I have recently joined a Masters program in Pure Mathematics in an Asian University.
My course does not have a research component, only coursework like - Field Theory, Algebraic Topology, Topology-I,II, Differential geometry, Module Theory, Fourier Analysis, Computational Differential Equations, Measure Theory , Complex Analysis, Algebraic Number Theory, Homology Theory etc.
Though, I would love to do research and publish a paper, however, some of the topics above would be new to me. So, I am not sure, if I would even get time to do research and do well in the coursework as well.
I plan to apply to the US for a PhD after my masters. So, would the school expect a research publication towards the end of my masters? Will not doing so affect my application for a PhD?