MarcusSolarz Posted July 24, 2015 Share Posted July 24, 2015 (edited) Hi, I want to apply to a PhD program, but I am having a difficult time figuring out where I "fit in", so to speak. The following, I hope, will explain my predicament. BACKGROUND: I have a MS in math, and have worked for many years in various labs solving mathematical problems that arise from basic research in science and engineering. I have 17 publications in peer-reviewed journals (PNAS, IEEE, J. Chem. Phys., etc). During the course of my last research experience in statistical signal processing, I have gravitated towards statistics and would like to work on real world problems in statistics. I suppose the applied nature of statistics, the fact that it is in some senses more like logic than math proper, and its ability to be applied in many settings appeals to me. PROBLEM: I very much to go back for my PhD in statistics, but I've run into a problem. Most "traditional" PhD programs seem to want students who are research oriented. Unfortunately, I don't fall into this camp: I basically like using math to solve problems, not for the sake of the subject itself. In other words, I am more interested in the process of solving the puzzle than the pieces themselves. I have considered doing a PhD in mathEd or perhaps try a PhD program in math designed for non-specialists that would allow me to teach and do contract work and my own investigations on the side (I very much enjoy teaching statistics and feel there is a huge need for educators specialized in statistics, however there are very few programs in statistics education), but I am wondering if there are other options or programs that perhaps I have overlooked. Thank you for taking the time to read my problem, and I appreciate any help/advice anyone may have. Marcus Edited July 24, 2015 by MarcusSolarz Link to comment Share on other sites More sharing options...

TakeruK Posted July 24, 2015 Share Posted July 24, 2015 By definition, PhD programs are designed to train students to become researchers in their field. The PhD dissertation is an investigation that pushes our current knowledge of a specific topic. So it sounds a little weird that you say you want to do a PhD but you don't want to do research. Note that although I say that the PhD programs are meant to train you to become a researcher, this does not mean that the only desired outcome of a PhD is to do academic research. The PhD training is great training for a lot of other non-academic careers and it would enrich your skills of using math to solve problems. However, the PhD "certification" is that you are a trained researcher. The reason why a PhD is a valued asset for non-academic careers is that you would be bringing the experience of someone trained to do academic research to your workplace (even if the workplace is not academic research work). I'm not saying you have to like Math for the sake of the subject itself and not even saying that you have to like Math research. Instead, why do you actually want a PhD? The PhD is training to become an academic researcher and if you don't want that training, then why get a PhD? However, if you do want that training, but just don't want to do academic research beyond the PhD, then that makes a lot of sense. You will just have to get through the parts of the PhD that you don't like and hopefully the benefits of being trained as a researcher will benefit you in the future. Link to comment Share on other sites More sharing options...

TakeruK Posted July 24, 2015 Share Posted July 24, 2015 I noticed I might have made an oversight in my post above. In that post, I assumed that you were not interested in any kind of academic research at all. However, this might be a bad assumption, since you simply said that you are not interested in Math as a subject but you really enjoy using mathematical methods to solve problems! So another suggestion is to find another field where you can apply mathematical expertise to solve academic research problems! If you're not opposed to the idea of academic research overall, many astronomy and physics fields will take math majors if they at least have the basic physics undergrad courses (which you can take if you need them). And another non-degree suggestion is that you can try to find work in these fields as a staff scientist or other permanent professional research staff in various research groups at Universities, industry, government labs, etc. You can and should certainly expand to fields beyond Math. Many fields, such as my own, have limited understanding of statistical methods and really need experts to help us get the most out of our sparse (and expensively obtained) data. Link to comment Share on other sites More sharing options...

MarcusSolarz Posted July 24, 2015 Author Share Posted July 24, 2015 (edited) TakeruK "By definition, PhD programs are designed to train students to become researchers in their field. The PhD dissertation is an investigation that pushes our current knowledge of a specific topic. So it sounds a little weird that you say you want to do a PhD but you don't want to do research." I want to understand the theoretical basis of statistics better and some of the main areas currently in practice (unsupervised learning, multivariate methods, random matrix theory, etc) so I can then use these methods to solve real world problems. I just want to know more so I can do what I've been doing faster and in a more rigorous manner (prove my solutions "work", have certain properties, etc). For that reason, I'm not sure a PhD in another area will help me (because I won't get the depth of theory I need and moreover I'll still have to specialize). Moreover, my position puts me at a distinct disadvantage in applying to grad programs (which seem to favor applicants with well defined research goals that are related to those of the faculty). One of my colleagues has told me "well at some point you have to specialize", but I beg to differ. In every field I've ever worked I've had no specialized skills coming into that field and was capable of doing good independent research. Moreover, I've seen a lot of pure mathematicians (based on their general knowledge of math) be able to make significant contributions without any training in that field either. (as one mathematician told me "It's always easier to go down".) I guess I find it strange that in a time when we have a need for generally well-trained people with a broader array of techniques to solve problems of an interdisciplinary, we don't have programs that fill this more general need. Edited July 24, 2015 by MarcusSolarz Link to comment Share on other sites More sharing options...

TakeruK Posted July 24, 2015 Share Posted July 24, 2015 I want to understand the theoretical basis of statistics better and some of the main areas currently in practice (unsupervised learning, multivariate methods, random matrix theory, etc) so I can then use these methods to solve real world problems. I just want to know more so I can do what I've been doing faster and in a more rigorous manner (prove my solutions "work", have certain properties, etc). For that reason, I'm not sure a PhD in another area will help me (because I won't get the depth of theory I need and moreover I'll still have to specialize). I see. In this case, I definitely do not think the PhD is the best route to get this. You might be lucky and find one that fits your needs, but in general, PhD programs do not train you in this way. For example, in my program, all of the core classes are very introductory. I am in a multidisciplinary field so each of our core classes would be at the level of a upper level undergraduate course in that field. All additional training comes from specialization that you learn from doing research, not in formal coursework. To me, if you "just want to learn more", then I think you should look into other programs like the ones you mentioned in your original post. I'm not in your field so I don't have exact suggestions. But would you be able to just take advanced courses in the topics you want to learn from a University? Coursework is a tiny tiny part of a PhD program**, so it doesn't make sense to me to enter a PhD program if you just want what you wrote here. If you keep your regular work you can probably afford to pay for the courses. (** in fact, in many programs, courses are so poorly taught because they are very low priority. We're expected to learn as we do our research, the coursework is just there to provide some very basic fundamental training) One of my colleagues has told me "well at some point you have to specialize", but I beg to differ. In every field I've ever worked I've had no specialized skills coming into that field and was capable of doing good independent research. Moreover, I've seen a lot of pure mathematicians (based on their general knowledge of math) be able to make significant contributions without any training in that field either. (as one mathematician told me "It's always easier to go down".) I guess I find it strange that in a time when we have a need for generally well-trained people with a broader array of techniques to solve problems of an interdisciplinary, we don't have programs that fill this more general need. I agree that specialized skills are not necessary to create good research. However, the way our academic system is set up, we want to train highly specialized people (with PhDs) and then have them do more general work. Their work would be coloured and shaped by their specialized training. In my interdisciplinary field, at the grad student, postdoc, and faculty levels, we generally take in people who have majored (for grad students) or specialized (for postdocs/faculty) in one particular field and then have them apply their training to solve the wider problems. We have grad students who have BS in Physics, Astronomy, Chemistry, Biology, Geophysics, or Geology. Each one of us is somewhat specialized and we apply our background to the wide interdisciplinary problems. And although each one of us might not have a ton of knowledge beyond our background and core classes, the idea is that the combination of all of us working on small parts of a big problem can lead to solutions in our interdisciplinary field. Our faculty are hired in this similar way too. In my opinion, when we do have need for a broad array of interdisciplinary techniques (as in my field), I would rather see the problem worked on by 3 or 4 different specialists rather than one person trained in all aspects. For better or for worse, this is how academia tends to approach it, which is why, as you correctly said, you will be at a disadvantage when you apply to grad programs but do not identify research interests that align with existing faculty. I don't think your desire for advanced mathematical training is a good fit for a PhD program. Link to comment Share on other sites More sharing options...

Igotnothin Posted July 24, 2015 Share Posted July 24, 2015 I think TakeruK's advice is big-picture, on PhD training in general. I have a few comments regarding stats/biostats PhD programs in particular: 1. Coursework is not a small component of PhD programs. You will learn a ton about statistical theory, proving that a certain estimator has good properties, etc. 2. I'd say less than one-third of stats/biostats PhDs pursue academic research after graduating. Many go into industry (biotech, pharmaceuticals, start-ups, tech), government (NIH, CDC), applied work (e.g. as an epidemiologist/data analyst), consulting, etc. 3. You mention that you like "using math to solve problems, not for the sake of the subject itself." This philosophy is perfectly compatible with biostatistics PhD and I'd say statistics PhD for the most part. Math PhD programs seem to take pride in the study of math whether it's useful or not. In biostatistics, virtually every paper relates to a real problem that arises in clinical or epidemiological studies. From what you've written I think stats/biostats PhD could be a nice fit. TakeruK 1 Link to comment Share on other sites More sharing options...

Desi_Enigma Posted July 27, 2015 Share Posted July 27, 2015 (edited) Hi MarcusSolarz, I can totally understand and relate to your motivations and expectations. I came to the US two years ago for a PhD in EE at USC. I would soon be transferring/shifting to a PhD in applied math or operations research. I have some suggestions which might be useful for you. First, I should I say largely agree with many points raised by TakeruK and Igotnothin. As TakeruK pointed out, the idea of doing PhD is to become a world leader in research. There is no other reason to do a PhD. However, research is by no means is confined to academic research, and does not necessarily have to culminate with a publication. For example, quantitative finance in wall street firms have very high research activity. However, you'll never see a paper coming out of there (possibly a few patents). A similar argument can be made for some industrial research labs like IBM too where the number of publications do not reflect the research activity. Research and innovation happen in a variety of ways, and PhDs are by no means confined to academic research. I also agree with Igotnothin. Biostats/stats is a very active field solving "real-world" problems. Naturally, most PhDs in this area end up at industrial labs solving very "practical" problems ranging from pharma to experiment design for clinical trials. However, I would offer a word of caution. There are many fields that specialize in applying math to solve real problems. This is by no means a new thing, and such programs, thoughts, and ideas have existed for decades! Some such programs are applied mathematics (duh!), operations research (for some reason, not many are aware of this wonderful field), statistics (the flavor varies from place to place), and virtually all branches of engineering. All these vary in flavor and what sort of real world problems they want to tackle. I suggest that you spend time in realizing which real world problems you want to solve, because there are too many problems in the world, and each requires a different skill set. For example, I am switching from engineering to applied math, which should tell you that the nature of problems tackled are quite different, though most of these areas largely use the same or similar mathematical tools. Applied Math (aka computational science) basically develops math tools to help people with "domain expertise" (generally engineers) solve problems. This is ideal for someone who wants to build techniques and be involved in solving real world problems, but don't want to get their hands dirty with the actual problems. This might fit your requirements very well since a) you majored in math; b ) it teaches skills you want to learn (computational modeling, data science, fast solvers for large problems etc.); c) Is aimed precisely at cultivating interdisciplinary ideas to help solve real world problems which people with traditional training are not equipped to by themselves. Operations Research (OR) uses techniques from optimization, statistics, and engineering to solve a wide range of practical problems. The problems addressed in this field tend to have a "business" flavor, and a good chunk of PhDs end up in quant finance or related areas. It asks questions like how should I design my supply chain, how should I schedule jobs to prevent bottle necks, optimal resource allocation problems, decision making in face of uncertainty etc. Optimization and stochastic modelling (probability theory) are the "core" of OR. Statistics largely works with problems involving data. Some of these problems are also addressed in OR, and for this reason OR and Statistics are mostly combined into one unit, or work very close to one another. Pick the sort of real world problems that you like the most, and see where they best fit in the spectrum. There is of course considerable overlap between the fields above (in tools used), and people do move between them after PhDs. I know a few OR and biostat PhDs working at Facebook on social network analysis, many EE PhDs in quant finance, and quite a few applied math PhDs in drug design. I think you can develop a good set of skills through coursework and actually solve real world problems in your PhD itself if you work in above areas (I can personally attest to OR). Enigma Edited July 27, 2015 by Desi_Enigma TakeruK and eeee1923 2 Link to comment Share on other sites More sharing options...

Desi_Enigma Posted July 27, 2015 Share Posted July 27, 2015 Just a few additional points, so that my previous post can be understood in context. During the course of my last research experience in statistical signal processing, I have gravitated towards statistics and would like to work on real world problems in statistics. My points were primarily targeted at this line. You should realize that this is simply too broad, and there are tons of areas (the ones I mentioned) which look at subsets of this problem. It is also not humanly possible for someone to address all the different problems which can be categorized according to your statement. For example, I am an EE major who focused primarily on statistical signal processing. These ideas are used in the context of EE to do channel estimation, stochastic control, synthesis of adaptive systems etc. all of which are great examples of "real-world" or practical problems. Each of these are used in day to day life ranging from communication, guidance and navigation, to industrial automation. People use exactly the same mathematical tools in departments like OR, statistics etc. for financial time series analysis. In applied math, some version of this could be used for weather forecasting, modelling complex systems (e.g. systems biology) and a whole lot more. All of these are using statistical signal processing to solve "real-world" problems. But the problems addressed are vastly different though mathematically, they are extremely close. So the real question is which real world problem are you talking about? I very much to go back for my PhD in statistics, but I've run into a problem. Most "traditional" PhD programs seem to want students who are research oriented. Unfortunately, I don't fall into this camp: I basically like using math to solve problems, not for the sake of the subject itself. In other words, I am more interested in the process of solving the puzzle than the pieces themselves. I suspect that you have just come out of the shell of a pure math major, and are trying to characterize problems and programs as "pure or traditional" vs "real world or non-traditional". This cannot be further from the truth. The number of fields where people use math to solve practical problems far out number pure math or pure science programs. "In other words, I am more interested in the process of solving the puzzle than the pieces themselves." - this is not new at all, and comes across as very broad and ill-informed. One of my colleagues has told me "well at some point you have to specialize", but I beg to differ. In every field I've ever worked I've had no specialized skills coming into that field and was capable of doing good independent research. Moreover, I've seen a lot of pure mathematicians (based on their general knowledge of math) be able to make significant contributions without any training in that field either. (as one mathematician told me "It's always easier to go down".) I guess I find it strange that in a time when we have a need for generally well-trained people with a broader array of techniques to solve problems of an interdisciplinary, we don't have programs that fill this more general need. I would disagree on this point. Though the core math tools used are nearly the same, it is not possible for someone trained only in the math tools to actually solve real problems. A key component which mathematicians overlook is the domain knowledge. Though the math tools would allow one to move across different fields, it is unlikely that they would know which problems are worth solving, which approach or solution is acceptable or practical, and which ones are nonsensical. For this reason, if you just have the tools, you can never "own" your project, and would likely be "contributing" to someone's project. You can keep moving from one project to another, helping out with your tools and ideas, but never owning any project or actually identifying a practical problem to be solved. If this is what you want to do, an applied math degree will fit your bill perfectly. On the other hand, if you have some burning question, and want to solve a real world problem, it is important to develop expertise in the math tools as well as develop domain knowledge. (A vague example would be something like solving energy crisis, how one can use mathematical methods for scheduling to minimize wastage, load balancing etc.) I have seen students with interests spanning across the entire spectrum, so your first job should be to figure out where you fit in. Once this is done, the choice of program will come out by itself. I'll also add a comment that there is at least one acceptable department or program for each point in this whole spectrum. Link to comment Share on other sites More sharing options...

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