geometry
计算共形几何(理论篇) 豆瓣
作者: 顾险峰 / 丘成桐 出版社: 高等教育出版社 2020 - 5
计算共形几何是丘成桐先生和顾险峰教授共同创立的跨领域学科,将现代几何拓扑理论与计算机科学相融合,将经典微分几何、黎曼面理论、代数拓扑、几何偏微分方程的基本概念、关键定理和思想方法推广到离散情形,转换成计算机算法,并且广泛应用于计算机图形学、计算机视觉、计算机辅助几何设计、数字几何处理、计算机网络、计算力学、机械设计以及医学图像等领域。
书中涵盖了前沿的现代几何理论,例如离散曲面Ricci流理论,离散曲面单值化理论等,同时给出了具有巨大应用价值的高效算法,可以直接应用于工程和医疗等领域的科研和产品开发之中。
Birational Geometry of Algebraic Varieties 豆瓣
作者: Janos Kollár / Shigefumi Mori 出版社: Cambridge University Press 2008 - 2
One of the major discoveries of the last two decades of the twentieth century in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the a comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.
Metric Structures for Riemannian and Non-Riemannian Spaces 豆瓣
作者: Mikhail Gromov 译者: S. M. Bates 出版社: Birkhäuser Boston 2006
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
The Fractal Geometry of Nature 豆瓣
作者: Benoit B. Mandelbrot 出版社: W. H. Freeman and Company 1982
"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
The Geometry of Biological Time 豆瓣
作者: Winfree, Arthur T. 出版社: Springer Verlag 2001 - 6
Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular, the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.
几何世界的邀请 豆瓣
幾何への誘い
作者: [日]小平邦彦 译者: 李慧慧 出版社: 人民邮电出版社 2017
平面几何是观察判断与逻辑思考的精妙结合,是初等数学教育中培育创造力的好途径。本书为日本数学家、菲尔兹奖得主小平邦彦先生的几何入门作品,书中以欧几里得几何、希尔伯特几何、复数与几何为轴线,由浅入深,层层深入,从作为图形科学的几何、作为数学的几何等不同角度介绍完整的几何世界,是几何入门、训练思维与创造力的佳作。
The Projective Cast 豆瓣
作者: Robin Evans 出版社: The MIT Press 2000 - 8
Winner of the 1997 Alice Davis Hitchcock MedallionAnyone reviewing the history of architectural theory, Robin Evans observes, would have to conclude that architects do not produce geometry, but rather consume it. In this long-awaited book, completed shortly before its author's death, Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form. He shows that geometry does not always play a stolid and dormant role but, in fact, may be an active agent in the links between thinking and imagination, imagination and drawing, drawing and building. He suggests a theory of architecture that is based on the many transactions between architecture and geometry as evidenced in individual buildings, largely in Europe, from the fifteenth to the twentieth century.From the Henry VII chapel at Westminster Abbey to Le Corbusier's Ronchamp, from Raphael's S. Eligio and the work of Piero della Francesca and Philibert Delorme to Guarino Guarini and the painters of cubism, Evans explores the geometries involved, asking whether they are in fact the stable underpinnings of the creative, intuitive, or rhetorical aspects of architecture. In particular he concentrates on the history of architectural projection, the geometry of vision that has become an internalized and pervasive pictorial method of construction and that, until now, has played only a small part in the development of architectural theory.Evans describes the ambivalent role that pictures play in architecture and urges resistance to the idea that pictures provide all that architects need, suggesting that there is much more within the scope of the architect's vision of a project than what can be drawn. He defines the different fields of projective transmission that concern architecture, and investigates the ambiguities of projection and the interaction of imagination with projection and its metaphors.
直观几何(上册) 豆瓣
Geometry and the Imagination
作者: D.希尔伯特, S.康福森 译者: 王联芳 出版社: 高等教育出版社 2013 - 2
《数学概览:直观几何(上册)》的目的是从直观、直觉的方面,呈现几何学之貌,“几何”在《数学概览:直观几何(上册)》中得到非常广泛的解释,除了平面曲线的解析几何,曲线和曲面的微分几何之类的一般几何外,它还包括了共形映射、极小曲面、数的几何及其在数论中令人惊奇的应用、位形空间之几何、多面体与曲面的拓扑等。
黎曼几何选讲 豆瓣
作者: 伍鸿熙 出版社: 北京大学出版社 1993 - 6
内 容 简 介
本书主要讲述大范围黎曼几何的研究中具有重要意义的五个专题.内容包括:
Hodge理论,和乐群,非紧非负曲率流形的结构,Gauss-Bonnet定理,黎曼流形
的收敛性等.本书反映了大范围黎曼几何研究的概貌,有些内容是首次以讲义的形式
作系统的讲解.例如,详细给出Hodge定理的一个完备的初等证明,比较全面地综
述和乐群理论的过去和现状,以及在当代几何研究中的应用;剖析了陈省身关于
Gauss-Bonnet定理的内在证明;介绍了Gromov关于黎曼流形收敛性的理论,
把读者带进大范围黎曼几何的最新领域.
本书叙述条理清楚,推理严谨,富有启发性.本书还特别注重介绍黎曼几何的历
史背景、基本思想以及各专题之间的内在联系.
本书可作为综合大学、师范院校数学系高年级学生选修课教材和研究生教材,也
是广大数学工作者了解大范围黎曼几何课题的重要参考书.
圆锥曲线的几何性质 豆瓣
A Treatise on Geometrical Conics
作者: [英] A. 科克肖特, F. B. 沃尔特斯 出版社: 上海教育出版社 2002 - 1
《圆锥曲线的几何性质》采用综合法,从图形到图形,以平面几何知识为主,立体几何知识为辅,介绍了圆锥曲线的大批几何性质。主要内容包括:抛物线、正射影、椭圆、双曲线、直角双曲线、圆柱面和圆锥面的截线等等。
Noncommutative Geometry 豆瓣
作者: Alain Connes 译者: Berberian, Sterling K. 出版社: Academic Press 1995 - 1
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. It includes features such as: first full treatment of the subject and its applications; written by the pioneer of this field; broad applications in mathematics; of interest across most fields; ideal as an introduction and survey; examples treated include: @subbul; the space of Penrose tilings; the space of leaves of a foliation; the space of irreducible unitary representations of a discrete group; the phase space in quantum mechanics; the Brillouin zone in the quantum Hall effect; and a model of space time.
黎曼几何引论(上册) 豆瓣
作者: 陈维桓 / 李兴校 出版社: 北京大学出版社 2002
《黎曼几何引论(上)》可供综合大学、师范院校数学系、物理系学生和研究生作用教材,并且可供数学工作者参与。“黎曼几何引论”课是基础数学专业研究生的基础课。从1954年黎曼首次提出黎曼几何的概念以来,黎曼几何学经历了从局部理论到大范围理论的发展过程。现在,黎曼几何学已经成为广泛地用于数学、物理的各个分支学科的基本理论。《黎曼几何引论(上)》上册是“黎曼几何引论”课的教材,前四章是黎曼几何的基础;第五与第六章介绍黎曼几何的变分方法,是大范围黎曼几何学的初步;第七章介绍黎曼几何子流形的理论。每章末都附有大量的习题,书末并附有习题答案和提示,便于读者深入学习和自学。
希尔伯特几何基础 豆瓣
作者: [德] 希尔伯特 译者: 江泽涵 / 朱鼎勋 出版社: 北京大学出版社 2009 - 9
第一章五组公理 第二章公理的相容性和互相独立性 第三章比例论 第四章平面中的面积论 第五章德沙格定理 第六章巴斯噶定理 第七章根据公理Ⅰ—Ⅳ的几何作图
本书属于科学元典丛书。本书是数学史上的一本名著,它以严格的公理化方法重新阐述了欧几里得几何学,为二十世纪数学的公理化运动开辟了道路。本书中译本第二版是根据德文最新版即第十二版翻译的,全书包括正文、德文第七版的俄译本序言与注解,以及五个附录和五个补篇。本书可供高等院校数学系师生、中学教师以及广大数学工作者阅读。本书译者是数学界老前辈著名数学家江泽涵,朱鼎勋。