Bøker av Tom Carroll

This textbook provides a second course in complex analysis with a focus on geometric aspects. It covers topics such as the spherical geometry of the extended complex plane, the hyperbolic geometry of the Poincaré disk, conformal mappings, the Riemann Mapping Theorem and uniformisation of planar domains, characterisations of simply connected domains, the convergence of Riemann maps in terms of Carathéodory convergence of the image domains, normal families and Picard's theorems on value distribution, as well as the fundamentals of univalent function theory. Throughout the text, the synergy between analysis and geometry is emphasised, with proofs chosen for their directness.The textbook is self-contained, requiring only a first undergraduate course in complex analysis. The minimal topology needed is introduced as necessary. While primarily aimed at upper-level undergraduates, the book also serves as a concise reference for graduates working in complex analysis.

All of us are living in a time of volatility and unrest. It is not unusual for us to long for a moment of peace and quiet. This little book is a collection of vignettes, each written to stimulate the reader to think of something new and different for a moment or two and give our brains a rest. The primary intention of this book is to let you think of some totally outside of your normal routine and just let your mind exhale and experience a new calm. I could call the book a short cut meditation experience, but I would like each reader to use the book to take a break and enjoy a new thought or action. Use the book over and over and it will bring you many hours of interesting transformation. Enjoy!

This is a story that will warm your heart with the simplicity and beauty of childhood friendship and wonder. The fluid charm of the watercolor illustrations bring you back to those long beach days spent playing in the waves and in this case, avoiding mischievous seagulls.