Schools Going to grad school and lacking a little confidence

[Fellowroot]

Hi, I'm applying this semester to get into a Phd program, math or possibly physics and am serious about it, however I have only completed a Bachelor level degree and while I studied very hard and know as much as I can it just keeps on surprising me when I see the level of degree of the work involved at the higher levels.

Normally I just do it and don't worry about how hard something is. I solved some very difficult problems in complex analysis one time and that didn't bother me, BUT when I look at this qualifying exam in basic analysis from Duke University.

http://www.math.duke.edu/graduate/wqual/analysis_aug2014.pdf

It just seems as if no matter how much you know you can always find something that exceeds all of your knowledge.

Am I wrong in lacking confidence when I see something like this? Is it okay to apply to a program even if you aren't at this level yet?

Or am I just supposed to REACH this level once I've been there several years training?

Does anyone else ever feel this way?

 

[jedishrfu]

Everyone feels this way, its part of learning at the higher levels. Each year of undergrad work is roughly 3 years of high school work and each year of graduate school is correspondingly harder.

When you become a PhD you're still at the beginning of a long road to total mastery of your subject where you now know what you don't know. ( or maybe not :-) )

Its a lot like earning a black belt where it takes 2 years of concentrated practice to achieve it and then another 2 years to get to 2nd degree and 4 years to get to third degree...

But you should not let that deter you from moving ahead. Fellow students will be trekking along the same path, overcoming the same obstacles striving for the same goal.

 

[Fellowroot]

thank you for your thoughts jedishrfu

 

[homeomorphic]

I took a similar exam and it did look intimidating at first. If you've done well in the past, though, if you study hard, you can probably do it. The difficulty shouldn't be down-played, though, since most of the people in my program who didn't finish were blocked by an exam just like that.

I think your fears might be somewhat justified. Determination, hard/smart work, and persistence can go a long way. Be that as it may, a math PhD is not something I can honestly recommend to all but a handful of people.

It's okay to apply to the program, but whether or not that exam looks scary, a number of issues should seriously be considered.

First of all, if you study math, you might find yourself very far from reality and applications. If that bothers you, I would strongly recommend doing physics, or at least going as far towards the applied side of math as you can possibly manage (or at least looking into it, if that doesn't sound appealing at first glance). Even if it seems not to matter to you now, that can change. For me, it was the staggering complexity and massive amount of work required, combined with how removed from reality it was that made me call it quits (I went through the motions to finish the PhD, and now I'm looking for another career).

Secondly, teaching is actually quite a big deal, unless you are a super-star at research. So, you have to give some serious thought to whether that is your cup of tea. My imagination told me it would be; reality told me otherwise when I tried it out. I can't handle lecturing (especially to low-level students) because it's like having a completely one-sided conversation. Tutoring, I can handle because they get to talk back to you and let you know if they don't understand. That can happen in lecture, but not on the same level. Plus, people are more likely to pay attention to you. Anyway, I think you should have several years of tutoring under your belt before attempting to lecture because otherwise, there's probably going to be a massive communication barrier. It's hard to know what they don't know, unless you get a lot of practice talking to them. I have developed all kinds of tricks, like talking about pizza slices for fractions, and it's hard to imagine gaining proficiency with that sort of thing without actually interacting with students one on one, at least for me. Lecturing still terrifies me, even after all that, and not in the sense of being afraid to speak in front of an audience.

Thirdly, you can jump through lots of scary hoops and still not get a tenure-track position at the end of it. Math is probably the best subject if you want to make it to be a prof, but it's pretty low odds. I just read an article to that effect yesterday. So, it helps to have an exit plan (in math or physics). It helps to have jobs in mind from the beginning, if you want a job in industry.

It is a lot of work, the pay is not great, and it may not turn out to be worth it in the end, so it is definitely worth questioning. I can't agree with people who say that it's still worthwhile if you don't get a faculty position (and for me, it wouldn't even be worth it, then). A PhD is training to be an academic. It doesn't make sense for 9/10 people to put so much effort into it, and then have to go find something else to do after drowning their life in a very narrow subject for years and years. It is true that you can develop other skills while you are at it, which lessens the problem slightly, but in many cases, it would be better just to study more specifically for the job you want to get at the end.

 

[Fellowroot]

Thank you for your reply.

While doing my degree I've worked at a community college as a tutor. I've tutored many subjects and even taught a physics SI class.

I do not mind teaching at a university at all.