数学++: 基础课程之外的精选论题（影印版）

样章

作者：

Ida Kantor, Jiří Matoušek, Robert Šámal

定价：

135.00 元

版面字数：

607千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059313-6

物料号：

59313-00

出版时间：

2023-03-15

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

通用

暂无

目录
- 前辅文
- Chapter 1. Measure and Integral
  - §1. Measure
  - §2. The Lebesgue Integral
  - §3. Foundations of Probability Theory
  - §4. Literature
  - Bibliography
- Chapter 2. High-Dimensional Geometry and Measure Concentration
  - §1. Peculiarities of Large Dimensions
  - §2. The Brunn–Minkowski Inequality and Euclidean Isoperimetry
  - §3. The Standard Normal Distribution and the Gaussian Measure
  - §4. Measure Concentration
  - §5. Literature
  - Bibliography
- Chapter 3. Fourier Analysis
  - §1. Characters
  - §2. The Fourier Transform
  - §3. Two Unexpected Applications
  - §4. Convolution
  - §5. Poisson Summation Formula
  - §6. Influence of Variables
  - §7. Infinite Groups
  - §8. Literature
  - Bibliography
- Chapter 4. Representations of Finite Groups
  - §1. Basic Definitions and Examples
  - §2. Decompositions into Irreducible Representations
  - §3. Irreducible Decompositions, Characters, Orthogonality
  - §4. Irreducible Representations of the Symmetric Group
  - §5. An Application in Communication Complexity
  - §6. More Applications and Literature
  - Bibliography
- Chapter 5. Polynomials
  - §1. Rings, Fields, and Polynomials
  - §2. The Schwartz–Zippel Theorem
  - §3. Polynomial Identity Testing
  - §4. Interpolation, Joints, and Contagious Vanishing
  - §5. Varieties, Ideals, and the Hilbert Basis Theorem
  - §6. The Nullstellensatz
  - §7. B´ezout’s Inequality in the Plane
  - §8. More Properties of Varieties
  - §9. B´ezout’s Inequality in Higher Dimensions
  - §10. Bounding the Number of Connected Components
  - §11. Literature
  - Bibliography
- Chapter 6. Topology
  - §1. Topological Spaces and Continuous Maps
  - §2. Bits of General Topology
  - §3. Compactness
  - §4. Homotopy and Homotopy Equivalence
  - §5. The Borsuk–Ulam Theorem
  - §6. Operations on Topological Spaces
  - §7. Simplicial Complexes and Relatives
  - §8. Non-embeddability
  - §9. Homotopy Groups
  - §10. Homology of Simplicial Complexes
  - §11. Simplicial Approximation
  - §12. Homology Does Not Depend on Triangulation
  - §13. A Quick Harvest and Two More Theorems
  - §14. Manifolds
  - §15. Literature
  - Bibliography
- Index