Available in the MAA Store and the MAA eBook Store.
Read the introduction of Explorations in Complex Analysis (pdf)
Explorations in Complex Analysis is written for mathematics students who have encountered basic complex analysis and want to explore more advanced projects and/or research topics. It could be used as
- a supplement for a standard undergraduate complex analysis course, allowing students in groups or as individuals to explore advanced topics,
- a project resource for a senior capstone course for mathematics majors,
- a guide for an advanced student or a small group of students to independently choose and explore an undergraduate research topic, or
- a portal for the mathematically curious, a hands-on introduction to the beauties of complex analysis.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
There are 16 Java applets and a Java application, CirclePack, that allow students to explore the research topics without purchasing additional software. The electronic version of the book contains links to the applets and CirclePack. The print book (available soon in the MAA Store) contains information for downloading everything.