Geometries
暫譯: 幾何學

Platis, Ioannis D.

Geometries
  • 出版商: Springer
  • 出版日期: 2026-02-19
  • 售價: $5,780
  • 貴賓價: 9.5 折 $5,491
  • 語言: 英文
  • 頁數: 347
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032080150
  • ISBN-13: 9783032080158
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

The work is an exploration to geometry that transcends traditional approaches, placing Felix Klein's transformative Erlangen Program firmly at its heart. It aims to reveal the essence of geometry through the unifying power of transformation groups and their actions on space. Klein's genius was to define each geometry by the group of transformations that preserve its fundamental properties. This book makes this powerful conceptual framework accessible and compelling. The reader is guided through this perspective, demonstrating how the structure and symmetries of each geometric realm - Euclidean, Similarity, Affine, Spherical, Projective, Inversive, Hyperbolic - are fundamentally defined and understood by the transformations that leave them invariant.

It develops a sophisticated understanding of geometry through the intrinsic symmetries defined by transformation groups. Geometries is an invitation to experience the elegance, power, and breathtaking unity of geometry through the transformative lens pioneered by Klein. The reader is invited to master the language of symmetry and transformation groups, conquer challenging exercises with confidence, and unlock the interconnected universe of geometric spaces, where the abstract becomes tangible, and the transformation is the key. This book is a precise and clear mathematical presentation suitable for advanced undergraduates and graduate students, but also for mathematical educators as well as self-learners.

商品描述(中文翻譯)

這本書是一個超越傳統方法的幾何探索，將費利克斯·克萊因（Felix Klein）變革性的埃爾朗根計畫（Erlangen Program）置於核心。它旨在通過變換群及其在空間上的作用，揭示幾何的本質。克萊因的天才在於通過保留幾何基本性質的變換群來定義每一種幾何。這本書使這一強大的概念框架變得易於理解且引人入勝。讀者將通過這一視角進行引導，展示每個幾何領域的結構和對稱性——歐幾里得（Euclidean）、相似（Similarity）、仿射（Affine）、球面（Spherical）、射影（Projective）、反演（Inversive）、雙曲（Hyperbolic）——是如何通過保持不變的變換來根本定義和理解的。

它通過變換群所定義的內在對稱性，發展出對幾何的深刻理解。《幾何學》（Geometries）是一次邀請，讓人們通過克萊因所開創的變革性視角，體驗幾何的優雅、力量和驚人的統一。讀者被邀請掌握對稱和變換群的語言，自信地征服挑戰性的練習，並解鎖幾何空間的互聯宇宙，在那裡抽象變得具體，而變換則是關鍵。這本書是一個精確且清晰的數學呈現，適合高年級本科生和研究生，但也適合數學教育工作者以及自學者。

作者簡介

Ioannis D. Platis is a professor in the Department of Mathematics at the University of Patras, Greece, specialising in differential geometry, complex geometry, and geometric structures on manifolds. With a strong academic background, he earned his Ph.D. from the University of Crete and has since conducted extensive research on hyperbolic, complex hyperbolic, CR and sub-Riemannian geometries. Ioannis has held visiting positions at international institutions and collaborates with researchers worldwide. His work has been published in prominent journals, contributing to advancements in geometric analysis and its applications. At the University of Patras, he teaches advanced geometry courses among others, and supervises graduate students. Additionally, he has participated in numerous conferences and organised workshops, promoting geometric research in Greece. His expertise also includes interdisciplinary applications of geometry in physics and engineering. Ioannis is an active member of the Greek mathematical community, fostering academic exchange and research development.

作者簡介(中文翻譯)

Ioannis D. Platis 是希臘帕特雷斯大學數學系的教授，專攻微分幾何、複幾何以及流形上的幾何結構。他擁有堅實的學術背景，於克里特大學獲得博士學位，並自此進行了大量有關雙曲、複雙曲、CR 及次黎曼幾何的研究。Ioannis 曾在國際機構擔任訪問職位，並與全球的研究人員合作。他的研究成果發表於知名期刊，對幾何分析及其應用的進展做出了貢獻。在帕特雷斯大學，他教授高級幾何課程等，並指導研究生。此外，他參加了許多會議並組織工作坊，促進希臘的幾何研究。他的專業知識還包括幾何在物理和工程中的跨學科應用。Ioannis 是希臘數學社群的活躍成員，促進學術交流和研究發展。

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