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Books on complex analysis and algebra

  • #1
Titan97
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Main Question or Discussion Point

can you recommend a good book on complex analysis? I would like a book that can sharpen my skills in solving complex number problems through graphs and also improve the algebraic part like solving problems related to roots of unity etc.
(I have studied calculus myself. I have done a lot of self study in maths and physics)
 

Answers and Replies

  • #2
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Freitag and Busam is my favorite complex analysis book. It contains a lot of material, including the most important theorem in single variable complex analysis: Cauchy integral theorem, Cauchy integral Formula, Minimum and maximum modulus principle, Residue theorem, Riemann mapping theorem, Weiertrass and Mittag-Leffler constructions. It ends with a proof of the prime number theorem. It's written in a truly excellent way. They even have a follow-up book "complex analysis 2" which deals with Riemann surfaces and the theory of several variables. Highly recommended.
 
  • #3
Titan97
Gold Member
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Maybe I misunderstood "complex analysis". These topics:
Cauchy integral theorem, Cauchy integral Formula, Minimum and maximum modulus principle, Residue theorem, Riemann mapping theorem, Weiertrass and Mittag-Leffler constructions
are beyond my scope.
I meant analyzing complex number problems and complex number equations through geometry and improving my problem solving skill on the same topic. (like straight line equations and ellipses in complex number form or roots of unity etc...)
 
  • #4
jasonRF
Science Advisor
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Have you tried googling for example complex number problems? One minute yielded:
http://tutorial.math.lamar.edu/Classes/Alg/ComplexNumbers.aspx

Otherwise, you probably do no want a complex analysis book. My Calculus book (Thomas, 7th edition I think) at least had an appendix on complex numbers that we covered 2nd semester. Many pre-calculus books probably have this as well (mine did). So look in your books that you have - it may be there.

Anyway, I think that online you should be able to find plenty of example problems and solutions with no book needed.

jason
 

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