图书信息
图书目录
数学++: 基础课程之外的精选论题（影印版）
暂无简介
作者：
Ida Kantor, Jiří Matoušek, Robert Šámal
定价：
135.00 元
出版时间：
2023-03-15
ISBN：
978-7-04-059313-6
物料号：
59313-00
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
重点项目：
暂无
版面字数：
607.000千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次印刷时间：
2023-01-20
- 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
