The Probabilistic Method 2nd Edition by Noga Alon, Joel H Spencer ISBN 0471370460 9780471370468

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Product details:

ISBN 10: 0471370460 
ISBN 13: 9780471370468
Author: Noga Alon, Joel H. Spencer

The Probabilistic Method 2nd Table of contents:

Part I: METHODS
1 The Basic Method
1.1 The Probabilistic Method
1.2 Graph Theory
1.3 Combinatorics
1.4 Combinatorial Number Theory
1.5 Disjoint Pairs
1.6 Exercises
The Probabilistic Lens: The Erdős-Ko-Rado Theorem
2 Linearity of Expectation
2.1 Basics
2.2 Splitting Graphs
2.3 Two Quickies
2.4 Balancing Vectors
2.5 Unbalancing Lights
2.6 Without Coin Flips
2.7 Exercises
The Probabilistic Lens: Brégman’s Theorem
3 Alterations
3.1 Ramsey Numbers
3.2 Independent Sets
3.3 Combinatorial Geometry
3.4 Packing
3.5 Recoloring
3.6 Continuous Time
3.7 Exercises
The Probabilistic Lens: High Girth and High Chromatic Number
4 The Second Moment
4.1 Basics
4.2 Number Theory
4.3 More Basics
4.4 Random Graphs
4.5 Clique Number
4.6 Distinct Sums
4.7 The Rödl Nibble
4.8 Exercises
The Probabilistic Lens: Hamiltonian Paths
5 The Local Lemma
5.1 The Lemma
5.2 Property B and Multicolored Sets of Real Numbers
5.3 Lower Bounds for Ramsey Numbers
5.4 A Geometric Result
5.5 The Linear Arboricity of Graphs
5.6 Latin Transversals
5.7 The Algorithmic Aspect
5.8 Exercises
The Probabilistic Lens: Directed Cycles
6 Correlation Inequalities
6.1 The Four Functions Theorem of Ahlswede and Daykin
6.2 The FKG Inequality
6.3 Monotone Properties
6.4 Linear Extensions of Partially Ordered Sets
6.5 Exercises
The Probabilistic Lens: Turán ‘s Theorem
7 Martingales and Tight Concentration
7.1 Definitions
7.2 Large Deviations
7.3 Chromatic Number
7.4 Two General Settings
7.5 Four Illustrations
7.6 Talagrand’s Inequality
7.7 Applications of Talagrand’s Inequality
7.8 Kim-Vu Polynomial Concentration
7.9 Exercises
The Probabilistic Lens: Weierstrass Approximation Theorem
8 The Poisson Paradigm
8.1 The Janson Inequalities
8.2 The Proofs
8.3 Brun’s Sieve
8.4 Large Deviations
8.5 Counting Extensions
8.6 Counting Representations
8.7 Further Inequalities
8.8 Exercises
The Probabilistic Lens: Local Coloring
9 Pseudorandomness
9.1 The Quadratic Residue Tournaments
9.2 Eigenvalues and Expanders
9.3 Quasi Random Graphs
9.4 Exercises
The Probabilistic Lens: Random Walks
Part II: TOPICS
10 Random Graphs
10.1 Subgraphs
10.2 Clique Number
10.3 Chromatic Number
10.4 Branching Processes
10.5 The Giant Component
10.6 Inside the Phase Transition
10.7 Zero-One Laws
10.8 Exercises
The Probabilistic Lens: Counting Subgraphs
11 Circuit Complexity
11.1 Preliminaries
11.2 Random Restrictions and Bounded-Depth Circuits
11.3 More on Bounded-Depth Circuits
11.4 Monotone Circuits
11.5 Formulae
11.6 Exercises
The Probabilistic Lens: Maximal Antichains
12 Discrepancy
12.1 Basics
12.2 Six Standard Deviations Suffice
12.3 Linear and Hereditary Discrepancy
12.4 Lower Bounds
12.5 The Beck-Fiala Theorem
12.6 Exercises
The Probabilistic Lens: Unbalancing Lights
13 Geometry
13.1 The Greatest Angle among Points in Euclidean Spaces
13.2 Empty Triangles Determined by Points in the Plane
13.3 Geometrical Realizations of Sign Matrices
13.4 ε-Nets and VC-Dimensions of Range Spaces
13.5 Dual Shatter Functions and Discrepancy
13.6 Exercises
The Probabilistic Lens: Efficient Packing
14 Codes, Games and Entropy
14.1 Codes
14.2 Liar Game
14.3 Tenure Game
14.4 Balancing Vector Game
14.5 Nonadaptive Algorithms
14.6 Entropy
14.7 Exercises
The Probabilistic Lens: An Extremal Graph
15 Derandomization
15.1 The Method of Conditional Probabilities
15.2 d-Wise Independent Random Variables in Small Sample Spaces
15.3 Exercises

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Tags: Noga Alon, Joel H Spencer, Probabilistic Method