Introductory Complex Analysis - Cartan?

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SUMMARY

The discussion centers on the suitability of Henri Cartan's text for readers with a background in one-variable real analysis, linear algebra, and basic point-set topology. The participant expresses a preference for rigorous texts and considers alternatives such as Apostol's multivariable real analysis, Bak and Newman, Conway, and Boas. While they regard "Visual Complex Analysis" as the best resource, they acknowledge its lack of rigor, suggesting it serves as a supplementary text. Ahlfors is also mentioned as a decent option for complex analysis.

PREREQUISITES
  • One-variable real analysis (Rudin)
  • Linear algebra (Friedberg)
  • Basic point-set topology
  • Familiarity with differential forms (recommended for deeper understanding)
NEXT STEPS
  • Study rigorous multivariable real analysis using Apostol's text
  • Explore Henri Cartan's "Introduction to Complex Analysis"
  • Review "Visual Complex Analysis" for supplementary insights
  • Investigate Ahlfors' "Complex Analysis" for foundational concepts
USEFUL FOR

Students and educators in mathematics, particularly those transitioning from real analysis to complex analysis, as well as anyone seeking to deepen their understanding of complex variables and their applications.

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I would like a thorough but not overly comprehensive intro text for complex analysis. My background is one variable real analysis (Rudin), Linear Algebra (Friedberg), Abstract Algebra (Herstein). I know only basic point-set topology (from Rudin), and I haven't dealt at all with differential forms.

I've heard good things about Cartan. Is my background sufficient to tackle this text, or would it make more sense to learn rigorous multivariable real analysis first (from Apostol or something similar)? Other options are Bak and Newman, Conway, Boas...
 
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Visual Complex Analysis is by far the best, in my opinion, but it isn't rigorous, so you might view it as being kind of supplementary. The only other one I am familiar with is Ahlfors, which is decent.
 

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