Introductory Complex Analysis - Cartan?

In summary, the individual is looking for an introduction to complex analysis that is thorough but not overly comprehensive. Their background includes one variable real analysis, linear algebra, and abstract algebra, with only basic knowledge of point-set topology. They are considering Cartan as a potential text, but are unsure if their current background is sufficient. Other options mentioned include rigorous multivariable real analysis, Bak and Newman, Conway, Boas, and Visual Complex Analysis (which is not considered rigorous). The individual also mentions Ahlfors as a decent option.
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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.
 

Related to Introductory Complex Analysis - Cartan?

1. What is Introductory Complex Analysis - Cartan?

Introductory Complex Analysis - Cartan is a branch of mathematics that deals with the study of complex numbers and their properties. It is named after the French mathematician Élie Cartan.

2. What are complex numbers?

Complex numbers are numbers that have both real and imaginary components. They are represented in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit (√-1).

3. What are the applications of complex analysis?

Complex analysis has various applications in mathematics, physics, engineering, and other fields. It is used in the study of differential equations, harmonic functions, fluid dynamics, and quantum mechanics, among others.

4. What are some key concepts in Introductory Complex Analysis - Cartan?

Some key concepts in Introductory Complex Analysis - Cartan include complex functions, complex differentiation, Cauchy-Riemann equations, contour integration, and the Cauchy integral theorem.

5. What are some useful techniques in solving complex analysis problems?

Some useful techniques in solving complex analysis problems include the use of Cauchy's theorem and integral formula, the maximum modulus principle, residue theorem, and the method of conformal mapping. It is also important to have a good understanding of basic algebra and calculus.

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