Courses in Discrete and Computational Geometry
暫譯: 離散與計算幾何課程

Pach, János, Tóth, Géza

Courses in Discrete and Computational Geometry
  • 出版商: Springer
  • 出版日期: 2026-05-12
  • 售價: $6,970
  • 貴賓價: 9.5 折 $6,621
  • 語言: 英文
  • 頁數: 321
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032105021
  • ISBN-13: 9783032105028
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

In the Fall of 2023, the Erdős Center (Budapest) hosted a special semester on "Discrete Geometry and Convexity", which brought together some of the strongest experts in the field and many outstanding young researchers. The program featured intensive one-week mini-courses during a Summer School, followed by conferences and workshops presenting cutting-edge research. Part I of the present volume includes the notes of three lecture series on (1) approximation in discrete geometry, (2) random polytopes, and (3) a structure theory for graphs embedded in the plane. Part II starts with a classic: Matousek's until now unpublished elegant lecture notes concerning the algorithmic complexity of recognizing intersection graphs of segments and some other geometric objects. It is complemented by the first systematic and comprehensive survey of the corresponding complexity class: the existential theory of reals. This volume will be a valuable resource for graduate students, young researchers, and experts in related fields interested in discrete and computational geometry.

商品描述(中文翻譯)

在2023年秋季，厄爾德什中心（布達佩斯）舉辦了一個名為「離散幾何與凸性」的特別學期，聚集了該領域的一些頂尖專家和許多優秀的年輕研究者。該計畫在夏季學校期間提供了為期一週的密集迷你課程，隨後舉辦了會議和研討會，展示前沿研究。本卷的第一部分包括三個講座系列的筆記，主題為（1）離散幾何中的近似，（2）隨機多面體，以及（3）嵌入平面的圖的結構理論。第二部分以一部經典作品開始：Matousek至今未發表的優雅講義筆記，內容涉及識別線段交集圖及其他幾何物件的演算法複雜性。這部分還補充了對應複雜性類別的首次系統性和全面性調查：實數的存在理論。本卷將成為對於研究離散與計算幾何的研究生、年輕研究者及相關領域專家的寶貴資源。

作者簡介

János Pach is a research professor at the Rényi Institute, Budapest. His main fields of interest are discrete and computational geometry, convexity, and combinatorics. He has written more than 350 research papers. His books, "Research Problems in Discrete Geometry'' (with Brass and Moser) and ``Combinatorial Geometry" (with Agarwal) were translated into Japanese, Russian, and Chinese. He is the co-editor-in-chief of Discrete & Computational Geometry. He received the Lester Ford Award from the Mathematical Association of America (1990), the Rényi Prize and the Academy Award from the Hungarian Academy of Sciences (1993, 1998), and the Szele Prize from the Bolyai Mathematical Society (2019). He was elected the ACM Fellow (2011), a member of Academia Europaea (2014) and the Hungarian Academy of Sciences (2022). He was an invited speaker at the International Congress of Mathematicians (2014) and a plenary speaker at the European Congress of Mathematics (2021).

Géza Tóth is a research professor and the head of the Department of Geometry at the Rényi Institute, Budapest, working on problems in discrete and computational geometry and combinatorics. He received his PhD degree at Courant Institute, New York University in 1997, as a student of János Pach, winning the Best Dissertation Prize in mathematics and the Sokol Award, the highest university-wide prize for fresh PhDs. He wrote more than 100 research articles and he is the co-editor-in-chief of Studia Scientiarum Mathematicarum Hungarica and the editor of Computational Geometry and Acta Mathematica Hungarica. Among other distinctions, he received the Erdős Prize of the Hungarian Academy of Sciences in 2008 and the Rényi Prize of the Rényi Institute in 2010.

作者簡介(中文翻譯)

雅諾什·帕赫（János Pach）是布達佩斯雷尼研究所的研究教授。他的主要研究領域包括離散與計算幾何、凸性及組合數學。他已發表超過350篇研究論文。他的著作《離散幾何的研究問題》（與布拉斯和莫瑟合著）及《組合幾何》（與阿加瓦爾合著）已被翻譯成日文、俄文和中文。他是《離散與計算幾何》的共同主編。他曾獲得美國數學協會的萊斯特·福特獎（1990年）、匈牙利科學院的雷尼獎和學院獎（1993年、1998年），以及博爾雅數學學會的塞萊獎（2019年）。他於2011年當選ACM Fellow，2014年成為歐洲科學院的成員，2022年成為匈牙利科學院的成員。他曾在2014年國際數學家大會上擔任邀請演講者，並在2021年歐洲數學大會上擔任全體會議演講者。

蓋扎·托特（Géza Tóth）是布達佩斯雷尼研究所的研究教授及幾何系主任，專注於離散與計算幾何及組合數學的問題。他於1997年在紐約大學的庫朗數學研究所獲得博士學位，指導教授為雅諾什·帕赫，並獲得數學最佳論文獎及索科爾獎，這是針對新博士的最高大學獎項。他已撰寫超過100篇研究文章，並擔任《匈牙利數學科學研究》（Studia Scientiarum Mathematicarum Hungarica）的共同主編，以及《計算幾何》（Computational Geometry）和《匈牙利數學學報》（Acta Mathematica Hungarica）的編輯。他曾獲得的其他榮譽包括2008年匈牙利科學院的厄爾德什獎及2010年雷尼研究所的雷尼獎。

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