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Real analysis after finishing undergrad (Stat PhD applicant)


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I am applying for PhD programs in Statistics to start Fall 2020. I have heard that undergrad-level Real Analysis is generally important to have for PhD programs. I would like to take it, but I graduated in Spring 2019 and have been unable to find a local course to enroll in while also working full-time. My options now seem to be self-study, or taking it online such as through Harvard Extension school.

Would the cost of a Harvard Extension course be worth it as opposed to self-study? Are there any other online (especially self-paced) options? And how can I indicate in my applications that I am taking it now? Will admissions committees care about those, or would this be something purely for my own benefit? 


My profile:

Undergraduate: Top 40 liberal arts college

Major: Statistics and Sociology

GPA: 3.9 (for courses taken at the college I graduated from. My GPA was 3.7 for community college courses taken earlier)

Type of student: Domestic white female

Coursework: Calc II-III, Linear Algebra, Discrete Math, Combinatorics, Applied Regression Methods, Probability, Mathematical Statistics, Survey Sampling. 

Grades were all As except for an A- in Calc III. Differential Equations is on transcript with a W. 

GRE: 164 Q, 169 V, 5.5 W

(I’m retaking next month, but haven’t been able to get above a 164 Q on practice tests, so I’m not counting on improvement)

Research: Quantitative sociology honors thesis, not published anywhere

Letters of Recommendation: Stats assistant professor whom I took Math Stats with and TA'ed for, Sociology professor who advised my thesis, and math assistant professor who knows me well. I expect all of them to be strong, though the professors are not well-known, and none of them are tenure-track.

Additional information: I attended a two different community colleges and one other liberal arts college before completing my degree at the liberal arts school above. All of my math classes were taken at the college I graduated from, and my GPA at the other colleges averages to about 3.7. 

Applying to:

Not sure yet, advice welcome

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  • 5 weeks later...

Hi Cotopaxi,

I am also an undergrad applying for stats phd fall 2020 so I cannot comment on your application profile. But I am a math major who have taken real analysis so I can say something about this part. It seems like you have not taken any mathematical proof class so you may want to learn proofs before you do real analysis. I do see some departments put real analysis as recommended prerequisites so I guess it is better for you to have those material learned. I don't know what an online real analysis class look at and to be honest, people learn in different ways. You may learn just by reading the textbook or you may have to sit in a class and learn it from someone who explains it well. The text book I used for my real analysis class is "Introduction to real analysis" by Bartle and Sherbert. You can take a look and see if you can just understand it from reading or you need some explanation. You can also reach out to the real analysis professors at your previous schools, send them an email asking for self-teaching books or online class recommendations. 

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I don't know about the quality or cost, but another online option for courses is through University of Illinois. Here's a link:


I would say the name of the school doesn't matter too much in this context, and that therefore Harvard in particular may not be "worth the price," but I would recommend taking an actual course if possible. Someone else can comment about how self studied real analysis might look to selection committees, but Real Analysis is an important enough subject that you want to ensure you really know it before entering a PhD program.

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  • 2 weeks later...
On 10/24/2019 at 4:40 PM, SomeNerd said:

It seems like you have not taken any mathematical proof class so you may want to learn proofs before you do real analysis.

Thanks! That makes sense. My combinatorics class was proof-based, and in Discrete Math we looked at and wrote many formal proofs, though I'm not sure it was "proof-based." I will reach out to my undergrad professors and see what they think. 

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