first week switched to a pre-med track as I thought that it would ease the transition into medicine.

Here's where things take a turn for the worse. By the end of second year I absolutely hate medicine and I realise that I truly do love maths and physics. I had luckily taken a couple of the first year mathematics modules - multivariate calculus and intro to linear algebra and two 2nd year course as well - intro to DEs and intro to probability.

So I talk to my course office and beg them to let me transfer into a mathematics track, but I am only able to do courses where I have the prerequisites satisfied and hence now (end of 3rd year) - have done, in addition to the courses mentioned above, courses on: nonlinear dynamics, intro to stochastic processes, a modelling course and a course on systems of coupled dynamical systems.

However, my true passion had always been physics and not only have I not done any meaningful university physics, but also haven't learnt a lot of mathematics - analysis, algebra and geometry.

I am thinking of going on to do a masters and try as hard as possible to steer myself back onto the path of physics and mathematics, but I haven't done a lot of the necessary coursework. Furthermore, my family is low income (another factor pushing me into medicine (no parental pressure) but the thought of a good income was tempting) and so I don't think I can afford to take a couple years to essentially redo a bachelor's degree.

My question is: am I screwed? I am more than willing, and passionate, to learn these subjects by myself - through books. In fact that's how I've learnt most of the things I have to date. But I realise that universities want to see another university giving a student their stamp of approval saying - this student has successfully learnt (insert subject.) I truly believe most of the time these stamps are meaningless, but in the case of admissions it truly is everything.

Please help, any advice is much appreciated.

  • Without knowing where you are it is a bit difficult to offer you possibilities. The postgraduate scene in the US is different from in the UK and elsewhere. In the UK you might find that a 1 year "taught" masters degree in physics on top of what I think you are saying will end up being a mathematics undergrad w/ pre-med on top of it (?), coupled with your willingness to study outside of course requirements would bring you up to speed enough to move to doctoral study. In NZ and (maybe?) OZ you may be able to convince your Uni to let you do an honours year in physics before moving to a masters – GrotesqueSI Oct 7 '19 at 9:04
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    It is totally implausible that this question was written by an American student. – Anonymous Physicist Oct 7 '19 at 9:09
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    I voted to close because this is a rant, not a question. Your course office will have told you what to do; we will not know more than they do. – Anonymous Physicist Oct 7 '19 at 9:10
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    @AnonymousPhysicist 'State-wide' and 'Grade 12' aren't phrases that fit with coming from the UK either. – Lio Elbammalf Oct 7 '19 at 10:25
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  1. Maybe you could head for something a little in between like chemical physics or biophysics or chem engineering where some of the courses to date are useful?

  2. My advice is to push for getting your 4 year degree (assuming US) on time. Just see bad things when people delay too much from the switching. If you can switch majors while still getting done on time, fine. Otherwise, do some masters or the like. Perhaps after working.

  3. You have the wrong idea about the math needed for physics. Analysis (as opposed to "calculus"), algebra (of the abstract sort), and advanced geometry are all really pretty marginal for someone working on undergrad 'zoics. Read up on Feynman or just talk to physicists (not math types). You need to be very strong at calculus, high school algebra, and ODEs/PDES. That's probably your biggest gap right now--diffyQs. NOT the more theoretical math courses that people talk about on the Internetz.

  4. Getting through a "math methods" book would be good. If you learn this book from start to finish, that will put you in great stead: https://www.amazon.com/gp/product/B005G14K86/ref=dbs_a_def_rwt_hsch_vapi_tkin_p1_i0 (get a used earlier editions, don't spend $100, I have the 5th.) Many physicists like Mary Boas (little easier but similar). The traditional math methods for physics is Arfken Weber, but while it has a few harder topics, it's really a miserable grabbag and doesn't teach well. I like Kryezing better for self study.)

  5. Finally, I would caution you on the income aspect of physics (or math). Unless you are a real superstar (which can be rare), you will face huge competition for academic jobs. These forums are littered with people struggling to find jobs or unhappy with their advisor situation (and the relative subservience required in Ph.D. relationship). Getting a certified job like a physician is a great move financially and in terms of societal prestige.

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Starting Point

First, I would advise someone in your situation to work the puzzle backward for different cases.

Switch Degrees

Take the course requirements for the physics and math undergraduate degrees. Take your current transcript. Start backward from the senior year of the physics or math degree. Develop the sequence of courses that you need. Track backward until you hit the overlap between what you need and what you have. Fill in the blanks with the courses that are pre-requisites to a physics or math degree that you do not have. At that point, take a course schedule from the university where you are. Design your schedule going forward to switch to either physics or math. Determine the minimum additional time you would need to complete either degree. As best possible, include that you will take courses during a summer semester to make up what you lack. At the end, you will have a complete schedule for your current degree, supposedly to be complete in one more year, as well as complete schedules for switching to either physics or math, to be completed in Np or Nm additional years.

Go on to an MS Degree

Research the course offerings for an MS in physics or math. Pay particular attention to the senior-level undergraduate pre-requisite requirements for the first year courses. List their equivalents from your current university. By example, a graduate course in solid state physics will likely require math through partial differential equations as an explicit or implicit pre-requisite. Some graduate programs do the favor of listing a set of required transition courses for students who enter the graduate program from an undergraduate program that is not the same. When in doubt, find the equivalent graduate course at your university, find out who teaches that course, and go have a talk with that instructor to get the information you need. At the end you will have a list of senior-level undergraduate courses that you must have for an MS degree in either physics or math. Presume that you continue with your current degree to complete it in one year. Now repeat the exercise to track how long in time you will need just to take make-up courses in senior-level prerequisites.

Comparative Analysis

  • Based on what you have learned, which approach do you prefer? Suppose that all paths above require you to take one additional year beyond your current undergraduate degree. Which track is more appealing in its course list? Suppose all paths require the same or nearly the same types of courses. Which track is more appealing because it takes (or appears to take) less time?

  • Based on what you have learned, are any of the paths eliminated? Perhaps you cannot afford to take Np or Nm more years/semesters of courses. Perhaps you do not want to take partial differential equations ever at all.

You can do this comparative analysis for any other degree program (chemistry, biomedical engineering, biophysical sciences, ...). It will give you a grounding in what you face as a minimum and what you are unwilling to do as a rule.

Other Insights

I would not advise anyone in your situation who decides to pursue a graduate degree in a different program than their undergraduate degree to believe with any seriousness that they can simply make up courses that they lack just by reading on their own. You will be in competition with graduate students who know the undergraduate material backwards and forwards through rigorous training. You must have that a comparable level of confidence going in to a different graduate degree or you will more likely fail in your first year.

The reason that graduate programs require student applicants to validate certain pre-requisite information through official coursework rather than through a "read on your own" approach is to avoid that you will otherwise most likely fail in your first year courses.

The best advice you can get to help you make plans to continue to graduate school will come from faculty who are in the program where you want to move, who teach the first year graduate courses, and who advise students in research. Find them at your university. Go talk to them.

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