01 / Reading Guide
Reading Guide
Who this book is for
For incoming graduate students in a first complex analysis course. The author designed the text for Oklahoma State’s graduate sequence, so familiarity with proofs is essential. An undergraduate can use it with supplementary background study, but its purpose and later topics should not be mistaken for a formula-oriented elementary complex variables course.
Prerequisites
At least one semester of undergraduate real analysis is required. Metric spaces and multivariable differential calculus are important; appendices supply proven background results. Elementary linear and abstract algebra are also useful.
What it covers
The complex plane, holomorphic functions, contour integration, Cauchy theory, logarithms, zeros and singularities lead into normal families, the Riemann mapping theorem and harmonic functions. Later chapters develop factorization, rational approximation and analytic continuation. The initial sequence supports a semester, while the full book provides material beyond that core route.
How to use it
For each theorem, separate the local analytic assumption from the global topological condition on the domain. Draw the contour and identify every singularity before applying an integral formula. Try a counterexample after removing one hypothesis, then explain why the theorem avoids it. Reconstruct a proof without the book and compare its dependencies with the appendices. Choose exercises that alternate explicit computation and conceptual arguments, and postpone optional extensions until the core Cauchy theory is secure.
Edition and sources
The complete author PDF is version 1.9, July 11, 2026, with 304 pages. The author offers dual CC BY-SA 4.0 and CC BY-NC-SA 4.0 licensing. The revision date is specified here without treating a print-on-demand identifier as a separate digital edition.
