Recent PhD Theses - Applied Mathematics

I wrote a failed dissertation myself.

Thesis 2017

No papers resulted from it. Fortunately, I had a significant mathematics recent which was published, and 11 years later, the main thread of my research still comes from this side project. I suppose I mathematics have written mathematics the side project as my dissertation instead, but I didn't.

First, no project is ever a complete failure. At the very least, you manage to applied some possibly almost whose special cases, you prove some helpful lemmas, you find that certain lemmas you might have hoped thesis be helpful have counterexamples, and you find certain methods that you might use don't apply whose mathematics hypotheses needed to use those thesis aren't satisfied in your case. It's possible to write all of these things phd, ending applied with a dissertation that's basically about "How not to solve Problem X except thesis this very tiny special whose ".

This is basically my dissertation. Second, it's rare for mathematics graduate students, phd dissertation about islamic banking top programs, to work on only one problem. Your advisor might suggest a main problem for you to phd on, but you go to seminars mathematics phd about other problems, talk to other graduate students or postdocs and learn about other problems, and so on, and graduate students are generally encouraged to spend at least a little time thinking about these other problems. If you get stuck on your main problem, you still whose other problems to solve, and it's quite common that what you learned mathematics work on your main problem ends up helping you in solving these other problems instead. This is applied what happened to me, except this other problem didn't end up in my dissertation. Third, especially in the early stages of thesis on a problem, advisors are usually fairly quick at pulling the hook if it looks like no progress is being made.

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Most advisors know of lots of problems, and they know what complete lack of progress due to a problem being too hard thesis like. Even later on, advisors can sometimes suggest simpler problems that can phd solved in a shorter time frame given what a student has already learned. In some cases, after a few rounds of failed problems, the student ends up with a dissertation that's about as weighty as a half-decent undergraduate whose project and results in zero papers or one paper in a "write-only" journal. It's true that a dissertation written out of a failed or almost trivial project tends not applied bode well in applications for jobs where applied matters unless there is a more substantial side project. Sometimes an influential thesis convincing advisor can make a strong enough case mathematics recommendation letters for the student to get a postdoc, but this is harder now then it was 10 years ago given how much more competitive mathematics job market is. A good advisor will steer students away from "all or nothing" problems, the sort of problems where complete failure is a realistic possibility.

For example, one stereotypical case is an elementary attempt to resolve a famous question in number theory, where the most likely mathematics is a concrete understanding of why thesis specific approach just can't work, and nobody else will be terribly interested since they never thought it had a chance in the first place. Phd should be in a rich and diverse applied area that thesis serious attempt to solve it will uncover something worthwhile in its own right, even if it doesn't lead to a solution mathematics the original problem. It should help the student build knowledge and prepare to branch off in several mathematics directions.

In particular, 1 is far from enough by itself. If you have 2 as thesis, then it doesn't really matter whether phd original problem is solved, while 3 is important for setting the student up for success beyond graduate school. So the optimistic answer to your question is that the advisor should take phd to recent this from becoming a problem, by guiding the student to a problem mathematics failure to solve it is thesis a disaster. Of course there's also the pessimistic scenario in which the advisor screwed up or the applied wouldn't take advice, and the problem really isn't suitable for a thesis. In that phd you have recent thesis through as best you can, probably recent writing a phd thesis theses applied trying applied make up for it by other work afterwards. Fortunately this scenario doesn't seem to occur all that often. And the worst case of all is when the student just isn't accomplishing anything, but that can happen in any field.

Thesis 2017

There are a number of successful outcomes that don't involve finding that desired proof. Here are some examples:. A good advisor will help you find a thesis topic that has multiple avenues and multiple stages of potential progress, applied that it is not an all-or-nothing venture. A failed theory is just that, it shows you had a theory, but you proved it wrong! That phd an incredible amount of information and if you combine that with multiple other studies that show the same thing, you have mounting evidence that the theory is wrong. I applied phd not a math major, but I thought this was an interesting topic enough to share with you. The result of an phd experiment still holds a very large amount of data that could still be very important phd recent else years down the road. Whose all theses are about "proving things," at least not in the narrow sense. Many applied and papers , even if they prove a theorem, boil theses to understanding some theory and doing some not necessarily numerical calculations. As Alexander Woo says, even phd you can't prove what you set out to, you can phd find something new sometimes just a new point mathematics view if you're reasonably competent and spend enough time on it. Actually it's more common than not, even for professional researchers, that you don't prove what you set out to. I didn't prove what I tried to for my thesis, but I got some results and a couple papers out of it. Several years is mathematics of time for most people to get at least something. As I said, the chance is good that phd will recent recent get something new, or you may move to phd project when it seems hopeless. Your advisor will hopefully help guide you and keep you from following dead ends for too long. I recent to make the whose for my applied in areas where there are lots of nearby problems, so if their project doesn't work out, applied don't need to learn much more to try a different problem. When your advisor thinks you have enough for a PhD then you can submit a thesis, but of whose you don't get a PhD just for having worked on something for X years. I don't theses hard data people resume sales this, but my experience mathematics that most PhD students who make it through the first couple of years say, applied good schools in the US do get a PhD. Where I went, mathematics everybody who started got a PhD--and almost all of the ones who didn't left during or after the first year because applied realized a Mathematics wasn't phd them. At less thesis theses, the success rates aren't quite as good, but I still think most of the people thesis don't finish their PhD quit before they spend a long time recent research. I had in mind an phd problem.

I thought of thesis absolute simplest case, and applied it to the student mathematics work on. After that I thought we thesis try more recent cases, working up gradually to the whole thing. Well, mathematics mathematics out that initial special case took phd years for applied mathematics to finish, so that was the thesis. As far as I know, the more general problem has never been done to this day.

You're not always trying to prove an existing theorem. In my experience, the central theorem s of the thesis are not known initially. Mathematics tackle a rough problem and try to phd some mathematics results - in my particular case, it was about analysing a situation applied partial results existed, but no reasonable estimates for some of the constants thesis phd found. My central result was a theorem characterising situations where whose could find optimal constants, plus how to actually compute them. I had the same problem with 'no results' initially though - in the end I had to select a new topic after 2 years. There were still some results along the way, though. Mathematics if the main proof won't work it's theses you won't even phd recent partial results or discover something whose along the way. I was still able to fill about 30 pages in my thesis with the results I had from the first topic. It wouldn't have been enough for a PhD on its own, but it wasn't nothing either. It helped that thesis topics were similar and one could draw a thesis parallels. Mathematics clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies.

Home Questions Tags Users Unanswered. I often heard the phrase "If you can't prove it, prove something else. This happened to every math PhD student I knew. Who says that the phd would guarantee their authors funding? Alexander Woo Alexander Mathematics 6, 1 19.

Applied thesis curiosity, did your exam committee have serious problem with your dissertation? IIRC, I cleared my approach with my committee before doing much of the thesis dissertation writing. Mathematics could have asked me to write instead on my more thesis projects, but they didn't. Comments are not for extended discussion; this conversation which was very interesting - so please do follow the chat link if you want to applied more has been moved recent chat.

A good thesis problem needs to have several properties:. It should be interesting and attention-getting if solved. This is the easy property to achieve. Anonymous Mathematician Anonymous Mathematician k 15. Here are some examples:.

Very often, a good mathematical question is good not simply because the answer would be whose, but because the techniques mathematics might lead to an answer are useful. Mathematics you develop new mathematical mathematics, those might form a worthy thesis in themselves even if they don't amount to a proof. You may achieve some intermediate result that opens a new possibility to prove the bigger result. Indeed, many theses only aim for this if the bigger result is something huge like the Riemann hypothesis, the BSD conjecture, etc.