Course Advice

[superbean]

Hi everyone,

I will be starting my final year of my Masters degree (in Statistics) next semester and I am trying to decide what courses to take.  

My goal is to obtain a PHD (and ultimately work in academia... easier said than done)  and I was wondering if anyone could give me any input about what courses I should take in order to increase my chances of getting into a PHD program.  

My undergraduate was in physics, so I have taken Calculus I,II, III, Differential Eq. and Linear Algebra.  But that is all the math I have taken (one B, the rest were A's)

 

There are three classes I would like to take next semester, but I only have time to take two (There is one class that I need to take to graduate, so its out of consideration entirely.) and there wont be opportunity for me to take real analysis before I graduate.    

So here are my choices: 

 

Bayesian Statistics

Time Series Analysis and forecasting

Advanced Calculus I

 

I'm leaning towards Bayesian and Advanced Calculus, but Time Series also sounds interesting.  I wish I could take all three! At some point I have to sleep.   Any thoughts are appreciated 

[ParanoidAndroid]

What is the syllabus for Advanced Calculus? Is it a standard vector calculus course (Green's, Stokes', Gauss' theorems, etc.)?

Edited April 1, 2014 by ParanoidAndroid

[superbean]

Advanced calculus I appears to be a theory based course with lots of proofs. 

I couldn't find a syllabus with topics for this course, but here is the book they use (they go through the first five chapters) 

 

http://www.amazon.com/Elementary-Analysis-Calculus-Undergraduate-Mathematics/dp/1461462703#reader_1461462703

and a brief description

Sequential. Prerequisite: Departmental permission. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergences and uniform convergences, power series, improper integrals, transformations, line and surface integrals.

 

I took a vector calculus course (my undergraduate program called it calculus III),  this is quite different. 

[ParanoidAndroid]

I've used that book in the past. I think it's tailored towards a first course in real analysis to be honest. In many universities a standard real analysis course is given the title "Advanced Calculus". I think you should definitely take that course. 

[superbean]

Oh nice.   There is a real analysis class offered at the school, but it requires advanced calculus one and two as prereqs...  I'm not confident enough in my proof abilities or else I would just jump in there. 

Considering my lack of math experience, I think that advanced calculus is definitely the one to take.  Thanks

[ParanoidAndroid]

No worries, sorry I can't help you with Time Series vs. Bayes. 

 

There is a real analysis class offered at the school, but it requires advanced calculus one and two as prereqs.

 

If your advanced calculus course is a prereq, then this course most likely involves topology, measure theory and/or functional analysis. I might be mistaken though. 

[Stat Assistant Professor]

Take the advanced Calculus/real analysis class if you intend to go onto the PhD. Even if your area of research ends up being something very applied with few proofs, you will need to go through a bunch of theoretical, proof-based classes beyond the Casella & Berger-based year-long sequence (i.e. 1-2 semesters of measure theoretic probability, 1-2 semesters of linear models, at least 1 semester of theoretical stats/inference). You will most likely need to pass an additional qualifying exam in these topics as well. So you need to become good at proofs.

[wine in coffee cups]

With an eye towards improving your profile for PhD applications:

 

Agree with everyone else that you should definitely take the advanced calculus class. A course in proof-based analysis is a common prerequisite for PhD statistics programs, and even if you apply to programs that don't require it, it still looks good. You'll also have to put off PhD theory coursework until you've completed that, so you may as well get it over with now.

 

If you are equally interested in the Bayesian stat and time series material, you might take whichever class will give you the opportunity to impress the professor more so that you could hope for a strong recommendation (unless you are already confident about who will write your letters). Recommendation letters are very important and you'll want ones that credibly say you're one of the best students in the program and that you have the intellectual ability + motivation + curiosity to be a successful PhD student. Talk to other students who have taken these classes or had other classes with the instructors. Maybe the class that involves more project work might be preferable to a lecture course that is purely homework and exams, for example, in terms of the professor getting to know your interests a little better. Or maybe one class is taught by a professor who is known to be very accessible and helpful to students. Maybe one is more challenging and theoretical than the other, and doing well in it would be a good sign. In any case, ask around.

[biostat_prof]

As others have said, definitely take advanced calculus. That is a no-brainer. If you don't have that on your transcript, many (most?) programs will just trash your application immediately. It probably won't make a difference which one of the other two classes you take.