[PDF] advanced complex analysis pdf

  • What is advanced complex analysis?

    Complex analysis is a nexus for many mathematical fields, including: 1. Algebra (theory of fields and equations); 2. Algebraic geometry and complex manifolds; 3. Geometry (Platonic solids; flat tori; hyperbolic manifolds of dimen- sions two and three);
  • Is complex analysis worth taking?

    Complex Analysis is particularly well-suited to physics majors. It was noted that all “serious physics majors” should take Complex Analysis. The course is also very useful for students planning to go to graduate school in mathematics or applied mathematics.
  • Is complex analysis tough?

    Some topics that are often considered challenging in real and complex analysis include the rigorous construction of the real number system, the study of convergence and divergence of sequences and series, and the application of complex analysis to the study of functions of a complex variable.
  • Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms.
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