Prerequisites: MATH 351 or MATH 451 or permission from the Graduate Program Director.
A rigorous introduction to the algebra and geometry of complex numbers, topology of the complex plane, and the theory of functions of a complex variable, including: analytic functions, contour integrals, the Cauchy integral formula, harmonic functions, Laurent series, residues and poles, conformal mapping, analytic continuation, transfer theory, etc.
Outcomes: Students will master the mathematical rigor behind undergraduate complex analysis, gain exposure to advanced topics in complex analysis, and obtain preparation for further graduate courses in analysis and its applications.
A rigorous introduction to the algebra and geometry of complex numbers, topology of the complex plane, and the theory of functions of a complex variable, including: analytic functions, contour integrals, the Cauchy integral formula, harmonic functions, Laurent series, residues and poles, conformal mapping, analytic continuation, transfer theory, etc.
Outcomes: Students will master the mathematical rigor behind undergraduate complex analysis, gain exposure to advanced topics in complex analysis, and obtain preparation for further graduate courses in analysis and its applications.