Combinators A Centennial View 1st Edition by Stephen Wolfram ISBN 1579550444 9781579550448

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ISBN 10: 1579550444 
ISBN 13: 9781579550448
Author: Stephen Wolfram

Combinators have inspired ideas about computation ever since they were first invented in 1920, and in this innovative book, Stephen Wolfram provides a modern view of combinators and their significance. Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Schönfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas.

Combinators A Centennial View 1st Table of contents:

• Foundations of Combinatorics

  • Basic Counting Principles
  • Permutations and Combinations
  • Binomial Coefficients and the Binomial Theorem
  • Inclusion-Exclusion Principle

• Graph Theory and Combinatorial Structures

  • Introduction to Graph Theory
  • Planar Graphs and Graph Coloring
  • Eulerian and Hamiltonian Graphs
  • Trees and Network Flows

• Combinatorial Designs

  • Block Designs and Error-Correcting Codes
  • Latin Squares and Sudoku
  • Steiner Systems and Balanced Incomplete Block Designs
  • Applications of Combinatorial Designs

• Extremal Combinatorics

  • Extremal Set Theory
  • Ramsey Theory
  • Turán’s Theorem and Applications
  • Probabilistic Methods in Combinatorics

• Algebraic Methods in Combinatorics

  • Polynomials and Generating Functions
  • Symmetric Functions and Partition Theory
  • Algebraic Combinatorics and Representation Theory
  • Applications of Algebra in Combinatorics

• Enumerative Combinatorics

  • Counting Labeled and Unlabeled Structures
  • Recurrence Relations and Generating Functions
  • The Principle of Symmetry in Counting
  • Asymptotic Counting Methods

• Geometrical and Geometric Combinatorics

  • Convex Hulls and Voronoi Diagrams
  • Combinatorics of Polytopes
  • Geometric Graph Theory
  • Discrete Geometry and Arrangements of Lines

• Combinatorics and Computation

  • Algorithms for Counting and Generation
  • Complexity in Combinatorial Problems
  • Randomized Algorithms in Combinatorics
  • Computational Complexity and Approximation

• Applications of Combinatorics

  • Combinatorics in Cryptography
  • Coding Theory and Error Detection
  • Combinatorics in Biology and Bioinformatics
  • Applications in Physics and Engineering

• Open Problems and Directions for Future Research

  • Key Open Problems in Combinatorics
  • Emerging Areas of Study
  • The Role of Combinatorics in Interdisciplinary Research

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