Geometry of Derivation with Applications

Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.

《導出幾何學及其應用》是一系列關於組合幾何學的書籍的第五部作品（包括《子平面覆蓋網絡》、《平移平面的基礎》、《有限平移平面手冊》和《傳播和平行性的組合學》）。與前作一樣，本書主要涉及有限和無限情況下可導出網絡和平移平面理論的相關性。傳統上，非交換斜域上的平移平面在關聯幾何學中並沒有得到重要的代表，而斜域上的可導出網絡只有被邊緣理解。本書深入研究了這兩個問題，同時詳細描述了非交換代數的思想，並以幾何學的方式給出了必要的背景知識。

本書基於二十多年的組合幾何學研究工作，涵蓋了前四本書的內容，適合研究生和研究人員作為參考書。它包含了各種新的想法和對有限仿射幾何學已有工作的推廣，並且豐富地提供了例子和應用。

Norman L. Johnson is an Emeritus Professor (2011) at the University of Iowa where he has had ten Ph.D. students. He received his BA from Portland State University, MA from Washington State University and Ph.D. also at Washington State University as a student of T.G. Ostrom. He has written 580 research items including articles, books, and chapters available on Researchgate.net. Additionally, he has worked with approximately 40 coauthors and is a previous Editor for International Journal of Pure and Applied Mathematics and Note di Matematica. Dr. Johnson plays ragtime piano, enjoys studying languages and 8-ball pool.

Norman L. Johnson是愛荷華大學的名譽教授（2011年），他指導了十位博士生。他在Portland State University獲得學士學位，在Washington State University獲得碩士學位，並在同一所大學以T.G. Ostrom為導師獲得博士學位。他已經撰寫了580篇研究論文，包括文章、書籍和章節，這些都可以在Researchgate.net上找到。此外，他與大約40位合著者合作過，並曾擔任《International Journal of Pure and Applied Mathematics》和《Note di Matematica》的編輯。Johnson博士擅長演奏拉格泰姆鋼琴，喜歡學習語言和玩八球。