What math courses should I complete to be more competitive on my Stats Phd Application

[DachshundDad]

Hello Everyone!

This is my first post on this website, but I have read many posts regarding PhD Statistic programs.

I earned a BA in a unrelated field almost 20 years ago, but recently started a MS in Statistics program at a Public State School in my area.  I'm doing fairly well considering I do not have a large background in math or statistics.  I even was able to secure a Teaching Assistant position this year.  It turns out that I really like teaching college level students.

I have now decided that I would like to pursue acceptance into a PhD program.  My understanding from posts on this website and extensive research of PhD stat program online, it seems an extensive background in math is more important than one in statistics to be accepted into a program.  I will post my profile below for your evaluation, but I was wondering if you could make suggestions as to what math classes would be most helpful for gaining acceptance into a PhD program.  

Here is my current and planned math course completion:

I currently have completed the following math courses:

Calculus I, Calculus II, Calculus III, and Linear Algebra.

I plan to take the following math courses:

Discrete Mathematics, Differential Equations, Advanced Calculus I and II, Applied Regression Analysis.

Math courses I'm considering to take if time permits:

Abstract Algebra, Programming in Mathematics, Advanced Linear Algebra, Advanced Abstract Algebra, Intro to Mathematical Modeling, Number Theory, Numerical Matrix Analysis, "Group, Rings, and Fields", Matrix Theory with Linear Algebra, Cryptography, Applied Fourier Analysis.

Since programs all have different prerequisites for math backgrounds, here are the programs I'm considering:

Extra Long Reach - Carnegie Mellon 

Long Reach - Cornell, Iowa State, Texas A&M, Minnesota, Yale, California - San Diego

Reach - Iowa, Rice, Northwestern, Pittsburgh, Rochester, Maryland - College Park, Stony Brook, Washington University in St. Louis

Chance - SMU, California - Riverside, Utah

Back Up - Montana State, Utah State, Texas - San Antonio

I will appreciate any advice provided.

Here is my profile:

Type of Student: Domestic

Undergrad Institution: Top 30 Public National University

Major: BA Unrelated Field

GPA: 3.25

Related Courses (undergrad):  Calculus I (A)

Undergrad Institution: Various Community Colleges    

Major: Math

GPA: 4.0

Related Courses (undergrad):  Calculus II, Calculus III, Linear Algebra, Statistics

Planned Future Courses (undergrad):  Discrete Mathematics, Differential Equations (Taking at a community college to save money and save time by taking classes during the summer).

GRE: 153 Verbal, 163 Quantitative (Took without any studying and many years after being out of school.)

Graduate Institution:  Top 100 Ranked Statistics Program

Major: MS in Statistics (finishing Spring of 22/23)

GPA: 3.5

Related Courses (undergrad):  Mathematical Statistics I, Mathematical Statistics II, Actuarial Modeling

Related Courses (graduate): Theoretical Statistics I, Theoretical Statistics II, Linear Regression, Time Series Analysis

Planned Future Courses (undergrad): Applied Multivariate Analysis, Python Programming, Advanced Calculus I, Advanced Calculus II, (Maybe Abstract Algebra, Programming in Mathematics, Advanced Linear Algebra, Advanced Abstract Algebra, Intro to Mathematical Modeling, Number Theory, Numerical Matrix Analysis)

Planned Future Courses (graduate): Survival Analysis, Data Analysis Methods, Data Mining Statistical Methods, Applied Real Analysis, (Maybe Nonparametric Statistics, “Group, Rings, and Fields”, Matrix Theory with Linear Algebra, Cryptography, Applied Fourier Analysis)

Experience: 

• 3 years of teaching statistics at the university level by the time I graduate.
• Have over 25 years working in sales and service jobs.

 

 

[Stat Assistant Professor]

The most useful math classes to take, IMO, would be advanced linear algebra, real analysis, and optimization. Is Advanced Calculus I-II the undergrad sequence in real analysis? If so, then I don't think you need to bother with "Applied Real Analysis." Since you're in a Statistics MS program, I think just taking statistics classes, plus analysis, advanced linear algebra, and one or two other advanced undergrad math classes should suffice.  

In your case, I think your long reaches are all unrealistic. I would not spend money applying to those programs. I think your list of "reaches" should also be trimmed down, and you should target programs like University of Missouri, University of South Carolina, Kansas State, University of Maryland Baltimore County, etc. Since you seem like a somewhat nontraditional student, your statement of purpose and letters of recommendation might also carry more weight. So I would definitely spend some time crafting your SOP and detailing your motivations for wanting to get a Statistics PhD, your mathematical preparation, etc.

[DachshundDad]

Thank You for the advice.  It does appear that Real Analysis is part of the Advanced Calculus II course at my school.  Here is the class description:

“Formal definitions and analysis within the framework of single variable functions. Advanced concepts in analysis.”

I will also take the Advanced Linear Algebra and Optimization courses you recommended.

I will be taking my first Computer Science courses during the next few semesters. I plan to take programming courses in Python, Java, and C++ and courses covering SQL and Linux.  I’m proficient with R and can get by with SAS, but I have no formal training with coding/programming.

I have been reviewing my grades and it seems I have about a 3.35 GPA across my entire college career.  If the first 2 years are removed, I jump up to about 3.6.  My GPA for Quantitative courses is over 3.7.

Hypothetically, if I were to ace my remaining classes, my cumulative GPA would be 3.5 and Quantitative would be over 3.85.  Hopefully that would help me be more competitive.

I also plan to study the entire summer for the GRE.  I think I can reasonably get a 167 to 170 on Quant and a 158 to 160 on Verbal.

Hopefully I can get into one of my reach schools, by pulling off those results and writing a great SOP.  LOR will be a challenge though.  It has been hard to build relationships with professors over Zoom.  Some of my graduate level classes next semester will be recorded videos only.

Thanks again for your advice!

[llk]

I would definitely take real analysis and measure theory if at all possible. 

[DanielWarlock]

Seems your main motivation of getting a doctorate is to teach at college levels. Have you considered apply to graduate school of education? Some statisticians (e.g. Prof. Luke Miratrix) are actually professors of education school who does "regular" statistical research. I imagine you will be a much better candidate at education schools if that also fits your eventual goal of getting a doctorate.  

[bayessays]

On 1/5/2021 at 9:23 AM, Stat Assistant Professor said:

I think your list of "reaches" should also be trimmed down, and you should target programs like University of Missouri, University of South Carolina, Kansas State, University of Maryland Baltimore County, etc.

This was going to be my suggestion as well.  Get rid of the long and extra-long reaches entirely.  Schools around the area of South Carolina/Mizzou are good targets and will be more open to a non-traditional student.  Since it sounds like you like teaching, some of these schools are more open about preparing people to be teachers specifically.  As to @DanielWarlock's point, Miratrix got a PhD in statistics and just happens to teach in an education school.  Most of these people are doing applied research in education, and this would be similar to getting a PhD in a subject like Quantitative Psychology where you are applying statistics to some field.  There is, of course, the separate option of getting a PhD in math/stats education.  A lot of people do this and become lecturers at a university.  However, the options for people doing *statistics* education research, versus math, are significantly limited.

[DachshundDad]

I sent an email to my academic advisor last week about my intended plan of study for the next two years.  They replied by suggesting we meet on zoom to discuss this further.  After meeting today, I was provided with information that was a bit different from the responses I received to this post earlier this year.  It was suggested that I do not need to take Math Analysis or Advanced Calculus for a PhD program in Stats.  In fact, I was told that none of the prior students from my program that were accepted into PhD programs took Advanced Calculus or Real Analysis.  A few of these students are attending top 20 schools.

Since originally posting, I have narrowed down my list of prospective schools that are much more realistic.  After reviewing the prerequisites for these programs, none of them require Real Analysis and only 1 requires a semester of Advanced Calculus.  I'm assuming this is because most of the programs are applied based versus theoretical.  My advisor suggested that I take more courses related to Data Analysis/Computer Programming to be more competitive for these programs.

Here is what I'm planning to take over the next year or two:

Statistics Courses: Database Management and Predictions, Statistical and Machine Learning Methods, Advanced Data Analytics

Mathematics Courses: Programming in Math, Upper Division Linear Algebra, Numerical Matrix Analysis

I'm also taking Discrete Mathematics this summer at a community college.  However, my advisor suggested I just learn this material on my own. I'm a little hesitant to do so as all of the math classes I listed above have Discrete as a prerequisite.

Here are the programs I'm now considering:

Dreaming? - Rice, Pittsburgh

Reach? - Southern Methodist, UC - Riverside, New Hampshire, South Carolina

Safe? - Utah State, Montana State, UT - San Antonio

Only Pitt has a prerequisite of 1 semester of Advanced Calculus.  I have prerequisites covered for all other programs. South Carolina does not require real analysis, but their website states that admitted students often took real analysis.

Based on these schools, do you think I have a good plan of study?  I probably can fit two more classes into my schedule over the next 3 to 4 semesters.  Clearly taking a semester of Advanced Calculus would be good for Pitt, but would taking a two semester sequence of Advanced Calculus be worth it for any of these programs? How about Real Analysis? I definitely don't want to take the bare minimum of courses, but I also want to be as efficient as possible with my time.  Feel free to suggest any other classes I should take during my MS program.

Here are the course descriptions for my school:

Advanced Calculus I
Completeness of the real numbers and its implications, sequences of real numbers, and continuity and differentiability of functions of one real variable. 

This course is a proofs-based, rigorous examination of many of the results used in a first semester Calculus class. The purpose of this course is to provide students with the opportunity to develop mastery of rigorous thinking and the techniques needed to develop rigorous approximations in Calculus. The techniques and problem solving skills developed in this course are crucial to future success in courses in mathematics or in the teaching of mathematics since they form the core of how one thinks in a rigorously mathematical way.

Advanced Calculus II
Formal definitions and analysis within the framework of single variable functions. Advanced concepts in analysis.

The purpose of this course is to extend the notions seen in the Advanced Calculus I and complements your knowledge of the standard formalism used in analysis. Such knowledge is of importance for future (pure/applied) mathematicians who plan to have a career in the industry or in research and who need to learn the origin, as well as, to gain a clear understanding of the assumptions' validity. This course will give students the mathematical foundations needed for more advanced courses in mathematics and more specifically in analysis. The first half lectures will address the construction of Riemann integrals, convergence of series of numbers, introduce sequences and series of functions (in particular, we will explain the difference between pointwise and uniform convergence). The second half of lectures will be dedicated to the introduction of some basic topological concepts like metric spaces, open and closed sets, compact sets. The notion of continuity will be extended in the framework of metric spaces.

Applied Real Analysis - (Highly unlikely I will take this course.  I assume that Advanced Calc 1 or 2 is sufficient for Real Analysis)
Lebesgue measure and integration, metric spaces, Banach spaces, Hilbert spaces. 

The purpose of this course is to develop a strong core knowledge in analysis by generalizing concepts seen in advanced calculus in the case of single variable. Such knowledge is of importance for pure or applied mathematicians who plan to have a career in the industry or in research (the covered concepts will be useful to more advanced courses in mathematics like analysis, partial differential equations,...). This course will generalize some concepts learned during the advanced calculus sequences. All notions will be precisely defined and all results will be proven. First, basics about measure theory and Lebesgue integration theory will be presented. Next, the concepts of metric spaces, normed spaces, Banach spaces and Hilbert spaces will be developed. Finally, definitions and properties of bounded operators between spaces will be studied.

Linear Algebra
Vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence.

The goal of this course is to provide a rigorous exposition of the fundamental components of linear algebra: Linear Transformation on Vector- and Inner Product Spaces; and show some of the foundational results — including Diagonalization (or Non-Diagonalization) using eigen-bases, the Gram-Schmidt Method, the Riesz Representation Theorem, the Real and Complex Spectral Theorems, the Cayley-Hamilton Theorem — and finally discuss the Singular Value Decomposition, as well as similarity transformation of a matrix into Jordan Canonical Form.

Numerical Matrix Analysis
Singular value decomposition. Projections, QR-factorization, orthogonalization, conditioning and stability, Gaussian Elimination, LU-Factorization, pivoting strategies, Cholesky Factorization. Iterative methods for diagonalization and eigensystem computation. Tridiagonal, Hessenberg, and Household matrices. The QR algorithm.

Programming in Mathematics
Introduction to programming in mathematics. Modeling, problem solving, visualization. (Prerequisite for Numerical Matrix Analysis)

 

 

 

[StatsG0d]

7 hours ago, DachshundDad said:

It was suggested that I do not need to take Math Analysis or Advanced Calculus for a PhD program in Stats.  In fact, I was told that none of the prior students from my program that were accepted into PhD programs took Advanced Calculus or Real Analysis.  A few of these students are attending top 20 schools.

It's possible (and highly likely) that the other students had already taken the course (e.g., in undergrad). You definitely need to take real analysis for stats. You *might* be able to get away without taking it if you're doing biostats (although, this is becoming less common at the top 5-7 programs, as the field is becoming more competitive).

Even if you managed to get into a program without taking analysis, you would have wished that you'd taken it. Even in Casella-Berger level Math Stats, real analysis is very useful for making mathematically rigorous arguments / proofs. I feel like you (or anyone without real analysis) would struggle in a pure stats program without it.

7 hours ago, DachshundDad said:

Statistics Courses: Database Management and Predictions, Statistical and Machine Learning Methods, Advanced Data Analytics

Mathematics Courses: Programming in Math, Upper Division Linear Algebra, Numerical Matrix Analysis

...

Based on these schools, do you think I have a good plan of study?  I probably can fit two more classes into my schedule over the next 3 to 4 semesters.  Clearly taking a semester of Advanced Calculus would be good for Pitt, but would taking a two semester sequence of Advanced Calculus be worth it for any of these programs? How about Real Analysis? I definitely don't want to take the bare minimum of courses, but I also want to be as efficient as possible with my time.  Feel free to suggest any other classes I should take during my MS program.

Any/all of those courses will be useful when you reach the dissertation stage, but the reality is adcoms don't really care much about how many statistics courses are taken (unless they're mathematically rigorous courses e.g., linear models, probability theory, (martingale-based) survival analysis, etc.). If I'm on an adcom and I see that you've taken these stats courses, I'll think "OK, it's nice that they clearly have shown an interest in statistics, but how prepared are they to be successful in the program?" I'd look at the GRE and see a lower score relative to other applicants, and then think "well, perhaps this student had a lower GRE score, but has demonstrated mathematical maturity through courses." Then, when I see the lack of a single proof-based course on the profile, I would almost certainly reject the applicant. 

 

I think it's important for you to reflect deeply and see if you know what you're getting yourself into. If you are trying to avoid taking real analysis because you dislike theory, then I can assure you that you will not like doing a stats PhD, and you will burn out really quickly. The courses / qualifying exam is difficult even for those that have taken real analysis, and I truthfully can't imagine an individual doing well without it, especially relative to peers.

If you are more interested in the application of statistics, there are other fields you can consider that utilize advanced statistical methods (e.g., epidemiology, psychology, quantitative methods in the social sciences) without the need to dive into the theory. The purpose of a stats PhD is to make you equipped to develop your own methods.

[DachshundDad]

Thanks for your response StatsG0d.

6 hours ago, StatsG0d said:

It's possible (and highly likely) that the other students had already taken the course (e.g., in undergrad). You definitely need to take real analysis for stats. You *might* be able to get away without taking it if you're doing biostats (although, this is becoming less common at the top 5-7 programs, as the field is becoming more competitive).

That is what I was thinking as well.  The majority of students in my program have an undergraduate degree in Mathematics.  I think it is safe to assume they took Advanced Calculus and/or Real Analysis already.  

6 hours ago, StatsG0d said:

Even if you managed to get into a program without taking analysis, you would have wished that you'd taken it. Even in Casella-Berger level Math Stats, real analysis is very useful for making mathematically rigorous arguments / proofs. I feel like you (or anyone without real analysis) would struggle in a pure stats program without it.

I agree that I will struggle without Real Analysis.  The first year of my current program included a two course sequence using Casella-Berger.  I had to spend a vast amount of time studying mathematical concepts that my peers already learned in undergrad.  I managed to do well in this sequence of classes, but they easily required me to study 30 to 40 hours per week.

6 hours ago, StatsG0d said:

I think it's important for you to reflect deeply and see if you know what you're getting yourself into. If you are trying to avoid taking real analysis because you dislike theory, then I can assure you that you will not like doing a stats PhD, and you will burn out really quickly. The courses / qualifying exam is difficult even for those that have taken real analysis, and I truthfully can't imagine an individual doing well without it, especially relative to peers.

I'm definitely not trying to avoid Real Analysis, but I do need to make the most time and cost efficient decisions about my schedule.  The issue with taking the Applied Real Analysis course at my school is that it has prerequisites of taking Advanced Calc I and II.   I also still need to complete 3 graduate level stat classes to graduate.  In addition, I think it would be prudent to take Upper Division Linear Algebra and Numerical Mathematical Analysis.  Since I'm paying for graduate school without loans and the salary of being a TA, I can only afford to take two classes a semester. 

Here is what I think would make most sense for my next two years based on when classes are offered:

Fall 2021 - Database Management and Predictions, Statistical and Machine Learning Methods

Spring 2022 - Upper Division Linear Algebra, Advanced Data Analytics

Fall 2022 - Programming in Math, Advanced Calculus I

Spring 2023 - Numerical Matrix Analysis, Advanced Calculus II
 

Would these Advanced Calculus course be sufficient for learning Math Analysis?  If an additional class would be necessary in your opinion, the University of Illinois offers an online Real Analysis course.  I could take this course over the summer of 2023.

My question then becomes if I should apply to PhD programs in the fall of 2022 or wait until the following year after I have completed all of my courses.  What is your opinion? 

7 hours ago, StatsG0d said:

If you are more interested in the application of statistics, there are other fields you can consider that utilize advanced statistical methods (e.g., epidemiology, psychology, quantitative methods in the social sciences) without the need to dive into the theory. The purpose of a stats PhD is to make you equipped to develop your own methods.

I must admit that I do not fully understand the difference between applied stats PhD vs stats PhD programs.  My understanding is that a stats PHD would be to develop new methods.  An applied stat PhD program would be using advanced stat techniques to solve problems in other fields.  For example, I'm very interested in finding better ways to teach stats and math to students with learning disabilities.  Or finding a way to improve math and stats scores for poor performers instead of taking away advanced math programs from high performers in the name of equity.

Ultimately, I would like to teach and do research at a community college or state school.  I'm not interested in working in industry or at an elite university.  I have had corporate jobs and made good money in the past, but it made me fill like my life was pointless.  Teaching has been a huge eye opener for me and I can see myself doing it until the day I die. 

[bayessays]

You are taking this artificial distinction your school is making between advanced calculus and real analysis too literally.  The advanced calculus courses are what everyone here means you need to take.  It's kind of weird that it is a two semester course though, as usually all those topics are covered in one semester.  You do not have to take the Lebesgue class that your school calls real analysis, but with your profile you will not be competitive without taking the advanced calculus classes.  If possible, I would highly recommend taking them next year because otherwise they will not be on your transcript before applications are due.

[DachshundDad]

Thank You Bayessays!  That is exactly what I have been trying to figure out.  Even the math professors at my school told me conflicting information.  One said that Advanced Calc I and II are Real Analysis Courses (Advisor for Undergrad Math Students).  Another said they are not Real Analysis courses and I would need to take the Lebesgue class (Advisor for Graduate Math Students). Then my Graduate Stats advisor told me none of them are necessary to take.

I will find a way to take them next year so they are on my transcript when I apply to PhD program the following year.  I definitely don't want to put the process off for an additional year.  

 

 

Edited May 28, 2021 by DachshundDad
Grammar

[DanielWarlock]

I personally don't think advanced calculus on transcript would make a huge difference given that you have taken mathematical statistics I, II and theoretical statistics I, II. It seems to be more productive to take probability if you haven't. The graduate version should give you all the analysis background for studying statistics including basic measure theory, Lp spaces, convergence (stochastic) etc. But of course it's always good to learn more. 

[StatsG0d]

14 hours ago, DachshundDad said:

Thank You Bayessays!  That is exactly what I have been trying to figure out.  Even the math professors at my school told me conflicting information.  One said that Advanced Calc I and II are Real Analysis Courses (Advisor for Undergrad Math Students).  Another said they are not Real Analysis courses and I would need to take the Lebesgue class (Advisor for Graduate Math Students). Then my Graduate Stats advisor told me none of them are necessary to take.

I will find a way to take them next year so they are on my transcript when I apply to PhD program the following year.  I definitely don't want to put the process off for an additional year.  

I apologize if I confused you. I didn't mean the "applied real analysis" course specific--just a general course in what most institutions call real analysis. Advanced Calculus is the way to go. Perhaps that's the confusion surrounding your advisor's saying no one takes it.

[Stat Assistant Professor]

Agreed with @StatsG0d.  It would be very beneficial to take upper division, proof-based mathematics courses, especially Real Analysis and maybe upper division proof-based linear algebra. The first two years of coursework in any Statistics PhD program will be quite theoretical, and you will be required to take classes like measure-theoretic probability, linear models, advanced statistical inference, large sample theory, etc. At most Statistics PhD programs, it is possible to do a more "applied" dissertation with little/no theory -- this is true even at heavily theoretical programs like UPenn Wharton or Stanford (usually there will be at least a few faculty members who are more applied and don't really do theory, and you can ask them to supervise you).

But to even get to the research stage, you need to get through some pretty theoretical classes and pass qualifying exams on some of this material. The qualifying exams are also challenging, and there are always a few students who do not get a PhD pass on this exam and have to retake it or leave with a Masters. It doesn't really matter what the rank of the program is; the vast majority of ranked Statistics PhD program will be this way. 

More advanced math classes -- *not* more undergrad statistics classes -- would be the best preparation for a Statistics PhD program.

[DachshundDad]

19 hours ago, DanielWarlock said:

I personally don't think advanced calculus on transcript would make a huge difference given that you have taken mathematical statistics I, II and theoretical statistics I, II. It seems to be more productive to take probability if you haven't. The graduate version should give you all the analysis background for studying statistics including basic measure theory, Lp spaces, convergence (stochastic) etc. But of course it's always good to learn more. 

Thanks for your reply DanielWarlock.  Since my school does not have a Stats or Math PhD program, class selection is pretty limited at the graduate level.  I have completed all available classes that were related to Probability, but none of them were theory courses. 

[DachshundDad]

10 hours ago, StatsG0d said:

I apologize if I confused you. I didn't mean the "applied real analysis" course specific--just a general course in what most institutions call real analysis. Advanced Calculus is the way to go. Perhaps that's the confusion surrounding your advisor's saying no one takes it.

No apologies are necessary.  You actually cleared everything up for me.  Thank you.

[DachshundDad]

Thanks @Stat Assistant Professor

I will finish up my MS program with as many upper division math classes that I can fit into my schedule.  

I addition to these classes, I'm thinking about taking some computer programming classes online through UCSD Extension.  I have used SAS and R throughout my MS program, but I have never taken any formal programming classes.  UCSD Extension offers classes in R, SAS, Python, Machine Learning, and Data Mining.  Studying these subjects will help prepare me for the research period of a PhD program.  Due to time and financial constraints, which of these subjects would be most helpful with my future studies?  My guess is that R, Machine Learning, and Data Mining will be most helpful in an academic setting.

[bayessays]

The best thing you can do for your future PhD studies will be to spend all your time doing well in your real classes.  Your MS GPA is on the low side, so work on getting that up.  Online extension classes are not going to be useful for your application and are not necessary to learn programming.  Use the swirl package or download The Art of R Programming to learn some R.  SAS and Python will be a waste of time for most people.  Machine learning/Data Mining classes will essentially be extensions of your applied statistics classes and will also not be useful -- you can watch youtube videos to learn any of these subjects.

[DachshundDad]

Thanks @bayessays!  

I will follow your advice and spend as much time as possible on the real classes.  This summer will be spent taking a discrete math class and reading "How to Prove It: A Structured Approach" by Velleman.  Hopefully this will prepare me sufficiently for the transition to real mathematics. 

[DachshundDad]

I was hoping I could get an update on my potential to be accepted into a Statistics PhD program.  Due to financial aid issues that this year and that will continue through next school year, I was only able to take 6 credits per semester and will do the same next year.  I took 3 math courses: Discrete Mathematics, Mathematical Programming, and Advanced Calculus I.  Advanced Calculus I was an introductory course to Real Analysis.  The course covered the first 6 chapters of Bartle’s “Introduction to Real Analysis”.   In addition, I took a statistical consulting course that could only be take Pass/Fail.

To complete my statistics master’s degree program next year, I need to complete 2 statistics courses (6 credits), a seminar (1 credit), pass two qualifying exams (2 credits), and complete 1 upper division mathematics course (3 Credits).  Due to limited availability of statistic courses, I intend to take Advanced Biostatistics Methods I, the seminar, and qualifying exams in the Fall.  In the spring, I will complete the degree program by taking either Advanced Biostatistics Methods II or another graduate level statistic course (if available) and either Advanced Calculus II, Advanced Linear Algebra, or Numerical Matrix Analysis.

Fortunately, my university has very friendly professor and they are willing to let me be an observer (not auditor) in their classes this summer and next school due to my financial aid issues.  I intend to observe an Advanced Linear Algebra course this summer and Abstract Algebra and Number Theory courses in the fall.   I won’t get a grade or credit, but I believe that it will help me prepare for taking the Math GRE Subject test and widen my mathematical knowledge that I may need when I’m in a PhD program.

I have included several variations of my GPA below.  In addition, I have included the grades I have received in all Math and Stat courses.  The Max GPAs I have included assume I earn As in my last three graded courses (9 credits).  Please be brutally honest on what schools I should be considering and if I even have a chance of being accepted into any program.    Any advice on what math course(s) I should take would also be appreciated.  I intend to apply in the Fall of 2023.  I’m open to take more classes in the Fall of 2023 to improve my GPA and mathematical background.  My university offers graduate level course in Applied Math Analysis and Optimization.

GRE: 168 Math, 155 Verbal, 3.0 Writing

GPA:                                                      Current - 3.416 (209 Credits)       Max – 3.440

GPA w\o First 60 Credits:              Current - 3.620 (150 Credits)       Max – 3.642

Post - Undergraduate GPA:         Current - 3.705 (61 Credits)         Max – 3.743

Graduate GPA:                                  Current - 3.478 (27 Credits)         Max – 3.608

Graduate Program GPA                 Current - 3.383 (18 Credits)         Max – 3.589

Quantitative Course GPA:             Current - 3.705 (69 Credits)         Max – 3.729

Mathematic Courses GPA:           Current 3.805 (27 Credits)            Max – 3.824

Statistics Courses GPA:                  Current 3.464 (28 Credits)            Max – 3.559

Math Course: Finite Mathematics – B+, Calculus I – A, Calculus II – A, Calculus III -A, Linear Algebra – A, Discrete Mathematics – B (I was one of 18 students of the 180 that could mathematically earn an A going into the final.  This class is notoriously difficult at my school.  However, it is taught by an exceptional professor that has prepared me very well for future mathematical studies.  First B I was happy to earn in my life), Mathematical Programming – A (Upper Division), Advanced Calculus I – A (Upper Division)

Stat Courses: Business Statistics – A, Prob and Math Statistics I – B (Upper Division), Prob and Math Statistics II – A- (Upper Division), Advanced Math Stats I – B+ (Graduate), Advanced Math Stats II – B+ (Graduate), Linear Regression Models – B (Graduate), Actuarial Modeling – A- (Upper Division), Time Series Analysis – A- (Graduate), Applied Multivariate Analysis – B+ (Upper Division)

Advanced Math Stats I and II covered chapters 1 - 10 of Casella and Berger.

I will have 3 years of TA experience by the time I apply to PhD programs.  Will this justify not having any research experience?  Or should I make it a priority to have some research experience on my CV? My school will not allow grad students to be a TA and RA at the same time.  Since RAs do not receive any health insurance, I can't justify switching positions as my wife and I both need the health insurance that the TA position provides.  In addition, the statistics department is really small at my university.  There simply is not enough research opportunities for every graduate student.  Would an independent research study be impressive to PhD admission officers?  I would like to test some new teaching methods to see if there a significant improvement in my students grade percentage.

I’m currently looking at a total of 40+ programs.  I plan to narrow it down to 12 to 15 by the time I apply.  Maybe even down to 8.  I picked these schools based on ones that I believe would accept me based on rank, cost of living, climate, or if there is a PhD program nearby for my wife who wants to study Special Education/Applied Behavior Analysis.  Clearly, I will need to do more analysis on what research opportunities are availble at these various schools.

 

Iowa State University - Ames

Ohio State University - Columbus

Rice University

Colorado State University - Fort Collins

University of Pittsburgh

University of Missouri - Columbia

Virginia Tech

University of Utah

Boston University

University of California - San Diego

University of California - Riverside

University of California - Santa Barbara

University of California - Santa Cruz

University of Colorado - Boulder

University of Rochester

University of Illinois - Chicago

University of Massachusetts - Amherst

Southern Methodist University

Washington University in St Louis

Oregon State University - Corvallis

Northeastern University

University of Notre Dame

Baylor University

University of Nebraska - Lincoln

University of Colorado - Denver

Lehigh University

Worcester Polytechnic Institute

University of New Mexico - Albuquerque

Washington State University - Pullman

Syracuse University

Utah State University - Logan

Montana State University - Bozeman

New Jersey Institute of Technology

University of Nevada - Reno

Colorado School of Mines

Stevens Institute of Technology

Illinois Institute of Technology

New Mexico State University

University of Montana - Missoula

Clarkson University

University of Idaho - Moscow

University of New Hampshire - Durham