Real Algebraic Geometry
暫譯: 實代數幾何

Arnold, Vladimir I., Itenberg, Ilia, Kharlamov, Viatcheslav

Real Algebraic Geometry
  • 出版商: Springer
  • 出版日期: 2013-05-03
  • 售價: $3,020
  • 貴賓價: 9.5 折 $2,869
  • 語言: 英文
  • 頁數: 100
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3642362427
  • ISBN-13: 9783642362422
  • 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

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images.

At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century).

In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

商品描述(中文翻譯)

這本書關注數學中最基本的問題之一：代數公式與幾何圖像之間的關係。

在第一次國際數學大會（於1900年在巴黎舉行）上，希爾伯特以他的第16個問題的形式陳述了這個問題的一個特例（這是他從19世紀留下的23個問題中，作為對20世紀的遺產）。

儘管這個問題簡單且重要（包括其眾多應用），但至今仍未解決（儘管，正如你將看到的，已經發現了許多顯著的結果）。

作者簡介

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work.

His first mathematical work, which he did being a third-year student, was the solution of the 13th Hilbert problem about superpositions of continuous functions. His early work on KAM (Kolmogorov, Arnold, Moser) theory solved some of the outstanding problems of mechanics that grew out of fundamental questions raised by Poincare and Birkhoff based on the discovery of complex motions in celestial mechanics. In particular, the discovery of invariant tori, their dynamical implications, and attendant resonance phenomena is regarded today as one of the deepest and most significant achievements in the mathematical sciences.

Arnold has been the advisor to more than 60 PhD students, and is famous for his seminar which thrived on his ability to discover new and beautiful problems. He is known all over the world for his textbooks which include the classics Mathematical Methods of Classical Mechanics, and Ordinary Differential Equations, as well as the more recent Topological Methods m Hydrodynamics written together with Boris Khesin, and Lectures on Partial Differential Equations.

作者簡介(中文翻譯)

弗拉基米爾·阿諾德（Vladimir Arnold）是我們這個時代偉大的數學科學家之一。他以其工作的廣度和深度而聞名。

他在大三時期完成的第一個數學作品是解決第十三個希爾伯特問題，該問題涉及連續函數的疊加。他在 KAM（科爾莫哥洛夫、阿諾德、莫澤）理論上的早期工作解決了一些力學中的突出問題，這些問題源於龐加萊（Poincare）和比爾科夫（Birkhoff）提出的基本問題，這些問題基於在天體力學中發現的複雜運動。特別是，對不變托里（invariant tori）的發現、其動力學意涵及相關的共振現象，今天被視為數學科學中最深刻和最重要的成就之一。

阿諾德指導了超過60位博士生，以他發現新穎且美麗問題的能力而聞名於世。他的教材在全球廣為人知，包括經典著作《經典力學的數學方法》（Mathematical Methods of Classical Mechanics）和《常微分方程》（Ordinary Differential Equations），以及與鮑里斯·赫辛（Boris Khesin）共同撰寫的較新著作《拓撲方法與流體力學》（Topological Methods in Hydrodynamics）和《偏微分方程講義》（Lectures on Partial Differential Equations）。

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