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Need advice/reccomendations on PhD programs

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Hello. I am an upcoming senior and I am seeking advice on statistics PhD programs. I am interested in applied stats and machine learning. My profile is very weak compared to what I saw on this site. I have no research experience and no letters of rec since I don't really have any relationships with any professors. So would it be better to take a gap year and focus on research experience and letters of rec during my senior year, then apply the year after. I am leaning towards a gap year, and I hope I can get a job related to stats during that time. Here is my profile:


Undergrad Institution: Top 10 public university according to US news
Major(s): Math and Stats (double)
GPA: 3.68
Type of Student: Male, Domestic
GRE General Test: I have not taken it yet. Probably fall
Programs Applying: PhD in Statistics
Research Experience: Absolutely zero research experience

Awards/Honors/Recognitions: Dean's List

Pertinent Activities or Jobs: N/A
Letters of Recommendation: none

Math and Stat Courses:
Lower Division: A's in Calc 1-3, Differential Equations, Linear Algebra
Upper Division: A's in Intro Analysis, Real Analysis I, Graph Theory, Operations Research, Linear Algebra 1-2 ,  Complex Variables, PDE's, Probability and Stats 1-2, Abstract Algebra I
A- in Regression Analysis, Stochastic Processes II, Topology
B+ in Real Analysis II, Real Analysis III, Stochastic Processes I
And a C- in Abstract Algebra II  lol. I can retake this again to get a better grade and boost my GPA. Is it worth it?

Applying to Where:   I have no idea. I was hoping to get recommendations from you all.
Also should I take some grad courses my senior year. I have the option to take a measure theory course for probability, a grad course in data mining and time series, and also just grad real analysis. Or would it better to focus on research if I can get a position with a professor. Or both?? 
Any advice on what to do or work on for my application is appreciated. Thanks so much for your time.
Edited by Tsukuyomi
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You won't be able to get any meaningful research experience in a few months, so I would suggest taking more advanced mathematical coursework. Your "in" to a good program will be preparation, i.e., that you have a more extensive mathematical background than many applicants. You are hoping that schools will therefore view you as a "safer" bet to succeed in the coursework than others with less preparation. 

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@cyberwulf Thanks for the reply. So you think I should just focus on taking a couple grad courses my last year? Also would you advice retaking a Abstract Algebra to boost my GPA to probably a 3.7.

What do you mean by "meaningful research experience"? I don't think I would be able to publish a paper, but my reasoning was that I can hopefully get some exposure to research and also build a relationship with a professor so that it helps my application? 

Also what is your opinion on gap years. I was thinking of taking one so I can build a relationship with some professors to write me a letter a recommendation for the following application year.

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If you are seriously considering applying for the Fall 2018 I would sign up for the GRE very quickly.  At least in my area the spots fill up pretty quickly. I think a great GRE score (95% on Math) would improve your odds.   I might consider taking the GRE Math subject test to show that you have a strong math background.  You may not have strong relationships with your professors, but do you think you can at least get 1 decent letter from one of your statistics professors?  I would focus on applying to less competitive schools if you decide to go straight into a PhD program. Look at the results survey and find where people with similar stats got in.  Make sure to mainly focus on the results for domestic students, since the application process is usually more competitive for international. The results survey doesn't show all factors, but there have definitely been people with worse GPAs that have gotten in to some programs.  What is your GPA in just your math and stat classes?  It looks like it would be higher than a 3.68.  If it is higher highlight it on your CV.    I would also apply to masters programs as a back up. I don't think their are a lot of opportunities to gain statistics research experience outside of a graduate program (I might be wrong though).   Doing a year or two in a masters program may not be a bad thing.  You could get rec letters and research experience and then you would know if you really like research.  

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If you have a year of school left, you definitely have enough time to focus on research. My advice is to not worry about classes too much, find a professor who'll let you do research with her/him, and dedicate all your time and energy to whatever project the prof gives you. 

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I agree with cyberwulf. Take another math class. I had research experience but nearly 3 years of it going into grad school. I doubt that less than 1 year of it will be a difference maker.

Regarding Abstract Algebra II, I'd be interested to see what other people have to say. I'd say if you think you can manage a B+ or better it's probably worth retaking it, but anything less than that I either think it won't make a difference or it may hurt you (that you've performed "average" or less twice on the same class).

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