I'm an incoming third-year undergraduate planning to apply to start my PhD in fall of 2020. I'll be applying in 2019. Since I've only finished two years, I don't have grades information for all the classes I plan to take, but I just want to know if I'm generally on the right track so far.
Profile:
Gender: Female
Ethnicity: Caucasian
Undergraduate Major: Applied Math and Economics- top Ivy League university
Undergraduate GPA (overall): 3.9
Undergraduate GPA (math): 3.92
Undergraduate GPA (econ, all mathematical/quantitative courses): 3.75
Math/Statistics Courses: Multivariable Calculus (A), Linear Algebra I (A-), Applied Math Modeling (A), Intro to Set Theory, Group Theory, and Real Analysis (A), Advanced Econometrics (forthcoming), Probability Theory (forthcoming), Real Analysis (forthcoming), Linear Algebra II or Differential Equations (forthcoming-see below)
Economics Courses: Advanced Intermediate Macroeconomic Theory (mathematical) (A-), Advanced Intermediate Microeconomic Theory (mathematical) (A-), Political Economics (empirical research seminar) (A), Capital Markets (mathematical finance theory) (A-), Monetary Policy (forthcoming), Economics Seminar (forthcoming)
Research Experience: I've worked as an RA for a well-known professor at my university for the past year and plan to continue researching for them throughout my remaining two years of undergrad. I have done one summer of economic research work as an intern for a well-known top financial institution, I'm planning to work as an RA on campus for an entire additional summer (forthcoming), and I'm planning to write a senior thesis (forthcoming).
Programming: Basic/intermediate econometrics work in R, pretty proficient in MATLAB, I will learn advanced econometrics in Stata (forthcoming) and a solid introduction to about six other languages in forthcoming computer science classes.
Questions/Concerns:
1. Am I on the right track so far? Is there anything I'm missing?
2. What are my chances of being admitted to a top 5, or top 10, program?
3. Will my research experience be enough, or should I take two years after undergrad before applying?
4. I will likely only be able to take one of Linear Algebra II/Data Analysis or Differential Equations (ODE and PDE) next year. My intro to linear class was very badly taught and I got an A- in it; I'm confident I can learn linear better with another course. However, I have no experience with differential equations at all. Which of these classes should I take if I can only take one?
5. Do I need a lot more math or statistics than what I already have taken and have planned?