Engineering background => PhD statistics?

[creed_the_third]

I'm a Scandinavian student currently in a 5 year MSc in industrial engineering program (you go into it directly from high school, first 3 years = bachelor, 2 last years = master). I'm in my third year now and I've started thinking about pursuing graduate school. Unfortunately it is a little to late to switch major, but I'm planning on taking as many math classes I can and my masters concentration will be in financial engineering. Starting in the fall I will do a year abroad at a top 10 US engineering school. Currently I've taken the following math courses: calculus in one variable, calculus in several variables, linear algebra, mathematical statistics basic course, analytic functions, systems and transforms, optimization (will take stochastic processes and numerical analysis before summer). Also of course engineering courses and a few finance courses. My grades so far are 4,6/5,0 with top grade in all but one math course.

Okay given my background, what courses should I take to prepare me for graduate studies? I've read a lot about real analysis being necessary. As part of my concentration in financial engineering I will plan to take financial statistics, Monte Carlo and empirical methods for statistical inference, statistical modelling of extreme values, econometrics and a few more. What I'm worried about is that my math background isn't as rigorous as someone who majored in math. For example I have no discrete mathematics, topology etc. Will this be a big problem? Should I apply directly to a PhD or to a MS in statistics/math first? Also my university has a master in math statistics which I can take and count some of my credits from my MSc in engineering. Though it would mean that my graduation would be prolonged by a year.

Would really appreciate some insight on the topic

[rockrs]

Well, I think you know that PhD in the US is 5 years, as it also includes the Master degree - the first 2 years. It will be good to take some stats classes, so that you could be able to demonstrate interest in statistics. Real analysis will really be important as almost everything in stochastic processes depends on measure theory and the like. However, do not underestimate optimisation, if you have a course which covers Kuhn_Tucker and so on, be sure to take it, as statistics is really about optimisation...Do not prolong your graduation if you are going to go to US - you will be studying statistics there! If you want however, to study in Europe, say, UK, you need to have a master before a PhD

[creed_the_third]

Well, I think you know that PhD in the US is 5 years, as it also includes the Master degree - the first 2 years. It will be good to take some stats classes, so that you could be able to demonstrate interest in statistics. Real analysis will really be important as almost everything in stochastic processes depends on measure theory and the like. However, do not underestimate optimisation, if you have a course which covers Kuhn_Tucker and so on, be sure to take it, as statistics is really about optimisation...Do not prolong your graduation if you are going to go to US - you will be studying statistics there! If you want however, to study in Europe, say, UK, you need to have a master before a PhD

Thanks for the reply. How strict are they in US colleges with prerequisits? I looked at the real analysis course at the college where I'm going to study at next year, and one prereq is a course in how to write proofs. I haven't taken such a course. Do you think that will be a problem?

The optimization course I have taken covers KKT theory, linear and nonlinear programming, convex optimization etc.

Edited March 6, 2012 by creed_the_third

[cyberwulf]

You don't need discrete math, topology, etc. to be competitive for admission to US stat programs. In fact, by the time you graduate you will probably have more math than the typical applicant to stat PhD programs (remember, many of these applicants will be coming straight out of undergraduate programs, and in the US even a math major isn't taking a ton of math credits).

I would suggest you take Real Analysis; the "proof-writing" course you see listed on some programs' sites is usually a "baby" version of RA, so taking the real thing is more than adequate to meet that requirement. Don't worry about taking a lot of statistics courses other than mathematical statistics (covering stat inference); you will be taking them as part of your Masters/PhD anyway. And on that note, I would suggest that you apply directly to PhD programs.

[rockrs]

Thanks for the reply. How strict are they in US colleges with prerequisits? I looked at the real analysis course at the college where I'm going to study at next year, and one prereq is a course in how to write proofs. I haven't taken such a course. Do you think that will be a problem?

The optimization course I have taken covers KKT theory, linear and nonlinear programming, convex optimization etc.

Given you have a good recommendation and from your sop one can see that you know where are you going, say, high dimensional multivariate statistics or nonstationary time series or machine learning, and most importantly, fits to your background and coursework experience , not that strict. Don't bother for the proof requirement. I mean in the US there is generally such a course, in my country for instance, we don't have calculus but straight go to analysis and thus the proofs. Furthermore, most programs will ask you to take the real real analysis, no matter if you have or not have the baby one . Good luck.

[ANDS!]

Do you think that will be a problem?

The number one complaint that a very well known statistician had was that incoming students to her graduate program didn't know how to write a proof. This is why stats departments like math majors - they generally have all the tools, except the stats, available. It is much easier introducing a class to concepts of sigma-fields and probability spaces if one has had an analogous introduction in perhaps analysis or algebra - topics stat undergrads aren't necessarily exposed to.

. . .and in the US even a math major isn't taking a ton of math credits

Not sure what programs you're looking at. In the past three years I've taken 3 non-math courses. A math major - depending on the track/program requirements - is more than certainly going to have more math than this gentleman. I will say they will most assuredly have one and a half years of calculus, upper and lower division linear algebra, and at minimum one semester of real analysis and algebra (our program requires full years of both).

[creed_the_third]

Maybe I wasn't very clear in my opening post but I will do a student exchang (as part of my engineering program) next year at a US university and it is during this exchange that I plan to take real analysis. My question was if I would be able to take real analysis during my exchange year abroad, because one prereq for it was a proof writing course. That question had nothing to do with PhD programs. So when I apply to PhD programs after I get my MSc in engineering I will have real analysis (again, if I'm allowed to take it).

Edited March 8, 2012 by creed_the_third

[ANDS!]

It is highly unlikely that they will allow you to take Real Analysis without first having taken an introduction to proofs course. Depending on the school you are doing an exchange at, you can possibly take this class in the fall, and then grab Real Analysis in the spring.

[creed_the_third]

It does also state under prerequisites "or consent of instructor" so maybe I can talk my way out of that requirement?

[creed_the_third]

It does also state under prerequisites "or consent of instructor" so maybe I can talk my way out of that requirement?

[R Deckard]

It does also state under prerequisites "or consent of instructor" so maybe I can talk my way out of that requirement?

Some schools don't actually enforce prerequisites (mine doesn't). In fact, I skipped 4 prerequisites for a course I am taking this semester and nobody said anything.

The question is whether you will be ready for analysis without having familiarity with writing rigorous mathematical proofs. This depends on your background, your willingness and ability to learn quickly, and the rigor of the course. I would say that if you are pretty bright and the course is an "intro" level analysis course, then you will be fine. Do you know what book it uses?

Edited March 9, 2012 by tyler88

[ANDS!]

It does also state under prerequisites "or consent of instructor" so maybe I can talk my way out of that requirement?

If you feel like you can handle it, go for it. However none of the courses you've had so far will have prepared you for the rigor that will be demanded of an analysis proof.

[Agradatudent]

I would agree with tyler.

Even if they allow you to do so, you may not want to. If you are at a school who's intro to analysis course uses baby Rudin, you really don't have much of a chance to get a decent grade. Without being used to doing proofs and having a level of "mathematical maturity", it will be ridiculously difficult to keep up. Not only that, but a book of that level will thrust you into many topics past analysis, including topology which you already mentioned.

I think you should take the prereq regardless. Your background really just says you can do engineering, and it says nothing about upper level mathematics involved in statistics.

Remember, if the disciplines were so similar, they wouldn't be separate.

Edited March 9, 2012 by toypajme

[creed_the_third]

Thank you guys for the input. I'll think I'll read up a bit on my own during the summer and try to take the course directly. The book they use is Kenneth Ross: Elementary Analysis: The Theory of Calculus.

Edited March 9, 2012 by creed_the_third

[Agradatudent]

I have heard that book is manageable. Instead of reading it, I recommend reading a book like introduction to proofs by chartrand (sp?) and not only read it but do every exercise that's how you actually prepare. Reading doesn't do much. You must engage the material

[R Deckard]

Thank you guys for the input. I'll think I'll read up a bit on my own during the summer and try to take the course directly. The book they use is Kenneth Ross: Elementary Analysis: The Theory of Calculus.

"Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses."

[Agradatudent]

It never hurts to have a background in logic. The book most likely won't stress things like contra positive and the subtlety of proving if and only if

[ANDS!]

That book doesn't stress it at all; and it shouldn't. It's still a pretty "light" treatment on Real Analysis, which goes with the topic of the class I suppose. Having flipped through it (a brisk 300 pages), I would say the OP could probably tackle the subject matter if the class is taught in a similar fashion to the book.

[Agradatudent]

I agree the OP would most likely be fine, but I think for the OP's own good down the line he should learn the basic logic constructs.

[creed_the_third]

I'm currently doing my year as an exchange student at a US university and doing okay so far (btw, glad I read up a bit on my own on writing proofs since I wasn't able to register for the prereq for real analysis). I'm pretty clueless how I should go about getting LORs from professors here at this university in the US, since when I'll be applying for phd programs I'll be back in Sweden. Should I just email them when I apply? I doubt they will remember me... Or would it be appropriate for me to go and speak to them after I finnish my courses and explain my situation?

Also, I'm think it would be good for me to get some research experience here, so how does one go about contacting professors if they need help with their research? Email or office hours?