The Mathematics of Paul Erdős I

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Graham, Ronald L. (Επιμελητής έκδοσης), Nešetřil, Jaroslav (Επιμελητής έκδοσης), Butler, Steve (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2013.
• Έκδοση: 2nd ed. 2013.
• Θέματα: Mathematics.; Convex geometry.; Discrete geometry.; Number theory.; Probabilities.; Mathematics, general.; Number Theory.; Convex and Discrete Geometry.; Probability Theory and Stochastic Processes.

This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' research are covered in a single project. Because of overwhelming response...

Πίνακας περιεχομένων:

• VOLUME I
• Paul Erdős — Life and Work
• Paul Erdős Magic
• Part I Early Days.-  Introduction
• Some of My Favorite Problems and Results
• 3 Encounters with Paul Erdős
• 4 Did Erdős Save Western Civilization?
• Integers Uniquely Represented by Certain Ternary Forms
• Did Erdős Save Western Civilization?
• Encounters with Paul Erdős
• On Cubic Graphs of Girth at Least Five
• Part II Number Theory
• Introduction
• Cross-disjoint Pairs of Clouds in the Interval Lattice
• Classical Results on Primitive and Recent Results on Cross-Primitive Sequences
• Dense Difference Sets and their Combinatorial Structure
• Integer Sets Containing No Solution to x+y=3z
• On Primes Recognizable in Deterministic Polynomial Time
• Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture
• On Landau's Function g(n)
• On Divisibility Properties on Sequences of Integers
• On Additive Representation Functions
• Arithmetical Properties of Polynomials
• Some Methods of Erdős Applied to Finite Arithmetic Progressions
• Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires
• 1105: First Steps in a Mysterious Quest
• Part III Randomness and Applications
• Introduction
• Games, Randomness, and Algorithms
• The Origins of the Theory of Random Graphs
• An Upper bound for a Communication Game Related to Time-space Tradeoffs
• How Abelian is a Finite Group?
• One Small Size Approximation Models
• The Erdős Existence Argument
• Part IV Geometry
• Introduction
• Extension of Functional Equations
• Remarks on Penrose Tilings
• Distances in Convex Polygons
• Unexpected Applications of Polynomials in Combinatorics
• The Number of Homothetic Subsets
• On Lipschitz Mappings Onto a Square
• A Remark on Transversal Numbers
• In Praise of the Gram Matrix
• On Mutually Avoiding Sets
• Bibliography.