Which Textbook Is Best for Learning Several Complex Variables?

Click For Summary
SUMMARY

The discussion focuses on recommending textbooks for undergraduates transitioning from real and complex analysis to several complex variables. Key suggestions include "An Introduction to the Theory of Analytic Functions of One Complex Variable" by Lars Ahlfors and "Elementary Theory of Analytic Functions of One or Several Complex Variables." The latter is noted for its assumption of prior knowledge in general topology. Additionally, the Hormander and Krantz texts are mentioned as graduate-level resources requiring familiarity with functional analysis and measure theory.

PREREQUISITES
  • Understanding of real and complex analysis
  • Familiarity with general topology
  • Knowledge of functional analysis
  • Basic concepts of measure theory
NEXT STEPS
  • Research "An Introduction to the Theory of Analytic Functions of One Complex Variable" by Lars Ahlfors
  • Explore "Elementary Theory of Analytic Functions of One or Several Complex Variables"
  • Investigate graduate-level texts by Hormander and Krantz
  • Study general topology to strengthen foundational knowledge
USEFUL FOR

Undergraduate students in mathematics, educators seeking textbook recommendations, and anyone interested in advancing their understanding of several complex variables.

Knissp
Messages
72
Reaction score
0
Can anyone recommend a good textbook for an undergrad who has done real and complex analysis and wants to learn about several complex variables? Thanks!
 
Physics news on Phys.org
try the bookon complex analysis by ahlfors
 
Ahlfors book is on "An Introduction to the Theory of Analytic Functions of One Complex Variable". Some references for what I'm looking for are on wikipedia (http://en.wikipedia.org/wiki/Several_complex_variables), but I was wondering if anyone had any experience with such books to recommend. Thanks again
 
You might want to look at Elementary Theory of Analytic Functions of One or Several Complex Variables. You can look at the Table of Contents at the Amazon link. The author assumes that you know some general topology. The Hormander and Krantz books in your Wikipedia link are graduate-level. They assume knowledge of subjects such as functional analysis and measure theory, for example.

HTH

Petek
 

Similar threads

Insights An Overview of Complex Differentiation and Integration
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Key difference between two real and single complex variable?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Help needed with derivation: solving a complex double integral
  • · Replies 1 ·
Replies
1
Views
2K
High School Simple Derivation Of Euler's Formula And Applications
  • · Replies 2 ·
Replies
2
Views
2K
Textbook Recommendations: Complex Analysis
  • · Replies 18 ·
Replies
18
Views
8K
Insights What Are Numbers? - Insights for Beginners
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad Textbook of complex variables function
  • · Replies 5 ·
Replies
5
Views
3K
Courses Complex Analysis Courses or Complex Variable Courses?
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Real integrals with complex coefficients
  • · Replies 1 ·
Replies
1
Views
2K