What is necessary for mathematics graduate school? I am an undergrad junior at a top 60 institution (big state school in the United States) majoring in Pure Math. Course selection for Spring 2020 is coming around, and I want to know which courses to take for the strongest graduate school applications.

I'm currently planning on going into either combinatorics, graph theory, or theoretical CS. I have done internships in Software Engineering and Data Science (Machine Learning). My GPA is a 3.75 and the courses I have taken/am planning on taken are the following:


Calculus I - III
Linear Algebra I and II
Differential Equations
Advanced Calculus I (Real Analysis)
Mathematical Statistics
Discrete Math I and II (II is graph theory)
Numerical Analysis I and II
Abstract Algebra I and II
Programming I, II, Data Structures, Computer Architecture,Theory of Computation, Analysis of Algorithms
Topology I
Complex Analysis


Classes I might take if they look better for graduate school:


Advanced Calc II
Number Theory
Mathematical Logic




Along with these courses, I have some interdisciplinary research in neuroscience under my belt, but I plan on doing research with a math professor next semester.

Will my chances of getting into a good graduate school (top 60) be affected heavily if I don't have a full year of Real Analysis? Also, would I be well suited for a PhD in computer science (TCS)?
It's hard to say.  Your background sounds strong.  Your interests are more to the applied side of pure or the pure side of applied.  Really, a bit more towards applied than pure from my impression (e.g. CS interest).  

I don't think you could go wrong taking another stats class (applied or theoretical, time series, whatever) or an operations research class.  (Not on your list, but a guess.)

If you restrict to choosing from the list, consider number theory.  Kind of useless but a lot of fun. Don't grind something you don't like just to look good.  I would pass on the second semester of theoretical calculus.