Graduate course as a UG: Complex Analysis or Topology?

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SUMMARY

The discussion centers on the decision between taking Complex Analysis and Topology as a graduate-level course for undergraduate students. The participant has completed undergraduate Complex Analysis and is currently enrolled in undergraduate Topology. They express a preference for Complex Analysis, noting its importance in analytic number theory, which aligns with their graduate school aspirations. The consensus suggests prioritizing Complex Analysis for its relevance and personal interest, while recommending to take Topology later for a well-rounded mathematical foundation.

PREREQUISITES
  • Understanding of undergraduate-level Complex Analysis concepts
  • Familiarity with undergraduate-level Topology principles
  • Basic knowledge of analytic number theory
  • Awareness of graduate school requirements in mathematics
NEXT STEPS
  • Research the applications of Complex Analysis in analytic number theory
  • Explore advanced topics in Topology for future study
  • Investigate graduate school programs focusing on number theory
  • Review syllabi for both Complex Analysis and Topology graduate courses
USEFUL FOR

Undergraduate mathematics students, prospective graduate students in mathematics, and anyone considering the impact of course selection on future academic goals.

atlre
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As an undergraduate, which graduate-level course will prepare me better for grad school, Complex Analysis or Topology? I probably can't fit both into my schedule, but I can definitely fit one. I have already taken undergraduate complex analysis and I'm taking now undergraduate topology. My impression right now is that I like complex analysis slightly better, but I haven't finished topology yet, so this might change.

As for grad school plans, I have number theory in mind, but of course this might also change. I know complex analysis is essential to analytic number theory, what about topology?
 
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I'd take the complex analysis since you know you like it and take the topology later on. This way you add variety to your schedule and get more time to digest what you learned in topology before tackling it again.
 
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