Is it easy to change your major after starting your PhD or masters, if it is necessary?

Question

I’m a mechanical engineering student and I am about to apply for a PhD. I am certain about my desire to pursue advanced studies. However, I have serious doubts in what I want to pursue my studies on.

I have done research on structural health monitoring and power electronics. At some point I thought that I had interest in electrical engineering and after some research I got interested in mathematical physics and then in applied mathematics.

I started doing undergraduate research when I was a sophomore in the area of structural health monitoring. However my job was to write an algorithm to implement the methodology. I realize now that what interested me was not structural health monitoring, but to study the origin and derivation of the theoretical equations. I saw the profiles of various faculty in applied mathematics and I found some of their research interesting. Doubts about applying:

• Although I have a GPA above 3.60 some programs require certain number of courses in mathematics. I only have the mathematics included in the mechanical engineering program and one course of elementary statistics. I have taken 5 courses in mathematics. However I don’t show strength because out of the 5 courses, in 2 of them I got B when I was a freshman. I think that the taking the elementary statistic course last semester was not a good idea. I should have taken a more advanced course.

• I have not taking any advanced course in mathematics.

• The application to the program requires the GRE, TOEFL and subject test in math. Some graduate programs say that the GRE math are not mandatory but not taking it puts you in disadvantage. I am not sure I will have time to prepare for it and as a result I don't know if I will do well.
• I have research experience, but it is not in this area. In addition, the reference letters will be made by engineering professors and not math professors.
• Since I am about to finish next semester, I don’t have much time to take more courses or do research in the area.

I looked at a few topics that I found interesting in applied mathematics but I haven’t done research in them. As a result I don’t know if I will get tired or if I will change my mind once I start on the program. If I were to apply for this program and I change my mind would it be easier to change even if it means going to other department?

Answer 1

Unfortunately, no, it's not so easy to change PhD programs.

It isn't like changing your undergrad major, where you just have to fill out some forms and get your advisors to sign off. At the graduate level, each department does its own admissions. So if you are in a mechanical engineering program and want to switch to applied math, you have to submit an application to the applied math program just like anyone else. You'll be competing for a seat against every other applicant from around the world, most of whom will have completed a full undergrad mathematics major.

You might be able to improve your odds by getting to know faculty in the math program before you apply, perhaps discussing (or working on) research projects with someone there. However, keep in mind that you will also need to stay in good standing in the engineering program, and you won't have a lot of spare time to explore math opportunities.

Also, from your description, your math background sounds much too light for entry into a math grad program. Applied math can be more flexible than pure math, but having no advanced courses at all doesn't sound too good. In fact, I'd be concerned that without advanced coursework, you may not even have enough of a sense of the field to know that it's really what you want to do. Mathematics courses have a sharp change in flavor and difficulty as you transition from lower-level computational courses (calculus, differential equations, etc) to upper-level theory courses (real analysis, abstract algebra, topology). Entering a PhD program having only the former kind of courses would be roughly analogous to being a go-kart enthusiast racing in the Indianapolis 500. And it won't be easy to pick up extra math courses while in an engineering program; grad program requirements rarely allow for free electives.

Perhaps something that might better fit your situation is a post-baccalaureate ("post-bac") program. These are one-year programs designed for students who have completed a bachelors and want to attend grad school in math, but need further preparation. Such programs are offered by relatively few institutions, but I believe some of them are quite well-known in the community and have very good placement rates.

Answer 2

My advice is the same as Nate Eldredge's, but let me make a few points.

I am certain about my desire to pursue advanced studies. However, I have serious doubts in what I want to pursue my studies on.

To be very honest, for me the second sentence largely nullifies the first. Wanting to pursue a PhD in the abstract is a poor idea. In order to get any satisfaction out of a PhD program, you need to be pursuing a PhD in X because your love for X is so strong that you want to have a career doing X. If you think it might be X,Y or Z, I worry that you don't have a deep enough commitment to any of the three to make it worth the time, effort and career uncertainty of today's very harsh job market.

Perhaps by expressing "serious doubts" you are really explaining your desire to transition from your undergraduate field to mathematical physics / applied mathematics (henceforth I'll just say "math": that's where you would apply). I agree with Nate Eldredge that your coursework in mathematics is so minimal that you probably haven't been exposed to the flavor of graduate level mathematics....or at least, you haven't demonstrated that exposure in a way that would be convincing to an admissions committee. Further honesty: your self-described profile would make you a very likely decline from the math PhD program at UGA (about the 50th best in the country), except perhaps if you took the math subject GRE and did well on it. It would be a little surprising if you did well on that exam given your description of coursework...but of course it's possible, especially if you are very mathematically talented. It could be useful information for you to know how you might do on this exam, but unfortunately this exam is notorious for having had the same crappy study materials for the last 20 years (or more?). I don't know of any reliable way to gauge your score.

There are a lot more than 50 math PhD programs in the US, and I can't speak to your admit-worthiness for all of them, but honestly I would think twice about scraping the bottom of this particular barrel. The job market is so tight right now that degree pedigree is something to keep your eye on.

In conclusion, I come back to agreeing with Nate Eldredge: you are not currently a good PhD candidate in math, and math faculty like us would worry about your lack of exposure. Of course this does not mean that you are locked out of further study of mathematics: that never happens to anyone. But if you think you are interested, find out by taking more math courses, in a non-degree program if need be. I should say though that your stated background of five math courses required by an engineering degree -- at least two taken as a freshman -- is less than halfway to a graduate-preparatory math major. In your case, after enrolling in a non-degree program for a semester or a year, if you really discover that this is what you want to do, you might actually want to explore a second bachelor's program. Either that or really work hard to develop a relationship with a department so that you can essentially do this over the course of 2-3 years with a lot of faculty contact.

Good luck.

Answer 3

A PhD is not like an undergraduate degree where you can do a bit of this, a bit of that, add up your scores and get your final grade. It's about doing research in a fairly narrow area, leading to writing a focused thesis on a particular topic. Spending, say, a year doing electrical engineering would normally give you almost nothing that would be useful towards a PhD in mathematics, and vice-versa. As such, transfering from one department to another is, essentially, starting a new PhD and would likely be treated as such.

It sounds like you don't know much about what a PhD involves and you should definitely find out before committing several years of your life doing one! I'm also a little confused by your statement that you're certain you want to commit several years of your life to studying a fairly narrow topic but you're not even sure what broad area that topic will come from. It seems that you're much more excited by the idea of doing a PhD than about any of the areas that you might research, yet doing the PhD requires being in one of those areas that you seem to find less exciting than the PhD itself.

Answer 4

Much depends on the specific university and department arrangement.

However, moving departments at the PhD level is usually quite difficult because it involves changes in your financial package. Transferring from physics to mathematics, for example, would mean your funding is coming from a different source. It also means that physics is losing a student, which can be bad for the department. Things are even more complicated if your funding is tied to a lab or an individual faculty member.

Many places consider transfers alongside new applicants (meaning, you are, in effect, applying to graduate school for the second time). You would have a slight advantage of knowing your professors, and perhaps of having an advocate for your candidacy, but you still have to write essays and get recommendations along with everyone else. I would not count on a transfer as a plan. You could just as well not get in, losing support from your home department in the meantime.

For these reasons, I often recommend students take some time between graduation and graduate school. Get a job at a lab or with a firm, take some courses, travel. Graduate school is like marriage--a long-term commitment. It is not a good place to explore or experiment with careers. There is no rush to make the decision, but once you do, make sure you are committed to your department and to your chosen discipline.

Master's programs are a different ballgame, since they do not normally fund students. It is probably easier to switch out of a Master's program. But once again, you would probably have to apply anew.

Answer 5

Rick, you are not alone is feeling that the application process for PhD programs is enigmatic. It requires you to take knowledge that you have acquired and show evidence that you are committed to applying this already-obtained knowledge to a long-term research endeavor. Of course, you will learn a lot along the way, but depending on the institution, you will have very limited time to play catch-up. So, if you are absolutely set on your goals to pursuing a PhD program, either find a school that will be impressed with your credentials and allow you 1-2 years to settle into a research group, or you can work toward a more competitive school while maybe pursuing a master's degree in your chosen field of study.

Everything has its risk. Applying only to overly-competitive institutions can leave you stranded with no place to go. I recommend having a job or 10 lined up as a backup. Likewise, applying to only master's degree programs will mean spending more money. Sometimes, an employer will fund a master's program. I've been to career fairs where the recruiters brought that up without me asking about it - so it's quite common. If you want to pursue a prestigious PhD program safely, I recommend in the meantime finding an employer who hires engineers for math-oriented tasks (Two Sigma is a great example). Then see if they will fund your master's.

It may take you a few years, but there is plenty of time (assuming you are of traditional undergraduate age). I am 28 and will be finishing up my second bachelor's degree. I might not be that much more sure of myself in terms of research goals, and sometimes it feels like I'm faking it until I make it. But when the time comes to write your statement of purpose, show the department that you are competent in both research and your acquired knowledge at an appropriate level (we're talking at least two semesters of 400-level coursework in your target discipline).

Nate, Pete, and David give some very harsh but honest advice. Don't let that discourage you from pursuing advanced studies or ultimately a PhD program. If it takes you 7 years to finally get there, just remember, you're not alone. Just always have a backup plan.

Never forget: being intuitively skilled at math requires not only practice, but also an ability to recognize patterns and sameness among many things. In the words of Henri Poincare, an often-declared polymath, "Mathematics is the art of giving the same name to different things."