Introduction to Geometry and Topology
Introduction to Geometry and Topology
  • 定  價:NT$2250元
  • 優惠價: 92025
  • 可得紅利積點:60 點
  • 庫存: 無庫存,下單後進貨(採購期約45個工作天)
  • 加入購物車
  • 商品簡介
  • 作者簡介
  • This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems.

    The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula.

    The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension.

    This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

  • Werner Ballmann is Professor of Differential Geometry at the University of Bonn and Director at the Max Planck Institute for Mathematics in Bonn.

      • 文藝講堂
      • 優惠價:244元
      • 針灸腧穴定位
      • 優惠價:66元
      • 阿富汗史:文明的碰撞和融合(增訂三版)
      • 優惠價:198元
      • 說地:中國人認識大地形狀的故事
      • 優惠價:73元
      • 圖解人體實用經絡手冊:SOS家庭必備急救百科(附贈經絡穴位圖大開海報)
      • 優惠價:317元