CHAPTER I The Integers 1 §1. Terminology of Sets 1 §2. Basic Properties 2 §3. Greatest Common Divisor 5 §4. Unique Factorization 7 §5. Equivalence Relations and Congruences 12 CHAPTER II Groups 16 §1. Groups and Examples 16 §2. Mappings 26 §3. Homom
Preface v Chapter 0. Introduction 1 x0.1. Linear partial di erential equations 1 Chapter 1. A rst look at Banach and Hilbert spaces 5 x1.1. Warm up: Metric and topological spaces 5 x1.2. The Banach space of continuous functions 14 x1.3. The geometry
This is a slighty revised version of the 1985 edition of my logic book. Many ty- pos and errors have been corrected and the line drawings have been improved. Most mistakes were minor, except for a subtle error in Theorem 4.3.3. Indeed, the second pa
We give a simple technique for verifying the Restricted Isometry Property (as introduced by Cand`es and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inne
This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication
这本书在国内已经绝版。目录如下 Introduction Dorit S. Hochbaum 0.1 What can approximation algorithms do for you: an illustrative example 0.2 Fundamentals and concepts 0.3 Objectives and organization of this book 0.4 Acknowledgments I Approximation Algorithms for Sc
CONTENTS Contents v Preface to the Second Edition xv Preface to the First Edition xvii Acknowledgments for the Second Edition xxi Acknowledgments for the First Edition xxiii 1 Introduction and Preview 1.1 Preview of the Book 2 Entropy, Relative Entr
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. This method has now been applied to other areas of mathematics
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. This method has now been applied to other areas of mathematics
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. This method has now been applied to other areas of mathematics
A Note on Bore-Cantelli Lemma of Capacity，王增武，，In this note, we investigate the conditions under which Borel-Cantelli
Lemma holds of Choquet capacity, which is a reasonable generalization of traditional
Borel-Cantelli Lemma o
