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Preface; Acknowledgement;
1. The origins of complex analysis and a modern viewpoint;
2. Algebra of the complex plane;
3. Topology of the complex plane;
4. Power series;
5. Differentiation;
6. The exponential function;
7. Integration;
8. Angles, logarithms and the winding number;
9. Cauchy's theorem;
10. Homotopy versions of Cauchy's theorem;
11. Taylor series;
12. Laurent series;
13. Residues;
14. Conformal transformations;
15. Analytic continuation; Index.
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