Math course selection advice

[jmp9x]

Some help, if you please. Choose the two most beneficial to an applicant's profile. Already taken Calc II (A-), Calc III (Multivar) (A), Diff Eq. (A), Elementary Linear Algebra (IP), Basic Real Analysis (IP). Will take Math Prob this summer, and will take Grad Real Analysis in fall, in addition to two of these courses. The below are all Grad level.

Advanced Linear Algebra
Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory.

Stochastic Processes
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory.

General Topology
Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projectives spaces, as well as an introduction to the fundamental group will be covered.

[constrainedoptimizer]

Originally Posted by jmp9x

Some help, if you please. Choose the two most beneficial to an applicant's profile. Already taken Calc II (A-), Calc III (Multivar) (A), Diff Eq. (A), Elementary Linear Algebra (IP), Basic Real Analysis (IP). Will take Math Prob this summer, and will take Grad Real Analysis in fall, in addition to two of these courses. The below are all Grad level.

Advanced Linear Algebra
Introduction to algebraic systems, including groups, rings, fields, vector spaces, and their general properties, including subsystems, quotient systems, and homomorphisms. Study of basic examples such as permutation groups, polynomial rings, groups, and rings of matrices. Additional topics may include applications to linear algebra and number theory.

Stochastic Processes
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory.

General Topology
Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projectives spaces, as well as an introduction to the fundamental group will be covered.

I would think you would need a proof-based undergrad linear algebra class as a pre-requisite to the grad linear algebra class, so I would either take the undergrad proof-based LA in conjunction with the StochProc class (if your interests lie in Econometrics and/or finance, or the undergrad proof-based LA in conjunction with grad topology if your research interests lie in micro theory.

What specialties are you interested in?

[econandon]

the advanced linear algebra course will have little application to economics, but stochastic processes has applications to econometric theory and topology has applications to micro theory. unless you have some special reason for the advanced linear algebra course, choosing the latter would be best.

[jmp9x]

I'm interested in microeconomics and development, so it looks like Topology might be a good choice.