During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intuition necessary to understand this important area of mathematics.
Since its release in 1946, this has been one of the most widely recognized and respected resources for architects, engineers, and designers, bringing together the knowledge, techniques, and skills of some of the most well-known experts in the field. The new Eighth Edition takes a fresh, visual approach to the information architects need to access quickly, helping them save time and money by assuring they get it right the first time. Readers will find timely, new chapters on building security, natural disaster mitigation, building diagnostics, facility management, and much more.
This book is a collection of comprehensive background essays coupled with carefully edited Supreme Court case excerpts designed to explore constitutional law and the role of the Supreme Court in its development and interpretation. Well-grounded in both theory and politics, the book endeavors to heighten students’ understanding of this critical part of the American political system. New to the 18th Edition An account of the Trump impeachments and a full discussion of the recent Supreme Court transitions including recent Supreme Court transitions including the fraught Kavanaugh hearings, the death of Ruth Bader Ginsberg, and the nomination process surrounding Amy Coney Barrett. Fourteen new cases carefully edited and excerpted, including Chifalo v. Washington (2020) on the Electoral College, Masterpiece Cakeshop (2018) on gay rights, and three Trump cases as well. Thirty-one new cases discussed in chapter essays in addition.
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